Question

One year ago ratio of A's age to B's age was 5:6 after 4 years this ratio becomes 6:7 how old is A?

Answer 1

The present age of A is 26 years old

Solution:

Let,

Present age of A = x

Present age of B = y

A's age 1 year ago = x - 1  

B's age 1 year ago = y - 1

One year ago ratio of A's age to B's age was 5:6

Therefore,

$\frac{x-1}{y-1} = \frac{5}{6} \\\\6x - 6 = 5y - 5 \\\\6x - 5y = 1 ------ eqn\ 1$

A's age after 4 years ago = x + 4

B's age after 4 years ago = y + 4

After 4 years this ratio becomes 6:7

Therefore,

$\frac{x+4}{y+4} = \frac{6}{7}\\\\7x + 28 = 6y + 24\\\\7x - 6y = -4 ----- eqn\ 2$

Solve eqn 1 and eqn 2

Multiply eqn 1 by 6

36x - 30y = 6 ------ eqn 3

Multiply eqn 2 by 5

35x - 30y = -20  ------- eqn 4

Subtract eqn 4 from eqn 3

36x - 30y = 6

35x - 30y = -20

( - ) -----------------

x = 26

Thus present age of A is 26 years old

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