# Unitary Method , Consolidation, General Expression - Word Problems

The unitary method is a technique which is used for solving a problem by finding the value of a single unit.

1) 12 carpenters working for 4 hours to build a big toy house in 18 days. In how many days 4 carpenters will work for 8 hours to build the same toy house?

Solution:

This is a situation of indirect variation.

12 carpenters working for 4 hours build a toy house in 18 days

1 carpenters working for 4 hours build a toy house in 18 × 12 days.

1 carpenters working for 1 hour build a toy house in 18 × 12 × 4 days.

4 carpenters working for 1 hour build a toy house in (18 × 12 × 4)/4

4 carpenters working for 8 hours build a toy house in (18 × 12 × 4)/(4 × 8) days.

Therefore, 4 carpenters working for 8 hours build a toy house in 27 days.

2) If 72 masons can do a build a temple in 40 days, in how many days will 64 masons complete the same work?

Solution:

This is a situation of indirect variation.

Less masons will require more days to complete the work.

72 masons can do the work in 40 days

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

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

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

3) 11 potters can make 134 pots in 7 days. How many potters will be required to make 150 pots in 4 days?

Solution:

11 potters can make 134 pots in 7 days.

1 potter can make 134 pots in 7 × 11 days.

1 potter can make 1 pot in (7 × 11)/134 days.

Let the number of potters required be x, then;

x potters can make 1 pot in (7× 11)/( 134 × x) days

x potters can make 169 pots in (7 × 11 × 150)/(134 × x ) days

But the number of days given = 4

According to the problem;

(7 × 11 × 150)/(134 × x ) = 4

11550/134x = 4

536x = 11550

x = 11550/536

x = 21.54

Therefore, 21 potters are required to make 150 pots in 4 days.