Question 8 Simple and Compound Interest Exercise 8.1
Answer:
First Case: Principal (P1) = Rs 9600 Rate (R1) = 10% Period = (T) = 3 years 6 months = years = 7 / 2 years Simple interest = (P × R × T) / 100 = (9600 × 10 × 7) / (100 × 2) We get, = Rs 3360 Second case: Simple interest = Rs 3360 × 2 = Rs 6720 Rate (R) = 7.5% p.a. and Period (T) = 2 years Therefore, Principal = (S.I × 100) / (R × T) = (6720 × 100) / (7.5 × 2) = Rs (6720 × 100 × 10) / (75 × 2) = 6720000 / 150 We get, = Rs 44800
Video transcript hello everybody welcome to lido learning channel my name is rajna chaudhary and we have to solve the question which is a sum of money invested at 7.5 per annum simple interest for two years produce produces twice as much interest as 96 double zero in three years and six months as ten percent per annum a simple interest so uh the meaning of question is that a sum of money was invested and it is giving us twice interest twice as the interest as this sum is giving in three years so we have to find first of all the interest from the second case because if we will find the interest from the second case so uh the interest for the first case is twice of it so i'm writing k second first of all so case second so in case second principle is given to us 9600 rate is given 10 percent time is also given three years and six months so first of all we have to convert this three years and six months into years so uh 3 plus 6 upon 12 so after calculation it would be 1 by 2 that means 3 whole and 1 by 2 after further calculation we have 7 upon 2 years let's apply it in the formula so simple interest would be p into r into t upon 100 so because it was 7 upon 2 that's why we can write it like this way now two zeros are cancelled out here two can cancel out ten five times and then after further calculation we would have rupees 3 3 6 0 as the simple interest so this is the simple interest for case second now simple interest for case 1 is twice of this so let's find out the simple interest for case 1 so twice of 3 3 6 0 mean rupees 6 7 to 0. now this is the simple interest we know rate also that rate is 7.5 percent time is two years we can calculate principle so it would be like we know that simple interest is equal to prt upon 100 simple interest we have calculated 6720 is equal to principle we have to calculate rate is 7.2 7.5 i'm sorry and time is 2 years upon 100. we can transpose these uh 7.5 to 100 to the right hand side so equation would be like 6 7 2 0 multiplied by hundred upon seven point five multiply by two so two can cancel out uh this fifty times and then the it can be further calculated so i'm not wasting time and writing the answer as principle is 4 4 8 0 zero so i hope you understand the method see you in my next video don't forget to like share and subscribe the channel thank you for watching
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Q.1 Find the simple interest on Rs.68,000 at 16 2/3% per annum for 9 months 8000 8500 7500 9000
Ans . 8500
Q.2 Find Simple Interest on Rs.3000 at 6 1/4% per annum for the period from 4th Feb,2005 to 18th April,2005. 37.50 45.00 35.50 38.00
Ans . 37.50
S.I. = Rs.(3,000*(25/4)*(1/5)*(1/100))= Rs.37.50. Q.3 A sum at simple interests at 13 ½ % per annum amounts to Rs.2502.50 after 4 years find the sum. 2625 1615 1630 1625
Ans . 1625
Q.4 A sum of Rs. 800 amounts to Rs. 920 in 8 years at simple interest interest rate is increased by 8%, it would amount to bow mucb ? 950 992 192 882
Ans . 992
Q.5 Adam borrowed some money at the rate of 6% p.a. for the first two years , at the rate of 9% p.a. for the next three years and at the rate of 14% p.a. for the period beyond five years.1£ he pays a total interest of Rs. 11, 400 at the end of nine years how much money did he borrow ? 12,050 11,500 12,000 11,000
Ans . 12,000
Q.6 A certain sum of money amounts to Rs. 1008 in 2 years and to Rs.1164 in 3 ½ years. Find the sum and rate of interests. 208 ,13% 208 ,15% 308 ,13% 308 ,15%
Ans . 208 ,13%
Q.7 At what rate percent per annum will a sum of money double in 16 years. 7\(\frac{1}{5}\)% p.a 6\(\frac{1}{3}\)% p.a 7\(\frac{1}{4}\)% p.a 6\(\frac{1}{4}\)% p.a
Ans . 6\(\frac{1}{4}\)% p.a
Q.8 The simple interest on a sum of money is 4/9 of the principal .Find the rate percent and time, if both are numerically equal. 6\(\frac{1}{4}\)% p.a., 6 yrs 5 months 6\(\frac{2}{3}\)% p.a., 6 yrs 8 months 6\(\frac{2}{3}\)% p.a., 2 yrs 8 months 6\(\frac{1}{4}\)% p.a., 6 yrs 9 months
Ans . 6\(\frac{2}{3}\)% p.a., 6 yrs 8 months
