Exercise 6

What number is that of which the third part exceeds the fifth part by $4$?

The numerator of a fraction is $4$ less than the denominator. If $1$ is added to both its numerator and denominator, it becomes $\frac{1}{2}$. Find the fraction.

In class of $40$ pupils the number of girls is three-fifth of the number of boys. Find the number of boys in the class.

$\mathrm{A}$ and $\mathrm{B}$ together can finish a piece of work in $12$ days. If $\mathrm{A}$ alone can finish the same work in $20$ days and $\mathrm{B}$ alone can finish it in $k$ days, then find the value of $k$ days.

If a train runs at $40 \mathrm{kmph}$ it reaches its destination late by $11$ minutes. But if it runs at $50 \mathrm{kmph}$ it is late by $5$ minutes only. Find the distance to be covered by the train. Express your answer in $\mathrm{km}$.

One fourth of a herd of deer has gone to the forest. One third of the total number is grazing in a field and remaining $15$ are drinking water on the bank of a river. Find the total number of deer.

By selling a radio for $₹903$, a shopkeeper gains $5\%$. Find the cost price of the radio. Express your answer in $₹$.

Sekhar gives a quarter of his sweets to Renu and then gives $5$ sweets to Raji. He has $7$ sweets left. How many did he have to start with?