Question

18) A's present age in years is 20% of B's age. After
30 years, A's age will be 1/2 of B's. The sum of the present
ages of A and B is
A) 40 years
B) 60 years
C) 80 years
D) 100 years​

Answer 1

Solution

Given :-

• A's present age in years is 20% of B's age

• After 30 years, A's age will be 1/2 of B's

Find :-

• The sum of present age of A & B

Explanation

Let,

• Present age of A = x

• Present age of B = y years

Case 1.

==> x = y × 20%

==> x = y × 20/100

==> x = y /5

==> 5x - y = 0_____________(1)

Case 2.

==> (x + 30) = 1/2( y + 30)

==> 2x - y = 30 - 60

==> 2x - y = -30 _____________(2)

Subtract equ(1) & equ(2)

==> 5x - 2x = 30

==> 3x = 30

==> x = 30/3

==.>x = 10

keep value in equ(1)

==> 5×10 - y = 0

==> y = 50

Since

• Sum of age A & B is = 10 + 50 = 60

Hence

• Sum of age A & B will be = 60 years

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