WBCS Mains 2018 Official Paper-VI

When the numerator of a fraction increases by $4$, the fraction increases by $\frac{2}{3}$. The denominator of the fraction is

Average of ten positive numbers is $\bar{x}$. If each number is increased by $10\%$, then $\bar{x}$

A cricket team won $3$ matches more than they lost. If a Win gives them $2$ points and Loss $(-1)$ point, how many matches, in all, have they played if their score is $23$?

Free books were distributed equally among children of a class. The number of books each child got was one-eighth of the number of children. Had the number of children been half, each child would have got $16$ books. How many books were distributed in total?