Question

14 years ago, the ratio of the ages of A and B was 2:3 and after 4 years it becomes 5:7. Find their
present ages.​

Answer 1

Answer:

this is the answer,hope it will help you

Answer 2

Solution

Given:-

• 14 years ago, the ratio of the ages of A and B was 2:3
• after 4 years it becomes 5:7.

Find :-

• Present age of A & B

Explanation

Let,

• Age of A be = x years
• Age of B be = y years

Case 1.

==> (14-x):(14-y) = 2:3

==> (14-x)/(14-y) = 2/3

==> 3×(14-x) = 2×(14-y)

==> -3x + 42 = 42 - 2y

==> 3x - 2y = 0 _____________(1)

Again,

Case 2.

==> (4+x):(4+y) = 5:7

==> (4+x)/(4+y) = 5/7

==> 7×(4+x) = 5×(4+y)

==> 28 + 7x = 20 + 5y

==> 7x - 5y = -8 ______________(2)

Multiply by 5 in equ(1) & 2 in equ(2)

==> 15x - 10y = 0_____________(3)

==> 14x - 10y = -16____________(4)

Sub. equ(3) & equ(4)

==> (15-14)x = 16

==> x = 16

Keep in equ(3)

==> 15×16 - 10y = 0

==> 10y = 240

==> y = 240/10

==>y = 24

Hence

• present age of A = 16 years
• Present age of B = 24 years

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