NCERT Solutions for Chapter: Direct and Inverse Proportions, Exercise 1: Exercise

A ball of diameter $4 \mathrm{cm}$ is placed $8 \mathrm{cm}$ away from a point sized light source. Its shadow fell on the wall $12 \mathrm{cm}$ away from the ball

What is the area of the shadow cast by the ball?

The distance covered by an object falling freely towards earth is proportional to the square of the time the object takes to travel till it touches the ground. The food packets dropped from a helicopter flying at height of $490 \mathrm{m}$ takes $10$ seconds to touch the ground. At what height from the ground will the food packet be if $8$ seconds are elapsed since it was dropped from the helicopter?

The monthly energy charges levied by an electric distribution company is according to the monthly usage. If the electricity consumed is up to $60$ units, then the company charges certain amount per unit of electricity. However, the charges per unit of electricity is different if the usage is more than $60$ units in the month.

For example, consider the electricity consumed is $64$ units. The monthly bill is computed as per the rate under the first slab for $60$ units and the cost for the remaining $4$ units calculated as per the rate in next slab. Both amounts are then added to generate the final amount.

The units consumed and the amount paid by a household during the last two months is given in the table below.

The electricity consumed in the month of July was $70$ units.  What is the electricity bill for the month of July?

A sweet shop packed $2$ ladoos and samosa as takeaway snacks box at their shop. The shop is able to make $21$ packets based on the ladoos available with them. Since the samosa was not sufficient, they repacked to have $3$ ladoos along with one samosa in each packet. If each packet costs the shopkeeper $₹15$ then what was total cost incurred by the shop to make the sweet packets?

$10$ men can fence the perimeter of compound wall of length $400 \mathrm{m}$ in $8$ days. 

The number of days required for $6$ men to do build $300 \mathrm{m}$ of the same perimeter wall is _____ days.

The principal amount along with interest earned on a deposit against two periods of time is given below.

The principal along with interest at end of $18$ months is $₹$_____ .

If $a,b,c,d$ are in proportion, prove that

$\sqrt{\left(a+b+c\right)\left(b+c+d\right)}=\sqrt{ab}+\sqrt{bc}+\sqrt{cd}$

A water tank has two inlet pipes of different diameter, and each pipe let in a constant amount of water per minute. The table below gives the data on the time and the volume water ilet in by the pipes under different scenarios.

What will be the volume of the water let into the tank if both pipes are kept open simultaneously for $10$ minutes?