Q.9 The simple interest on a certain sum of money for 2 l/2 years at 12% per annum is Rs. 40 less tban the simple interest on the same sum for 3 ½ years at 10% per annum.Find the sum. 800 1000 900 750
Ans . 800
Q.10 A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2% higher rate, it would have fetched Rs. 360 more.Find the sum. 6500 5000 6000 5900
Ans . 6000
Q.11 What annual instalment will discharge a debt of Rs. 1092 due in 3 years at 12% simple interest? 325 225 300 425
Ans . 325
Q.12 A sum of Rs. 1550 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is Rs. 106, find the money lent at each rate. 700,900 650,650 650,700 650,900
Ans . 650 ,900
Q.13 Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually. 612 620 650 510
Ans . 612
Q.14 Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually. 2000 2109 3109 3000
Ans . 3109
Q.15 Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly 830 825.32 825 824.32
Ans . 824.32
Q.16 Find the compound interest on Rs. 16,000 at 20% per annum for 9 months,compounded quarterly 2000 2522 3522 3500
Ans . 2522
Q.17 If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate. 1261 1360 1260 1161
Ans . 1261
Q.18 In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually? 2 ys 3 yrs 4 yrs 2 yrs 5 months
Ans . 3 yrs
Q.19 If Rs. 600 amounts to Rs. 683.20 in two years compounded annually, find the rate of interest per annum. 8% p.a. 10% p.a. 5% p.a. 7% p.a.
Ans . 8% p.a.
Q.20 . If the compound interest on a certain sum at 16 (2/3)% to 3 years is Rs.1270, find the simple interest on the same sum at the same rate and f or the same period. 1080 1050 1110 2050
Ans . 1080
Q.21 The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is Rs. 631. Find the sum. Rs.53,110. Rs.63,100. Rs.60,000. Rs.73,100.
Ans . Rs.63,100.
Q.22 The difference between the compound interest and the simple interest accrued on an amount of Rs. 18,000 in 2 years was Rs. 405. What was the rate of interest p.c.p.a. ? 7%. 11%. 13%. 15%.
Ans . 15%.
Q.23 Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 4% per annum. Rs.676 and rs.665. Rs.676 and Rs.625. Rs.776 and Rs.725. Rs.576 and Rs.625.
Ans . Rs.676 and Rs.625.
Q.24 a certain sum amounts to rs.7350 in 2 years and to rs.8575 in 3 years.find the sum and rate percent. Rs.5200 Rs.5000 Rs.4400 Rs.5400
Ans . Rs.5400
Q.25 .a sum of money amounts to rs.6690 after 3 years and to rs.10,035 after 6 years on compound interest.find the sum. Rs.4460. Rs.4660. Rs.5560. Rs.3460.
Ans . Rs.4460.
Q.26 a sum of money doubles itself at compound interest in 15 years.in how many years will it beco,e eight times? 55 years 25 years 35 years 45 years
Ans . 45 years
Q.27 What annual payment will discharge a debt of Rs.7620 due in 3years at 16 2/3% per annum interest? Rs.4430 Rs.3550 Rs.3430 Rs.5430
Ans . Rs.3430
Q.28 1.Evaluate:(1)\(log_3\)(27) (2)\(log_7\)(1/343)(3)\(log_100\)(0.01) -3,-3,1s -3,-3,-1 3,3,1 3,-3,-1
Ans . 3,-3,-1
Q.29 (i) \(\log_{7} 1\)(ii)\(\log_{34} 34\) (iii)\(36^{\log_{6} 4} \) 0,0,16 0,0,0 4,2,16 3,0,4
Ans . 0,0,16Reference https://www.physicsforums.com/threads/how-to-write-log-in-latex.817954/
Q.30 if \(\log_{\sqrt{8}} x\)=3 (1/3), find the value of x. 28 26 32 30
Ans . 32
Q.31 (i) \(\log_{5} 3\)* \(\log_{27} 25\)(ii) \(\log_{10} 27\) – \(\log_{27} 9\) 3/2,6/5 2/3,5/6 3/2,5/6 2/3,6/5
Ans . 2/3,5/6
Q.32 Simplify :(log 75/16-2 log 5/9+log 32/243) 0 log 2 1 log 4
Ans . log2
Q.33 6.Find the value of x which satisfies the relation \(\log_{10} 3\)+\(\log_{10} (4x+1)\)=\(\log_{10} (x+1)\)+1 3/5 7/2 1 5/6
Ans . 7/2
Q.34 .Simplify:[1/\(\log_{xy} (xyz)\) +1/\(\log_{yz} (xyz)\)+1/\(\log_{zx} (xyz)\)] 3 1 0 2
Ans . 2
Q.35 If log 2=0.30103,find the value of log 50. 0.69897 1 1.69897 2.69897
Ans . 1.69897
Q.36 If log 2=0.3010 and log 3=0.4771,find the values of: i) log 25 ii)log 4.5 1.39,0.65 1.98,0.32 2,1 4,3
Ans . 1.39,0.65
Q.37 If log 2=.30103,find the number of digits in \(2^{56}\). 18 15 19 17
Ans . 17
Q.38 One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field. 130 \(m^2\) 110 \(m^2\) 120 \(m^2\) 100 \(m^2\)
Ans . 120 \(m^2\)
Q.39 A lawn is in the form of a rectangle having its sides in the ratio 2: 3. The area of the lawn is (1/6) hectares. Find the length and breadth of the lawn. 23/33,60 11/3,55 6/5,65 33/3,50
Ans . 33/3,50 So, 2x * 3x = 5000/3 <=> \(x^2\) = 2500/9 <=> x = 50/3 therefore Length = 2x = (100/3) m = 33(1/3) m and Breadth = 3x = 3(50/3) m = 50m. Q.40 Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs. 12.40 per square metre. Rs. 1934.40. Rs. 2934.40. Rs. 2234.40. Rs. 1834.40.
