INVERSE PROPORTION

 INVERSE PROPORTION

Where one quantity increases in the same ratio as another quantity decrease then the proportion is inverse.

inverse proportion are solved using The first by the first and the last by the last

Real life examples of the concept of inverse proportion

• The time taken by a certain number of workers to accomplish a piece of work inversely varies as the number of workers at work. This means that, the lesser the number of workers, the more time taken to finish the work and vice versa.

• The speed of a moving vessel such as a train, vehicle or ship inversely varies as the time taken to cover a certain distance. The higher the speed, the lesser the time taken to cover the distance.

It takes 8 days for 35 laborers to harvest coffee on a plantation. How long will 20 laborers take to harvest coffee on the same plantation.

Solution

• 35 laborers harvest coffee in 8 days

Duration taken by one worker = (35 × 8) days

• Now calculate the duration taken by 20 workers

= (35 × 8)/20

= 14 days
Therefore, 20 laborers will take 14 days.

 

Example 2

Nine taps can fill a tank in four hours. How long will it take twelve taps of similar flow rate to fill the same tank?

Solution

Let the ratios;

9×4 = 12x

⇒ x = 9×4/12

x = 3

Therefore, 12 taps will take 3 hours to fill the tank.

Practice Questions

1. An army barrack has enough food to feed 80 soldiers for 60 days. Calculate how long the food will last when 20 more soldiers joined the barrack after 15 days.
2. 8 taps having an equal flow rate can fill a tank in 27 minutes. If two taps s are not opened, how long will it take the remain pipes to fill the tank?
3. The total weekly wages for 6 laborers working for 8 hours a day is $ 8400. What will be the weekly wages of 9 laborers working for 6 hours a day?
4. 1350 liters of milk can be consumed by 70 students in 30 days. How many students will consume 1710 liters of milk in 28 days?
5. Either 15 women or 12 men can finish a certain task in 66 days. How long will 3 and 24 women and men respectively take to accomplish the same task?

Answers

1. 51 days
2. 36 minutes
3. $ 9450
4. 95 students
5. 30 days