Question

The ages of A and B are in the ratio 5:2 . After 5 years , their ages will be in the ratio 15:7 . The present age of A is​

Answer 1

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Answer 2

EXPLANATION.

=> Let the age of A be = x

=> Let the age of B be = y

=> x/y = 5/2

=> 2x = 5y

=> 2x - 5y = 0 .......(1)

After 5 years,their age will be = 15:7.

=> The present age of A = ( x + 5 )

=> The present age of B = ( y + 5 )

=> ( x + 5 ) / ( y + 5 ) = 15/7

=> 7 ( x + 5 ) = 15 ( y + 5 )

=> 7x + 35 = 15y + 75

=> 7x - 15y = 40 .......(2)

From equation (1) and (2) we get,

=> multiply equation (1) by 3

=> multiply equation (2) by 1

=> 6x - 15y = 0

=> 7x - 15y = 40

=> -x = -40

=> x = 40

put the value of x = 40 in equation (1)

=> 2(40) - 5y = 0

=> 80 - 5y = 0

=> 5y = 80

=> y = 16

Therefore,

=> Age of A = 40 years.

=> Age of B = 16 years.