# Mixed Problems Using Unitary Method

Mixed problems using unitary method we come across certain variations i.e. direct variation and inverse variation.

We know, in unitary method, we first find the value of one quantity from the value of the given quantity. Then we use this value to find the value of the required quantity. While working out the problems using unitary method we come across certain variations in which the values of two quantities depend on each other in such a way that a change in one, results in a corresponding change in the other; then the two quantities are said to be in variation and the two types of variation which occur are called direct and inverse variations.

Solved examples of mixed problems using unitary method:

1. If 24 painters working for 7 hours a day, for painting a house in 16 days. How many painters are required working for 8 hours a day will finish painting the same house in 12 days?

Solution:

24 painters working for 7 hours paint a house in 16 days.

1 painter working for 7 hours paints a house in 16 × 24 days.

1 painter working for 1 hour paints a house in 16 × 24 × 7 days.

Let the required number of painters be x, then;

x painters working for 1 hour a day paint the house in (16 × 24 × 7)/x days

x painters working for 8 hours a day paint the house in (16 × 24 × 7)/(x  ×  8) days

But the number of days given = 12

According to the problem;

(16 × 24 × 7)/(x × 8) = 12

2688/8x = 12

8x × 12 = 2688

96x = 2688

x = 2688/96

x = 28

Therefore, 28 painters working for 8 hours a day will finish the same work in 12 days.

2. 11 potters can make 143 pots in 8 days. How many potters will be required to make 169 pots in 4 days?

Solution:

11 potters can make 143 pots in 8 days.

1 potter can make 143 pots in 8 × 11 days.

1 potter can make 1 pot in (8 × 11)/143 days.

Let the number of potters required be x, then;

x potters can make 1 pot in (8 × 11)/( 143 × x) days

x potters can make 169 pots in (8 × 11 × 169)/(143 × x ) days

But the number of days given = 4

According to the problem;

(8 × 11 × 169)/(143 × x ) = 4

14872/143x = 4

572x = 14872

x = 14872/572

x = 26

Therefore, 26 potters are required to make 169 pots in 4 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