Q4 of 12 Page 55

A fraction is such that if the numerator is multiplied by 3 and denominator is reduced by 3 we get but if the numerator is increased by 8 and denominator is doubled we get . Find the fraction?

Given,


Let numerator be = x and denominator be = y


According to the problem,



⇒ 33x = 18(y-3)


⇒ 33x – 18y = - 54


……(i)


Also,



⇒ 5x + 40 = 4y ……(ii)


By substitution method,


Put value of x from eq (i) in eq (ii)




⇒ 90y - 270 + (40 x 33) = 33 x 4y


⇒ 132y -90y = 1320 – 270


⇒ 42y = 1050


⇒ y =25


Now put value of y in eq (i)




x = 12


Hence, the fraction is


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