5 years ago, a was thrice as old as b and ten years later, a shall be twice as old as b

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Ten years later, A will be twice as old as B and five years ago, A was three times as old as B. What are the present ages of A and B?

Text Solution

Solution : Let the present ages of B and A be x years and y years respectively. Then , <br> B's age 5 years ago = `( x- 5) ` years . <br> and A's age 5 years ago = ( y - 5) years. <br> ` therefore (y - 5) = 3 ( x - 5) rArr 3x - y = 10" " `... (i) <br> B's age 10 years hence = (`x + 10 `) years. <br> A's age 10 years hence = ` ( y + 10)` years. <br> ` therefore ( y + 10 ) = 2 ( x + 10 )rArr 2 x - y = - 10 " " `... (ii) <br> On substracting (ii) from (i), we get x = 20 <br> Putting x = 20 in (i), we get <br> ` ( 3 xx 20 ) - y = 10 rArr y = 60- 10 = 50 ` <br> `therefore x = 20 and y = 50 ` Hence, B's present age = 20 years. <br> and A's present age = 50 years.