Question

A fraction is such that if the double of the numerator and the triple of the denominator is changed by +10% and –30% respectively then we get 11% of 16/21. Find the fraction.

Answer 1

Let the numerator be x and denominator be y.

Then our fraction becomes [Math Processing Error]x/y

Now proceeding further as per the problem.

Increasing twice the numerator ie 2x by 10% we get :

[Math Processing Error]2x+2x∗10/100=2.2x

Decreasing thrice the denominator ie 3y by 30%

We get :

[Math Processing Error]3y−3y∗30/100=2.1y

Thus our new fraction obtained is [Math Processing Error]2.2x/2.1y

Now as per the problem this fraction is 11% of 16/21

Thus [Math Processing Error]2.2x/2.1y=(16/21)∗11/100

Solving for [Math Processing Error]x/y . We get

[Math Processing Error]