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Example 12: Shabnam takes 20 minutes to reach her school if she goes at a speed of 6 km/h. If she
wants to reach school in 24 minutes, what should be her speed?

6 × 1000
Solution: Given, speed = 6 km/h = m/min = 100 m/min.
60
Let the required speed be x m/min. Thus, we have the following table:

Speed (in m/min) 100 x

Time (in min) 20 24
For a constant or fixed distance, speed and time are inversely proportional.
100 × 20 250
Therefore, 100 × 20 = x × 24 ⇒ x = =
24 3
250 250 × 60
Thus, Shabnam’s speed should be m/min = = 5 km/h.
3 3 × 1000

Example 13: At a constant temperature, the volume of gas is inversely proportional to its pressure.
3
If the volume of gas is 720 cm at a pressure of 315 mm of mercury, then what will be the volume
of the gas if its pressure is 420 mm of mercury at the same temperature?
Solution: Given that, at constant temperature, pressure and volume of a gas are inversely
proportional. Let the required volume be V. Thus, we form the following table as follows:

3
Volume of gas (in cm ) 720 V
Pressure of gas (in mm) 315 420
720 × 315
Then, 720 × 315 = V × 420 ⇒ V = = 540
3
Thus, the required volume of the gas is 540 cm . 420
Example 14: In a scout camp, there is food provision of 350 cadets for 36 days. If 50 cadets leave
the camp, for how many days will the provision last?

Solution: Let the required number of days be x.
Thus, we have the following table:

Number of cadets 350 350 – 50 = 300

Food provision (in days) 36 x
The fewer cadets, the longer the provision will last. So, this is the case of inverse variation.
350 × 36
Therefore, 350 × 36 = 300 × x ⇒ x = = 42
300
Thus, the provision will last 42 days when 50 cadets leave the camp.
Example 15: If 24 workers can build a wall in 80 hours, how many extra workers will be required
to finish the same work in 60 hours?

Solution: To finish the work in fewer hours, more workers will be needed. Therefore, this is the
case of inverse variation.

Let the required number of extra workers be x. Thus, we have the following table:

Number of workers 24 24 + x
Time (in hours) 80 60

287 Direct and Indirect Variations