Proportion

### Direct proportion

- This is where two quantities increase or decrease in the same ratio.

- If one item increases it affects another to increase. If an item decreases it affects another to decrease.

- As the distance increases the time taken also increases in the same ratio.  This is known as Direct proportion.

### Indirect proportion

- This is also called inverse proportion.

- It is actually the opposite of direct proportion.

- If one quantity increases, the other one decreases and vice versa.

- As the number of people to paint the fence increases the number of days taken reduces by the same ratio.

- This is known as Indirect Proportion.

- As the number of people painting the fence reduces the number of days taken increase in the same ratio.

- This is known as Indirect Proportion

## KCPE Topical Questions

### Direct proportion

1. A watch loses 5 seconds every hour. If it is set right on a Wednesday at 12.10 a.m., what time would it show the following Wednesday at 12.10 a.m.?

A. 12.24 a.m.      B. 11.56 a.m.      C. 11.56 p.m.      D. 12.24 p.m.

2. A cube whose side measures 3 cm, weighs 1 kg 80 g. What is the weight of a similar cube whose sides measure 4 cm?

A. 2 kg 560 g     B. 1 kg 440 g     C. 4 kg 320 g     D. 1 kg 920 g

3. My watch loses one second every two hours. If I set it right on Monday at 12.00 noon, what time will it show on the following Saturday at 12.00 noon?

A. 11.59        B. 12.01      C. 11.00       D. 11.58

4. A rectangular container of length 15 cm and width 10 cm has 1200 cm3 of water. More water flows into the container at the rate of 60 cm3 per second. What will be the height of the water in the container after 5 seconds?

A. 10 cm       B. 8 cm      C. 6 cm       D. 2 cm

5. In a factory every 7 kg of coffee berries, when processed. Produce 1 kg of clean coffee beans. Leitich ended up with 2100 kg of clean coffee beans. How many tonnes of coffee berries had he sent for processing?

A. 0.3         B. 2.1         C. 14.7        D. 147

6. A matatu covers a distance of 420 km in one day. It consumes one litre of petrol for every 5 km. Petrol costs sh 15 per litre. How much money is spent on petrol in 7 days?

A. Sh 8820       B. Sh 1260      C. Sh 588        D. Sh 980

7. A rectangular tank measures 250 cm by 180 cm by 120 cm is full of water. Water flows out of the tank at a rate of 15 litres per minute. How many hours does it take to empty the whole tank?

A. 6          B. 60       C. 600        D. 6000

8. A watch gains 5 seconds every hour. It was set right on Monday at 11.48 a.m. What time will it show the following Monday at 11.48 a.m.?

A. 12.02 p.m.      B. 11.55 p.m.       C. 12.02 a.m.     D. 11.55 a.m.

9. In a factory, 1 kg of clean coffee beans is obtained after processing 7 kg of coffee berries. In one yea Wambugu sent 36.4 tonnes of coffee berries for processing. How many kilograms of clean coffee beans were obtained?

A. 254800 kg     B. 36400 kg     C. 5200 kg      D. 520 kg

10. Amina’s watch gains 5 minutes in one hour. The watch was set correct at 10.30 a.m. What time did it read at 5.30 pm?

A. 4.55 am     B. 4.55 pm      C. 6.05 am      D. 6.05 pm

### Indirect Proportion

1. To complete a project in 48 days a construction company requires 12 employees. How many more employees would the company require if the project is to be completed in 36 days?

A. 16       B. 9         C. 4          D. 3

2. It takes 8 people 10 days to make 40 sweaters. How many more days would it take 5 people to make the same number of sweaters if they all worked at the same rate?

A. 6        B. 16        C. 26        D. 7

3. A certain job is completed by 120 people in 12 days. If only 80 people turned up for the job, how many more days will it take them to complete the job?

A. 4              B. 6            C. 8           D. 18

4. Ten men are paid sh 5000 for working 5 days. How much will 8 men get for working 20 days if the payment is at the same rate?

A. Sh 1000      B. Sh 16000     C. Sh 1562.50      D. Sh 25000

5. In a factory, 4 machines fill 900 packets of milk in 15 minutes. How many packets will 6 such machines fill in the same period?

A. 1440         B. 1350       C. 600         D. 225

6. Four tailors can make a certain number of trousers in 12 days. How many more tailors would be required in order to make the same number of trousers in 3 days?

A. 16          B. 12           C. 9            D. 5

7. Eight men working at the same rate can unload a lorry in 3 hours. If 2 of the men are absent, how much more time will the unloading take?

A. 21 h       B. 9 h      C. 4 h        D. 1 h

8. Ten identical taps can fill a tank of water in 8 minutes. How many more such taps would be needed to fill the same tank in 5 minutes?

A. 6            B. 16            C. 4               D. 26

9. Six people working for 5 days were paid a total of sh 3600. How much more would the same number of people paid for 12 days?

A. 12240       B. 8640        C. 5040        D. 1440

10. Six taps take 5 hours to fill a tank with water. How much longer will 4 similar taps take to fill the tank?

A. 2 1/2 h       B. 7 1/2 h      C. 12 1/2 h        D. 25 h

11. A contractor hired five people to complete a job in 6 days. Two of the workers did not turn up for the job. How many more days were needed to complete the job?

A. 4            B. 9            C. 10             D. 16

### Sources

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