5 year hence, ratio of ages of A and B will be 7 : 5 and difference between their ages will be 4 years. What are present ages (in years) of A and B respectively ?

Options

A. 5,9
B. 6, 5
C. 9, 5
D. 9, 6

Answer

C

Explanation

Suppose the present age of A = x years
Present age of B = y years
According to question,
`(x + 5)/(y +5) = (7)/(5)`
`rArr 5 (x + 5) = 7 (y + 5)`
`rArr 5x + 25 = 7y + 35`
`rArr 5x - 7y = 35 - 25 = 10` . . . (i)
Again, (x + 5) - (y + 5) = 4
`rArr x + 5 - y - 5 = 4`
`rArr x - y = 4` . . . (ii)
From equations (i) and (ii) x = 9
Putting the value of x in equation (ii)
9 - y = 4
` rArr y = 9 - 4 = 5`