Nishit K Sinha Solutions for Chapter: Arithmetic, Exercise 4: Practice Exercises

A class consists of $20$ boys and $30$ girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by $3$ while the average score of the entire class increased by $2$. The increase in the average score of the boys is

The average height of $\mathrm{22}$ toddlers increases by $2$ inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original $22$, then the average height, in inches, of the remaining $20$ toddlers is

Amol was asked to calculate the arithmetic mean of $10$ positive integers, each of which had $2$ digits. By mistake, he interchanged the $2$ digits, say a and $\mathrm{b}$, in one of these $10$ integers. As a result, his answer for the arithmetic mean was $1.8$ more than what it should have been. Then $\mathrm{b}-\mathrm{a}$ equals

If $\mathrm{u}, \mathrm{v}$, weighted average and $\mathrm{m}$ are natural numbers such that $\mathrm{um}+\mathrm{vm}=\mathrm{wm}$ , then which one of the following is true?

For any given series of $100$ terms, if we know the last term and the first term, we can always calculate the average of all the $100$ terms.

State whether True or False

$\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}$, and $\mathrm{F}$ are six numbers, not necessarily natural numbers. They are divided into two groups - each group having three numbers each and we do not know which number belongs to which group. Final average of all the numbers can be calculated by calculating the average of individual average of the two groups.

State whether True or False

In the above question, final average will depend upon the set of numbers forming the group.

State whether True or False

$10$ natural numbers are taken. Average of all the possible pairs of numbers formed out of these ten natural numbers are calculated. It is possible to determine the average of all the ten natural numbers using this information.

State whether True or False