R. S. Aggarwal Solutions for Exercise 1: Exercise

A group of $1200$ persons consisting of captains and soldiers is travelling in a train. For every $15$ soldiers, there is one captain. The number of captains in the group is:

 A school organised a fete $\frac{1}{5}$ of the girls and $\frac{1}{8}$ of the boys participated in the fete. What fraction of the total number of students took part in the fete?

A number consists of two digits whose sum is $11$. If $27$ is added to the number, then the digits change their places. What is the number?

If a clock takes seven seconds to strike seven, how long will it take to strike ten?

Mr. X, a mathematician, defines a number as 'connected with $6$' if it is divisible by 6 or if the sum of its digits is $6$, or if $6$ is one of the digits of the number. Other numbers are all 'not connected with $6$'. As per this definition, the number of integers from $1$ to $60$ (both inclusive) which are not connected with $6$ is:

Mr Johnson was to earn $\pounds 300$ and a free holiday for seven weeks' work. He worked for only $4$ weeks and earned $\pounds 30$ and a free holiday. What was the value of the holiday?

An egg vendor calls on his first customer and sells half his eggs and half an egg. To the second customer, he sells half of what he was left with and half an egg, and to the third customer, he sells half of what he was then left with and half an egg. However, he did not break any eggs. If, in the end, the vendor was left with three eggs, how many eggs did he have initially?

Robin says, "If Jai gives me $₹ 40$, he will have half as much as Atul, but if Atul gives me $₹ 40$, then the three of us will all have the same amount." What is the total amount of money that Robin, Jai, and Atul have among them?