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.
Situations of Direct Variation
Situations of Inverse 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
7th Grade Math Problems
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Worksheet on Direct Variation using Unitary Method
Worksheet on Direct variation using Method of Proportion
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