WBCS Mains 2019 Official Paper-VI

By what least number must $1260$ be divided to make the quotient a perfect square?

The boys of a school can be arranged in $15$, $18$ or $24$ equal rows and also into a solid square. Find the least number of boys in the school.

$P$ 's age is $\frac{3}{4}\text{th}$ of $Q$ 's age and $R$ 's age is $\frac{1}{12}\text{th}$ of $Q$ 's age. If the age of $R$ is $30$ years, find the age of $P$.

The ratio of two numbers is $3:4$ and their L.C.M. is $180$. Find the numbers.

The ratio of two numbers is $5:8$ and their difference is $69$. Find the numbers.