# Problems on Unitary Method Using Inverse Variation

We will learn how to solve problems on unitary method using inverse variation.

We know, if two quantities are related in such a way that increase in one quantity causes corresponding decrease in the other quantity and vice versa, then such a variation is called an inverse variation or indirect variation.

Solved problems on unitary method using inverse variation:

1. 12 typists working for 4 hours to type a book in 18 days. In how many days 4 typists will work for 8 hours to type same book?

Solution:

This is a situation of indirect variation.

12 typists working for 4 hours type a book in 18 days

1 typist working for 4 hours types a book in 18 × 12 days.

1 typist working for 1 hour types a book in 18 × 12 × 4 days.

4 typists working for 1 hour type a book in (18 × 12 × 4)/4

4 typists working for 8 hours type a book in (18 × 12 × 4)/(4 × 8) days.

Therefore, 4 typists working for 8 hours type a book in 27 days.

2. 16 men can build a wall in 56 hours. How many men will be required to do the same work in 32 hours?

Solution:

This is a situation of inverse variation

More the number of men, the faster will they build the wall.

In 56 hours, the wall is built by 16 men.

In 1 hour, the wall is built by 16 × 56 men.

In 32 hours, the wall is built by (16 × 56)/32 men

Therefore, in 32 hours, the wall is built by 28 men.

3. If 72 workers can do a piece of work in 40 days, in how many days will 64 workers complete the same work?

Solution:

This is a situation of indirect variation.

Less workers will require more days to complete the work.

72 workers can do the work in 40 days

1 worker can do the same work in 72 × 40 days

64 workers can do the same work in (72 × 40)/64

Therefore, 64 workers can do the same work in 45 days.

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