Ans . Rs. 1934.40.
Q.41 If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle. 150 \(cm^2\) 110 \(cm^2\) 120 \(cm^2\) 100 \(cm^2\)
Ans . 120 \(cm^2\)
Q.42 The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle. 30 cm 10 cm 20 cm 15 cm
Ans . 20 cm
Q.43 In measuring the sides of a rectangle, one side is taken 5% in excess, and the other 4% in deficit. Find the error percent in the area calculated from these measurements. 0.5%. 0.8%. 1.8%. 1.6%.
Ans . 0.8%.
Q.44 A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq. metre. Rs. 715 Rs. 450 Rs. 680 Rs. 550
Ans . Rs. 680
Q.45 The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares. 24 cm 14 cm 34 cm 28 cm
Ans . 24 cm
Q.46 A room 5m 55cm long and 3m 74 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor. 150 166 160 176
Ans . 176
Q.47 Find the area of a square, one of whose diagonals is 3.8 m long 8.52 \(m^2\) 7.22 \(m^2\) 6.43\(m^2\) 4.2 \(m^2\)
Ans . 7.22 \(m^2\)
Q.48 The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas 7 : 25. 4 : 35. 3: 25. 4 : 25.
Ans . 4 : 25.
Q.49 If each side of a square is increased by 25%, find the percentage change in its area 55.15% 58.30% 56.25% 60.25%
Ans . 56.25%
Q.50 If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectang 60 cm 40 cm 50 cm 70 cm
Ans . 50 cm
Q.51 A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per m2 is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room. l=9,b=8,h=7 l=9,b=6,h=7 l=6,b=6,h=6 l=9,b=6,h=6
Ans . l=9,b=6,h=6
Q.52 Find the area of a triangle whose sides measure 13 cm, 14 cm and 15 cm 94 \(cm^2\). 84 \(cm^2\).. 74 \(cm^2\). 64 \(cm^2\).
Ans . 84 \(cm^2\)..
Q.53 Find the area of a right-angled triangle whose base is 12 cm and hypotenuse is 13cm. 30\(cm^2\) 20\(cm^2\) 40\(cm^2\) 50\(cm^2\)
Ans . 30\(cm^2\)
Q.54 The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare be Rs. 333.18, find its base and height. Base = 700 m and Altitude = 200 m Base = 800 m and Altitude = 300 m Base = 900 m and Altitude = 300 m Base = 600 m and Altitude = 200 m
Ans . Base = 900 m and Altitude = 300 m
Q.55 The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32cm. Find the area of the triangle. 60 \(cm^2\) 70 \(cm^2\) 50 \(cm^2\) 80 \(cm^2\)
Ans . 60 \(cm^2\)
Q.56 Find the length of the altitude of an equilateral triangle of side 3\(\sqrt{3}\) cm. 6.5 cm. 5.5 cm. 7.5 cm. 4.5 cm.
Ans . 4.5 cm.
Q.57 In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases. 17 : 9. 16 : 9. 11 : 3 13 : 7
Ans . 16 : 9.
