Question

Ages of ‘A’ and ‘B’ are in the ratio of 2 : 3
respectively. Six years hence the ratio of their
ages will become 8 : 11 respectively. What is
B’s present age?
(a) 18 years (b) 28 years
(c) 27 years (d) 25 years

Answer 1

Let the common multiple be x

So, let the present age of A be 2x and B be 3x

After 6 years,

Age of A = 2x + 6

Age of B = 3x + 6


According to the given condition

$\dfrac{2x + 6}{3x + 6} = \dfrac{8}{11}$

☛ 11(2x + 6) = 8(3x + 6)

☛ 22x + 66 = 24x + 48

☛ 66 - 48 = 24x - 22x

☛ 18 = 2x

∴ x = 9


∴ Present age of B ☛ 3x

☛ 3 × 9

☛ $\boxed{\boxed{\text{27\:years}}}$


∴ The answer is Option C i.e. 27 years

Answer 2

Hello!

Let the common multiple be y

let the present age of A = 2y and

B = 3y

-----------------------------------------------

According to question,

After 6 years,

Age of A = 2y+ 6

Age of B = 3y + 6

-----------------------------------------------

According to question,

2y+6/3y+6 = 8/11

=> 11(2y + 6)

=> 8(3y + 6)

=> 22 y + 66

=> 24y + 48

Therefore,

66 - 48 = 24y - 22y

-----------------------------------------------

=> 18 = 2y

therefore,

y = 9

=> Thats why,

Present age of B = 3y

=> 3 × 9

=> 27

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Therefore, present age of B is 27 years