Question

The ratio of ages of A and B at present is 2:3. After five years the ratio of their ages will be 3:4 What is the present age of A in years?

Answer 1

Hey!!!!

Good Evening :-)

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Let the present ages of A and B be 2x and 3x respectively.(in years)

Note : This assumption is made with the help of the given ratio of their ages

Now ATQ,

Their ratio after 5 years => 3 : 4

Thus after 5 years let the age of A be 3y and B be 4y.

Then

For A, 2x + 5 = 3y-------(1)

and

For B, 3x + 5 = 4y--------(2)

In (1), Multiply both sides by 3
=> 3(2x + 5) = 3(3y)
=> 6x + 15 = 9y
=> 6x - 9y = -15

In (2), Multiply both sides by 2
=> 2(3x + 5) = 2(4y)
=> 6x + 10 = 8y
=> 6x - 8y = -10

Now subtract (2) from (1)

=> 6x - 9y - (6x - 8y) = -15 + 10

=> 6x - 9y - 6x + 8y = -5

=> - y = -5

=> y = 5

Using y in original (1)

=> 2x + 5 = 3(5)

=> 2x = 10

=> x = 5

Thus present ages

1. A = 2x

=> A = 2(5)

=> A = 10

2. B = 3x

=> B = 15

Thus A is 10 years old and B is 15 years old at present

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Hope this helps ✌️

Answer 2

(2x+5)/(3x+5)=3/4
or,8x +20 =9x + 15
or,x=5
,so present age of a =2x=(2×5)=10