Q.58 The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height. 6 cm 9 cm 7 cm 4 cm
Ans . 6 cm
Q.59 Find the area of a rhombus one side of which measures 20 cm and 01 diagonal 24 cm. 384 \(cm^2\) 344 \(cm^2\) 388 \(cm^2\) 376 \(cm^2\)
Ans . 384 \(cm^2\)
Q.60 The difference between two parallel sides of a trapezium is 4 cm. perpendicular distance between them is 19 cm. If the area of the trapezium is 475 find the lengths of the parallel sides. 28 cm and 25 cm 25 cm and 20 cm 27 cm and 23 cm 30 cm and 28 cm
Ans . 27 cm and 23 cm
Q.61 Find the length of a rope by which a cow must be tethered in order tbat it may be able to graze an area of 9856 sq. metres. 54 52. 58. 56.
Ans . paste right option
Q.62 The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.40 per metre. Rs. 5808 Rs. 5765 Rs. 5450 Rs. 5907
Ans . Rs. 5808
Q.63 The diameter of the driving wheel of a bus is 140 em. How many revolution, per minute must the wheel make in order to keep a speed of 66 kmph ? 150. 450. 350. 250.
Ans . 250.
Q.64 A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel. 13 m. 15 m. 14 m. 11 m.
Ans . 14 m.
Q.65 The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle. 84 m 74 m 76 m 64 m
Ans . 84 m
Q.66 Two concentric circles form a ring. The inner and outer circumferences of ring are (352/7) m and (518/7) m respectively. Find the width of the ring. 7 m 8 m 4 m 5 m
Ans . 4 m
Q.67 A sector of 120', cut out from a circle, has an area of (66/7) sq. cm. Find the radius of the circle. 5 cm. 3 cm. 2 cm. 4 cm.
Ans . 3 cm.
Q.68 Find the ratio of the areas of the incircle and circumcircle of a square. 3 : 5. 1 : 3. 3 : 2. 1 : 2.
Ans . 1 : 2.
Q.69 If the radius of a circle is decreased by 50%, find the percentage decrease in its area. 85% 75% 70% 80%
Ans . 75%
Q.70 Find the volume and surface area of a cuboid 16 m long, 14 m broad and 7 m high. 768 \(cm^2\) 668 \(cm^2\) 868 \(cm^2\) 568 \(cm^2\)
Ans . 868 \(cm^2\)
Q.71 Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high. 16 m. 17 m. 15 m. 13 m.
Ans . 17 m.
Q.72 Tbe volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. metres. Find the breadth of the wall. 50 cm 40 cm 30 cm 20 cm
Ans . 40 cm
Q.73 Find the number of bricks, each measuring 24 cm x 12 cm x 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick, if 10% of the wall is filled with mortar? 45000. 55000. 50000. 35000.
Ans . 45000.
Q.74 Water flows into a tank 200 m x 160 m througb a rectangular pipe of 1.5m x 1.25 m @ 20 kmph . In what time (in minutes) will the water rise by 2 metres? 94min 95min 93min 96min
Ans . 96min
Q.75 Tbe dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box. 7.84 kg. 8.04 kg. 8.56 kg. 8.44 kg.
Ans . 8.04 kg.
Q.76 The diagonal of a cube is 63cm. Find its volume and surface area. 225 \(cm^2\) 116 \(cm^2\) 210 \(cm^2\) 216 \(cm^2\)
Ans . 216 \(cm^2\)
Q.77 The surface area of a cube is 1734 sq. cm. Find its volume. 5913 \(cm^3\). 4913 \(cm^3\). 3913 \(cm^3\). 4900 \(cm^3\).
Ans . 4913 \(cm^3\).
Q.78 A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes. 36. 37 40. 39.
Ans . 40.
Q.79 A cube of edge 15 cm is immersed completely in a rectangular vessel containing water . If the dimensions of the base of vessel are 20 cm x 15 cm, find the rise in water level. 10.50 cm 11.25 cm 10.25 cm 11.76 cm
Ans . 11.25 cm
Q.80 Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed. 486 \(cm^2\) 586 \(cm^2\) 466 \(cm^2\) 476 \(cm^2\)
Ans . 486 \(cm^2\)
Q.81 If each edge of a cube is increased by 50%, find the percentage increase in Its surface area. 120% 115% 125% 135%
Ans . 125%
Q.82 Two cubes have their volumes in the ratio 1 : 27. Find the ratio of their surface areas. 1:6 1:7 1:9 1:8
Ans . 1:9
Q.83 Find the volume , curved surface area and the total surface area of a cylinder with diameter of base 7 cm and height 40 cm. 987 \(cm^2\) 857 \(cm^2\) 957 \(cm^2\) 897 \(cm^2\)
Ans . 957 \(cm^2\)
Q.84 If the capacity of a cylindrical tank is 1848 m3 and the diameter of its base is 14 m, then find the depth of the tank. 11 m 13 m 12 m 14 m
Ans . 12 m
Q.85 2.2 cubic dm of lead is to be drawn into a cylindrical wire 0.50 cm diameter. Find the length of the wire in metres. 112 m. 110 m. 111 m. 122 m.
