Are two digit number is such that the product of the digits is 8 when 18 is added to the number then the digits are reversed?

Discussion :: Problems on Numbers - General Questions (Q.No.5)

A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

[A].	18
[B].	24
[C].	42
[D].	81

Answer: Option B

Explanation:

Let the ten's and unit digit be x and	8	respectively.
x

Then,		10x +	8		+ 18 = 10 x	8	+ x
x	x

10x2 + 8 + 18x = 80 + x2

9x2 + 18x - 72 = 0

x2 + 2x - 8 = 0

(x + 4)(x - 2) = 0

x = 2.

Saradhapriyanka.s said: (Aug 11, 2010)
I could not understood your answer, please explain in some other way.

Chandra said: (Aug 17, 2010)
There are only four two digit numbers whose product of the digits is 8. They are 18, 81, 24 and 42. We can get easily 24 is the answer.

Sun said: (Oct 4, 2010)
We can directly check out the answer through options. 24 + 18 = 42 which gives product 8.

Shanthi said: (Oct 23, 2010)
It is very simple. You can get answer from the options itself. 18+18=36 no. Not reversed. Tak 24+18=42 no. Reversed. 24 is reversed as 42.

Sudheer said: (Feb 12, 2011)
Products of 8 is 24, 42, 81, 18. But he is telling by adding 18 to it the digits are reversed means 24+18=42. 24 is changed to 42. So, the answer is 24.

May said: (Apr 17, 2011)
Oh. You great and feeling in so easy. Thanks you.

Sunny said: (Jul 5, 2011)
Why didn't you take 8x, 1/x and solve the problem?

Manojit said: (Feb 6, 2012)
Product of two digit means multiple of two digit. Suppose two digit is x, y. Then x*y=8 y=8/x Now two digit is x, 8/x. Then look the above problem.

Banty Kumar.biet Davangere said: (Sep 16, 2012)
xy=8,xy+18=yx; put xy=8 than 8+18=24 so, xy=24 ans

Vijay said: (Mar 17, 2013)
Find the least value of * for which 7*5462 is divisible by 9? Please answer the question.

Dinesh said: (Apr 1, 2013)
@Vijay. Its very simple. See the no 9 is divisible by only 3 (other than 1 & itself not to be considered). So to make 75462 divisible by 9, must be 0 or 3. Trying with 0 fails to give the ans so then try with 3 it gives u the correct answer.

SK.Gopinath Siva said: (Aug 10, 2013)

Let me explain the simplest way. The way is, Let take two digit no as x and y. x * y = 8. xy + 18 = yx. //xy = 8// . 8+18 = yx.

yx = 24.

Priya said: (Aug 16, 2013)
Why 18 should be added in the option to get the answer?

Pratik Thakur said: (Jul 7, 2014)
Two digits=x & y so two digit no = 10x+y. Product of digits is xy = 8. So (10x+y)+18 = 10y+x. i.e x-y = -2......(1). as xy=8 so x = 8/y. Hence equation (1) becomes 8/y-y = -2......(2). Solving equation(2) we get y = 2. Putting y=2 in equation (1) we get x = 4. So the two digited number xy = 42. So please tell me how answer comes to 24. Please correct me if I am wrong?

Nitika said: (Oct 30, 2014)
Above you write 8+18 = 24 but 8+18 is 26 how it is to be 24?

Bhavna said: (Dec 17, 2014)

First we have to check with the options then only we find answer easily. Here the first condition is that the multiple of that two digit number is 8. Then we check all the options. Given four options satisfying the 1st condition. Now go to 2nd condition, i.e if 18 is added to that two digit number the answer will be reversed. So we can check through all the options then we get 24 is the correct option. i.e 2*4 = 8. 24 + 18 = 42.

Hence the 2 conditions are satisfied.

Febin said: (Mar 1, 2015)
How can solve like this manner 8+18 = 24? 8+18 = 26. It's wrong. The product of the number is 8 not that number.

Abc said: (Apr 17, 2015)
Only 24 is the product of 8 in this number. So answer is 24.

Krans said: (Jul 18, 2015)
Can you said in another way?

Ayesha said: (Dec 29, 2015)
9x2+18x-72. How it is simplified further?

Vinod said: (Jan 18, 2016)
Two digit number 10x+y. xy = 8. 10x+y+18 = 10y+x. x-y = -2. (x+y)^2 = (x-y)^2+4xy. = (-2)^2+4*8 = 36. x+y = 6. x-y = (-2). x = 2. y = 4. Answer 24.

Sumithra Devi said: (Mar 3, 2016)
@Vinod. How x-y=-2 suddenly comes, next step what formula is that?

Sam said: (Jun 27, 2016)
Can anyone explain it in another way?

Anwar said: (Jul 17, 2016)
Why we take x and 1/8 explain?

Bgnr said: (Aug 4, 2016)
What is unit, ten digit and product.

Srinivas said: (Sep 24, 2016)
I can't understand. Please explain in a simple way.

