unitery method sums problem
Answers
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.