Ans . 112 m.
Q.86 How many iron rods, each of length 7 m and diameter 2 cm can be made out of 0.88 cubic metre of iron? 450 300 400 350
Ans . 400
Q.87 The radii of two cylinders are in the ratio 3: 5 and their heights are in tbe ratio of 2 : 3. Find the ratio of their curved surface areas 2.5 2.0 1.5 3.0
Ans . 2.5
Q.88 If 1 cubic cm of cast iron weighs 21 gms, then find the eight of a cast iron pipe of length 1 metre with a bore of 3 cm and in which thickness of the metal is 1cm. 28.3 kg. 26.4 kg. 23.8 kg. 25.14 kg.
Ans . 26.4 kg.
Q.89 Find the slant height, volume, curved surface area and the whole surface area of a cone of radius 21 cm and height 28 cm. 45cm 30cm 25cm 35cm
Ans . 35cm
Q.90 Find the length of canvas 1.25 m wide required to build a conical tent of base radius 7 metres and height 24 metres 340 m. 460 m. 400 m. 440 m.
Ans . 440 m.
Q.91 The heights of two right circular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4. Find the ratio of their volumes. 10 : 37 7 : 22 11 : 35 9 : 32
Ans . 9 : 32
Q.92 The radii of the bases of a cylinder and a cone are in the ratio of 3 : 4 and It heights are in the ratio 2 : 3. Find the ratio of their volumes. 7 : 8. 8 : 5. 9 : 8. 7 : 4
Ans . 9 : 8.
Q.93 A conical vessel, whose internal radius is 12 cm and height 50 cm, is full of liquid. The contents are emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the liquid rises in the cylindrical vessel 24 cm 29 cm 34 cm 26 cm
Ans . 24 cm
Q.94 Find the volume and surface area of a sphere of radius 10.5 cm. 4853 \(cm^{3}\),1378 \(cm^{2}\) 4851 \(cm^{3}\),1386 \(cm^{2}\) 4801 \(cm^{3}\),1360 \(cm^{2}\) 4785 \(cm^{3}\),1289 \(cm^{2}\)
Ans . 4851 \(cm^{3}\),1386 \(cm^{2}\)
Q.95 If the radius of a sphere is increased by 50%, find the increase percent in volume and the increase percent in the surface area 245.5%, 130%. 222%, 120%. 237.5%, 125%. 235%, 125%.
Ans . 237.5%, 125%.
Q.96 Find the number of lead balls, each 1 cm in diameter that can be a sphere of diameter 12 cm. 1728.7 1776 1754 1747.6
Ans . 1728.7
Q.97 How many spherical bullets can be made out of a lead cylinder 28cm high and with radius 6 cm, each bullet being 1.5 cm in diameter ? 1776 1734 1645 1792
Ans . 1792
Q.98 A copper sphere of diameter 18cm is drawn into a wire of diameter 4 mm Find the length of the wire. 343m 256m 243m 213m
Ans . 243m
Q.99 Two metallic right circular cones having their heights 4.1 cm and 4.3 cm and the radii of their bases 2.1 cm each, have been melted together and recast into a sphere. Find the diameter of the sphere. 3.5.cm 4.2.cm 3.4.cm 4.7.cm
Ans . 4.2.cm
Q.100 A Cone and a sphere have equal radii and equal volumes. Find the ratio of the sphere of the diameter of the sphere to the height of the cone. 1:7 1:2 1:3 1:5
Ans . 1:2
Q.101 Find the volume , curved surface area and the total surface area of a hemisphere of radius 10.5 cm. 1039.5 \(cm^{2}\) 1037.5 \(cm^{2}\) 1041.5 \(cm^{2}\) 1034.5 \(cm^{2}\)
Ans . 1039.5 \(cm^{2}\)
Q.102 Hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. How many bottles will be needed to empty the bowl 45 51 54 63
Ans . 54
Q.103 A Cone,a hemisphere and a cylinder stand on equal bases and have the same height.Find ratio of their volumes. 1:2:2 1:3:3 1:2:3 1:1:3
Ans . 1:2:3
Q.104 In a km race, A beats B by 28 metres or 7 seconds. Find A's timeover the course. 5 min. 6 s 3 min. 5 s 4 min. 3 s 7 min. 3 s
Ans . 4 min. 3 s
Q.105 A runs 1 ¾ times as fast as B. if A gives B a start of 84 m, bow far must winning post be so that A and B might reach it at the same time? 196 m 186 m 200 m 206 m
