Inverse Proportion Problems
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• Introduction
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Inverse proportion is to do with the rate at which one quantity increases as the other decreases.

The key to answering these problems is to consider 1 unit.

Example

2 builders take 6 days to build a wall.  How long would it take 5 builders to build a similar wall?

We need to consider 1 unit (i.e. 1 builder).

It would take 1 builder 2 times as long as it would take 2 builders.

So it would take 1 builder 12 days to build the same wall.

As the number of builders increases, so the time taken to complete the job decreases in inverse proportion.

So 5 builders take one fifth of the time it takes 1 builder.

It takes 5 builders 12 ÷ 5 = 2.4 days.

• Question 1
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3 builders take 5 days to build a wall.

How long would it take 5 builders to build a similar wall?

1 day

2 days

3 days

3¾ days

• Question 2
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3 builders take 5 days to build a shed.

How long would it take 4 builders to build a similar shed?

1 day

2 days

3 days

3¾ days

• Question 3
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3 mice take 5 days to eat a block of cheese.

How long would it take 1 mouse to eat a similar block of cheese?

15 days

2/3 day

3/5 day

2 days

• Question 4
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3 mice take 8 days to eat a block of cheese.

How long would it take 4 mice to eat a similar block of cheese?

10 days

6 days

4 days

7 days

• Question 5
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3 students take 10 days to pick the grapes in a vineyard

How long would it take 5 students to do the same job?

150 days

6 days

4 days

7 days

• Question 6
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10 students take 10 days to pick the grapes in a vineyard

How long would it take 25 students to do the same job?

25 days

6 days

4 days

7 days

• Question 7
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10 students take 10 days to pick the grapes in a vineyard

How many students would be needed to do the job in 20 days?

25 students

4 students

20 students

5 students

• Question 8
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6 mice take 4 days to eat a block of cheese.

How many mice would be needed to eat a similar block of cheese in 3 days?

8

12

6

4

• Question 9
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3 builders take 7 days to build a wall.

How long would it take 4 builders to build a similar wall?

9 days

5¼ days

5 days

3¾ days

• Question 10
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3 painters take 2 days to paint a wall.

How long would it take 4 painters to paint a similar wall?

24 days

5½ days

1 days

1½ days

Progress