Question

The present age of B will be half of A's age 4 years hence and double of A's age 5 years ago, then what is the present age of B?
(a) 6 years
(b) 4 years
(c) 8 years
(d) 12 years

Answer 1

Answer:

B's age = 10 years.

I'm sorry I can't write explanation for this but the answer is correct and the option is not correct

Answer 2

Given: Present age of B will be half of A's age after 4 year and double of A's age 5 years ago

To find: Present age of B

Let: B's present age = X years

      A's present age = Y years

Solution: According to the given problem,

Present age of B will be half of A's age after 4 years.

A's age after 4 years will be (Y + 4) years

⇒ X = $\frac{1}{2}$ x (Y + 4)       or    X = Y/2 + 4/2                   ...(1)

also, B's present age is double of A's age 5 years ago.

Age of A 5 years ago = (Y - 5)

⇒ X = 2 x (Y - 5)       or    X = 2Y - 10                      ...(2)

Comparing both the values of X from equation (1) and (2)

⇒ Y/2 + 4/2 = 2Y - 10      

⇒ 2Y - Y/2 = 4/2 + 10              

⇒ $\frac{4Y - Y}{2}$ = $\frac{4 + 20}{2}$                      

⇒ 3Y/2 = 24/2 =  12

⇒ 3Y = 12 x 2 = 24

⇒ Y = 24/3 = 8

Putting value of Y in equation (2)

X = 2 x (8 - 5)

X = 2 x 3 = 6

Therefore, present age of B (X) is 6 years.