Ans . 196 m
Q.106 A can run 1 km in 3 min. 10 sec. and B can cover the same distance in 3 min. 20 sec. By what distance can A beat B ? 64 m 48 m 50 m 68 m
Ans . 50 m
Q.107 In a 100 m race, A runs at 8km per hour. If A gives B a start of 4 m and still him by 15 seconds, what is the speed of B ? 5.13 km/hr 5.76 km/hr 4.76 km/hr 4.06 km/hr
Ans . 5.76 km/hr
Q.108 A, Band C are three contestants in a km race. If A can give B a start of 40 m and A can give C a start of 64m how many metre's start can B give C ? 806 m 906 m 936 m 986 m
Ans . 936 m
Q.109 In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ? 7 points 8 points 9 points 5 points
Ans . 8 points
Q.110 What was the day of the week on, 16th July, 1776? Wednesday Monday Sunday Tuesday
Ans . Tuesday
Q.111 What was the day of the week on 16th August, 1947? Sunday Saturday Monday Friday
Ans . Saturday
Q.112 What was the day of the week on 16th April, 2000 ? Sunday Saturday Friday Monday
Ans . Sunday
Q.113 On what dates of Jull.2004 did Monday fall? 6th, 13th, 20th and 27th 5th, 12th, 19th and 26th 4th, 11th, 18th and 25th 3th, 10th, 17th and 24th
Ans . 5th, 12th, 19th and 26th
Q.114 Find the angle between the hour hand and the minute hand of a clock when 3.25 29° 23° 49° 47*1/2°
Ans . 47*1/2°
Q.115 At what time between 2 and 3 o'clock will the hands of a clock be together? 110/13 min. past 8 12/11 min. past 28 120/11 min. past 2 12/19 min. past 20
Ans . 120/11 min. past 2
Q.116 At what time between 4 and 5 o'clock will the hands of a clock be at right angle? 53/11 min. past 14 4/11 min. past 40 40/41 min. past 7 40/11 min. past 4
Ans . paste right option
Q.117 Find at what time between 8 and 9 o'clock will the hands of a clock being the same straight line but not together. 120/11 min 113/11 min 123/13 min 110/13 min
Ans . 120/11 min
Q.119 At what time between 5 and 6 o'clock are the hands of a clock 3minapart? 36/11 min. past 9 346/11 min. past 5. 117/11 min. past 5. 316/13 min. past 5.
Ans . 346/11 min. past 5
Q.120 The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day does the clock gain or lose? 140/43 minutes 410/42 minutes 450/41 minutes 440/43 minutes
Ans . 440/43 minutes
Q.121 A watch which gains uniformly, is 6 min. slow at 8 o'clock in the morning Sunday and it is 6 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct? Wednesday Friday Thursday Tuesday
Ans . Wednesday
Q.122 A clock is set right at 6 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day? 1 a.m 12 p.m 11 p.m 2 a.m
Ans . 11 p.m
Q.123 A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day? 36 min. past 11 25 min. past 8 48 min. past 12 36 min. past 18
Ans . 48 min. past 12
Q.124 Find the cost of: (i) Rs. 7200, 8% stock at 90; (ii) Rs. 4500, 8.5% stock at 4 premium; (iii) Rs. 6400, 10% stock at 15 discount. Rs. 6480.,Rs. 4680,Rs. 5440 Rs. 6440.,Rs. 4660,Rs. 5440 Rs. 6560.,Rs. 4120,Rs. 5340 Rs. 6320.,Rs. 3680,Rs. 4440
Ans . Rs. 6480.,Rs. 4680,Rs. 5440
Q.125 Find the cash required to purchase Rs. 3200, 7(1/2) % stock at 107 (brokerage (1/2) %) Rs. (115/2),Rs. 1140 Rs. (215/2),Rs. 3440 Rs. (215/2),Rs. 1440 Rs. (315/2),Rs. 4440
Ans . Rs. (215/2),Rs. 3440
Q.126 Find the cash realised by selling Rs. 2440, 9.5% stock at 4 discount (brokerage (1/4) %) Rs. (324/4),Rs 2198 Rs. (383/4),Rs 2298 Rs. (313/4),Rs 1298 Rs. (333/7),Rs 2228
Ans . Rs. (383/4),Rs 2298
Q.127 Find the annual income derived from Rs. 2500, 8% stock at 106. Rs. 300 Rs. 200 Rs. 150 Rs. 250
Ans . Rs. 200
Q.128 Find the annual income derived by investing Rs. 6800 in 10% stock at 136. Rs. 300 Rs. 600 Rs. 400 Rs. 500
