Two years ago a mother was 4 times as old as her son. Six years from now her age will become more than double her son's age by 10 years. What is the present ratio of their ages ?

Options

A. `2:1`
B. `38: 11 `
C. `19:7`
D. `3:1`

Answer

B

Explanation

Let present age of son = `x yr`
and present age of mother = `y yr `
According to the question,
`4(x - 2) = y-2`
`4x - 8= y-2 `
`4x - y= 6 " " .....(i)`
Also, after 6 yr from now,
`2 (x + 6) + 10 = y + 6 `
`implies 2x + 12 + 10 = y + 6`
`2x - y = -16 " "..(ii)`
From Eqs. (i) and (ii),
`x = 11 `and
`y = 4 xx 11 - 6 = 38 `
`therefore` Required ratio = `38:11 `