Q25 of 29 Page 3

If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. Find the fraction.

Let the numerator be ‘a’ and denominator be ‘b’


Given, if the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5



⇒ 10a = 6b – 30


⇒ 5a = 3b – 15 ……(1)


Also, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5



⇒ 5a + 40 = 4b ……(2)


Subtracting eq2 from eq1


⇒ 5a – 5a – 40 = 3b – 15 – 4b


⇒ b = 25


Thus, 5a = 75 – 15


⇒ a = 12


Fraction is 12/25.


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