Ans . Rs. 500
Q.129 Which is better investment? 7(1/2) % stock at 105 or 6(1/2) % at 94. 7(1/2) % stock at 105 is better 6(1/2) % at 94 is better 7(1/2) % stock at 105 and 6(1/2) % at 94 is better none of them
Ans . 7(1/2) % stock at 105 is better
Q.130 Find the cost of 96 shares of Rs. 10 each at (3/4) discount, brokerage being (1/4) per share. Rs. 812 Rs. 912 Rs. 921 Rs. 902 cAns . Rs. 912
Q.131 Find the income derived from 88 shares of Rs. 25 each at 5 premium, brokerage being (1/4) per share and the rate of dividend being 7(1/2) % per annum. Also, find the rate of interest on the investment. Rs. 165, 6.2 % Rs. 155, 5.5 % Rs. 175, 7.2% Rs. 150, 5.6%
Ans . Rs. 165, 6.2 %
Q.132 A man buys Rs. 25 shares in company which pays 9 % dividend. The money invested is such that it gives 10 % on investment. At what price did he buy the shares? Rs. 32.50 Rs. 25.50 Rs. 22.50 Rs. 35.50
Ans . Rs. 22.50
Q.134 A man sells Rs.5000, 12 % stock at 156 and uinvests the proceeds parity in 8 % stock at 90 and 9 % stock at 108. He hereby increases his income by Rs. 70. How much of the proceeds were invested in each stock? Rs. 4500. Rs. 3500. Rs. 3800. Rs. 4200.
Ans . Rs. 4200.
Q.135 Evaluate: 30!/28! 770 870 850 800
Ans . 870
Q.136 Find the value of (i) \(_{60}^{3}\textrm{P}\) (ii) \(_{4}^{4}\textrm{P}\) 205320,24 205408,32 205439,30 205310,24
Ans . 205320,24
Q.137 Find the vale of (i) \(_{8}^{10}\textrm{C}\) (ii)\(_{98}^{100}\textrm{C}\) (iii) \(_{50}^{50}\textrm{C}\) 110,4550,1 120,4950,1 120,5050,0 100,5250,0
Ans . 120,4950,1
Q.138 How many words can be formed by using all letters of the word “BIHAR” 110 100 120 80
Ans . 120
Q.139 How many words can be formed by using all letters of the word ‘DAUGHTER’ so that the vowels always come together? 4320 4110 3370 2350
Ans . 4320
Q.140 How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together? 126 118 72 110
Ans . 72
Q.141 How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together? 2060 1180 2110 2160
Ans . 2160
Q.142 In how many ways can a cricket eleven be chosen out of a batch of 15 players ? 1365 1330 1265 1225
Ans . 1365
Q.143 In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies? 100 210 200 110
Ans . 200
Q.144 In a throw of a coin ,find the probability of getting a head 1/5 1/3 1/2 1
Ans . 1/2
Q.145 Two unbiased coin are tossed .what is the probability of getting atmost one head? 3/4 3/2 1/4 1/2
Ans . 3/4
Q.146 An unbiased die is tossed .find the probability of getting a multiple of 3 1/2 1/5 1 1/3
Ans . 1/3
Q.147 In a simultaneous throw of pair of dice .find the probability of getting the total more than 7 5/13 11/12 5/11 5/12
Ans . 5/12
Q.148 A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour. 7/11 7/15 2/15 3/11
Ans . 7/15
Q.149 Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6 5/13 7/11 7/18 2/3
Ans . 7/18
Q.150 Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen? 5/11 55/21 2/11 55/221
Ans . 55/221
Q.151 Find the present worth of Rs. 930 due 3 years hence at 8% per annum. Also find the discount. Rs. 180 Rs. 102 Rs. 192 Rs. 132
Ans . Rs. 180
Q.152 The true discount on a bill due 9 months hence at 12% per annum is Rs. Find the amount of the bill and its present worth.. Rs. 5000 Rs. 4500 Rs. 6000 Rs.5500
Ans . Rs. 6000
Q.153 The true discount on a certain sum of money due 3 years hence is Rb. 250 and the simple interest on the same sum for the same time and at the same rate is Rs. 375. Find the sumand the rate percent. 16 2/3%. 16 1/5%. 11 5/3%. 13 1/3%.
Ans . 16 2/3%.