Mahesh said: (Jan 3, 2017)
Could anyone please provide the shortcut method?

Dipak said: (Feb 20, 2017)
xy = 8 10x + y + 18 = 10y = x 9x - 9y + 18 = 0 x-y = -2 8/y - y = -2 So by solving above equation we get y = 4, by putting y=4 in xy=8 so we get x = 2. So the original no. is 10x+y = 24.

Dee said: (Apr 13, 2017)
Let's not look into the options to solve this. Let's solve from the scratch-- The product of 2 digits is 8:- 1 * 8 = 8 2 * 4 = 8 4 * 2 = 8 8 * 1= 8. So, the number has to be any of the above-given numbers i.e 18 or 24 or 42 or 81. Now, add 18 to all the above 4 numbers, only 24 will be reversed after adding 18. => 24 = 42 (reversed). So, 24 is the answer.

Pooja P Kumar said: (Apr 16, 2017)

Let the ten's and unit digit be x and 8/x because on multiplying x*8/x we get 8. That's what is actually said at the first line of the question. Now, suppose let's unit digit be 8/x and ten's digit be x. Now, the number becomes 10 * x + 8/x (let us consider this equation as equation number 1) According to the question, given that 10 * x + 8/x + 18 = 10 * 8/x + x. Further Solving by taking L.C.M on both sides we get the statement a 10x^2+8+18x = 80+x^2 (the sign (^) here denotes square of that number). 9x^2 +18x-72=0. Take 9 as common from above equation, you'll get, x^2 +2x-8 = 0. x^2+4x-2x-8 = 0. x(x+4)-2(x+4) = 0. (x+4)(x-2) = 0. Hence x = 2 (since x = -4 cannot be taken becoz the digit is negative). Now put x=2 in above equation number 1 Thus 10*x+8/x becomes =10*2+8/2 (since x=2) =20+4 =24 Hence the required answer is 24...

Any doubt plz ask ....!!

Sunil said: (Apr 26, 2017)
The sum of five numbers is 18, their average is 3. 6 and their difference is 1. What are the numbers? Can anyone tell me the answer?

Naina said: (May 4, 2017)
Hi @Gopinath. How 8+18 = 24? I think its 26.

Mitun C Das said: (Sep 2, 2017)
Answer is absolutely 24. I agree.

Ganga Bhavani said: (Nov 11, 2017)

First let us consider the the number is xy. Then the number value = 10x+y. Given that if we add 18 to the number then it would be equal to reverse of the number(yx which value is 10y+x). i.e 10x+y+18 = 10y+x. 10x+y+18-10y-x = 0. 9x-9y+18 = 0. x-y+2 = 0 ------------------------------------------------- (1). But we know product of digits is 8 i.e xy = 8. then x = 8/y. so substitute x = 8/y in equation 1. then 8/y -y + 2 = 0. i.e 8-y^2+2y = 0. y^2-2y-8 = 0. y^2 - 4y-2y -8 = 0. y(y-4)+2(y-4) = 0. y= -2 or 4. we take positive y, then y= 4. then x= 8/y = 8/4 = 2.

So the number is xy i.e 24.

Jason said: (Apr 22, 2019)
I am not understanding this answer.

KRISHNA GUPTA said: (May 30, 2019)
Lets number is xy; Given xy=8; -----> (1) 10x + y + 18 = 10y+x. y-x = 2 ----> (2). Put y=8/x in (1) So x^2+2x-8=0; the root is 2,-4 x=2 so y is 4. So the number is xy= 24.

Tamilarasi said: (Jun 14, 2019)
The two digits are 2, 4. 24+18(add 18), The answer is 42, Reverse the 42. Then the final answer is 24.

Pema Dechen said: (Sep 16, 2019)
Well the solution is such that; Given condition: xy = 8. xy*18 = yx. Now, let tens place be x and ones place be 8/x (using 1st condition). Using second condition we will have; 10x+8/x+18=80/x+x. Calculating we get; x=2 and y=4. Hence, combining we have and 2,4 i.e,24.

Soumi said: (Oct 21, 2019)
Two digits let be x and y So, two digit no. =10x+y. Given, xy=8. =>y=8/x or x=8/y...(1). So, (10x+y) +18=10y+x =>9x+18=9y =>x+2=y----(2). Putting the Value of x from eqn 1 in eqn 2. 8/y-y = -2. y^2-2y-8 = 0. y^2-4y+2y-8 = 0. y(y-4) +2(y-4) = 0. y = 4/-2, y can't be a negative integer. So y = 4. And x = 2. So, no. is 24.

Yash said: (Jun 30, 2020)
Why X is taken as in the tenth position while 8/X taken as in-unit? We could have taken X in unit and 8/X in tenth place? Please explain me.

Ishu said: (Oct 11, 2021)
Possibilities of getting a product 8 is 24 or 42. If 18 is added to 42, it gives 60 --> the reversing condition is not met. Else if you add 18 to 24 --> 18+24 = 42, the reverse of 24. Hence the answer is 24.