Question

Find the fraction which becomes 2/3 when the numerator is increased by 2 and is equal to 4/7 when the denominator is increased by 4

Answer 1

Let the fraction is x/y

Given numerator is increased by 2, then

(x + 2)/y = 2/3

3x + 6 = 2y

y = (3x + 6) / 2 ---------1

Given denominator is increased by 4, then

x/(y + 4) = 4/7

7x = 4y + 16 ---------2

Substitute the value of y in eqn 2

7x = 4 (3x +6)/2 + 16

7x = 2 (3x + 6) + 16

7x = 6x + 12 + 16

x = 28

Therefore, y = (3 * 28 + 6) / 2

                      = 90 / 2

                      = 45

Fraction is x/y = 28/45 

Answer 2

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