Q.154 The difference between the simple interest and true discount on a certain sum of money for 6 months at 12% per annum is Rs. 25. Find the sum. Rs.5500 Rs. 6200 Rs.5800 Rs. 6800
Ans . Rs. 6800
Q.155 A bill falls due in 1 year. The creditor agrees to accept immediate payment of the half and to defer the payment of the other half for 2 years. By this arrangement ins Rs. 40. What is the amount of the bill, if the money be worth 12% ?. Rs. 3200 Rs. 3000 Rs. 3600 Rs. 3500
Ans . Rs. 3600
Q.156 A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's discount, true discount, banker's gain and the money that the holder of the bill receives Rs. 5800 Rs. 5880 Rs. 4680 Rs. 4380
Ans . Rs. 5880
Q.157 If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker's discount on the same sum for the same time and at the same rate? Rs. 129 Rs. 109 Rs. 125 Rs. 119
Ans . Rs. 129
Q.158 The banker's discount on Rs. 1800 at 12% per annum is equal to the true discount on Rs. 1872 for the same time at the same rate. Find the time. 5 months 3 months 4 months 2 months
Ans . 4 months
Q.159 The banker's discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the sum and the rate percent. 13 7/11% 13 % 11 13/11% 11 17/13%
Ans . 13 7/11%
Q.160 The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker's discount and the banker's gain. Rs. 111 Rs. 121 Rs. 110 Rs. 119
Ans . Rs. 121
Q.161 The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain. Rs 12 Rs 11 Rs 15 Rs 13
Ans . Rs 15
Q.162 What rate percent does a man get for his money when in discounting a bill due 10 months hence, he deducts 10% of the amount of the bill? 13 1/3% 11 1/5% 7 1/3% 12 1/3%
Ans . 13 1/3%
Q.163 If the height of a pole is 2\(\sqrt{3}\)metres and the length of its shadow is 2 metres, find the angle of elevation of the sun.. \(30^{\circ}\) \(45^{\circ}\) \(60^{\circ}\) \(90^{\circ}\)
Ans . \(60^{\circ}\)
Q.164 A ladder leaning against a wall makes an angle of \(60^{\circ}\) with the ground. If the length of the ladder is 19 m, find the distance of the foot of the ladder from the wall. 7.5 9.5 6.5 8.5
Ans . 9.5
Q.165 The angle of elevation of the top of a tower at a point on the ground is \(30^{\circ}\). On walking 24 m towards the tower, the angle of elevation becomes \(60^{\circ}\). Find the height of the tower. 29 m 22 m 25.6 m 20.76 m
Ans . 20.76 m
Q.166 A man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is \(60^{\circ}\). When he retires 36 m from the bank, he finds the angle to be \(30^{\circ}\). Find the breadth of the river. 12 m 18 m 15 m 20s m
Ans . 18 m
Q.167 A man on the top of a tower, standing on the seashore finds that a boat coming towards him takes 10 minutes for the angle of depression to change from \(30^{\circ}\) to \(60^{\circ}\). Find the time taken by the boat to reach the shore from this position. 3 minutes 6 minutes 5 minutes 4 minutes
Ans . 5 minutes
Q.168 There are two temples, one on each bank of a river, just opposite to each other. One temple is 54 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are \(30^{\circ}\) and \(60^{\circ}\) respectively. Find the width of the river and the height of the other temple. 18 m 18 m 18 m 18 m
Ans . 18 m
The following table gives the sales of batteries manufactured by a company lit the years. Study the table and answer the questions that follow:
Q.169 The total sales of all the seven years is the maximum for which battery ? 4AH 7AH 32AH 55AH The total sales (in thousands) of all the seven years for various batteries are: For 4AH = 75 + 90 + 96 + 105 + 90 + 105 + 115 = 676 For 7AH = 144 + 126 + 114 + 90 + 75 + 60 + 85 = 694 For 32AH = 114 + 102 + 75 + 150 + 135 + 165 + 160 = 901 For 35 AH= 102 + 84 + 105 + 90 + 75 + 45 + 100 = 601 For 55 AH= 108 + 126 + 135 + 75 + 90 + 120 + 145 = 799. Clearly, sales are maximum in case of 32AH batteries. Q.170 What is the difference in the number of 35AH batteries sold in 1993 and 1997 ? Q.171 The percentage of 4AH batteries sold to the total number of batteries sold was maximum in the year: Q.172 In the case of which battery there was a continuous decrease in sales from 1992 to 1997 ? Q.173 What was the approximate percentage increase in the sales of 55AH batteries in 1998 compared to that in 1992 ?. NUMBER OF CANDIDATES APPEARED AND QUALIFIED IN A COMPETITIVE EXAMINATION FROM DIFFERENT STATES OVER THE YEAR
Q.174 Combining the states P and Q, together in 1998, what is the percentage of the candidates qualified to that of the canditates appeared? (a) 10.87% (b) 11.49% (c) 12.35% (d) 12.54%
Ans . 12.35% Required Percentage=(1020+1240) *100%=(2260*100)/18300% |
On what sum of money will the compound interest for 2 years at 5% per annum amount to rupees 768 point 75?
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