# Inverse Variation Using Unitary Method

Now we will learn how to solve inverse variations using unitary method.

We know, the two quantities may be linked in such a way that if one increases, other decreases. If one decreases, the other increases.

Some situations of inverse variation using unitary method:

● More men at work, less time taken to finish the work.

● More speed, less time is taken to cover the same distance.

Solved examples on inverse variations using unitary method:

1. If 52 men can do a piece of work in 35 days, then 28 men will complete the same work in how many days?

Solution:

This is a situation of inverse variation, now we solve using unitary method.

52 men can do the work in 35 days.

1 man can do the work in (35 × 52) days.

28 men can do the work in days. (35 × 52)/28 days

Therefore, 28 men can do the work in 65 days.

2. In a camp there is enough food for 500 soldiers for 35 days. If 200 more soldiers join the camp, how many days will the food last?

Solution:

This is a situation of inverse variation, now we solve using unitary method.

For 500 soldiers, food lasts for 35 days.

For 1 soldier, food lasts for (35 × 500) days.

Since 200 more join. So, now the number of soldiers is (500 + 200) = 700.

For 700 soldiers, food lasts for (35 × 500)/700 days

Therefore, for 700 soldiers, food lasts for = 25 days.

3. Sara starts at 8:00 AM by bicycle to reach school. She cycles at the speed of 18 km/hour and reaches the school at 8:22 AM. By how much should she increase the speed so that she can reach the school at 8:12 AM?

Solution:

This is a situation of inverse variation, now we solve using unitary method.

In 22 minutes the same distance is covered at the speed of 18 km/hr.

In 1 minute the same distance is covered at the speed of (18 × 22) km/hr.

In 12 minutes the same distance is covered at the speed of (18 × 22)/12 km/hr.

Therefore, in 12 minutes the same distance is covered at the speed of 16 km/hr.

4. 32 workers can complete a work in 84 days. How many workers will complete the same work in 48 days?

Solution:

This is a situation of inverse variation, now we solve using unitary method.

To complete the work in 84 days, workers required = 32

To complete the work in 1 day, worker required = (32 × 84)

To complete the work in 48 days workers required = (32 × 84)/48

Therefore, to complete the work in 48 days, 56 workers are required.

Problems Using Unitary Method

Situations of Direct Variation

Direct Variations Using Unitary Method

Direct Variations Using Method of Proportion

Inverse Variation Using Unitary Method

Inverse Variation Using Method of Proportion

Problems on Unitary Method using Direct Variation

Problems on Unitary Method Using Inverse Variation

Mixed Problems Using Unitary Method