**CBSE Class 8 Maths – MCQ and Online Tests – Unit 13 – Direct and Indirect Proportions**

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**CBSE Class 8 Maths – MCQ and Online Tests – Unit 13 – Direct and Indirect Proportions**

Question 1.

6 pipes are required to fill a tank in 1 hour. How long will it take if only 5 pipes of the same type are used ?

(a) 75 minutes

(b) 72 minutes

(c) 80 minutes

(d) 90 minutes.

## Answer

Answer: (b) 72 minutes

Explanation:

6 Ũ 60 = 5 Ũ ? ? ? = 72 minutes.

Question 2.

The scale of a map is given as 1 : 300. Two cities are 4 km apart on the map. The actual distance between them is:

(a) 1000 km

(b) 1100 km

(c) 1200 km

(d) 1300 km

## Answer

Answer: (c) 1200 km

Explanation:

1 : 300 = x : y

1/300 = 4/y

y = 4 x 300 = 1200

Hence, the distance between the two cities is 1200 km.

Question 3.

40 cows can graze a field in 16 days. How many cows will graze the same field in 10 days ?

(a) 60

(b) 64

(c) 80

(d) 75.

## Answer

Answer: (b) 64

Explanation:

40 Ũ 16 = ? Ũ 10 ? ? = 64.

Question 4.

If x = ky and when y = 4, x = 8 then k =

(a) 1

(b) 2

(c) 3

(d) 4.

## Answer

Answer: (b) 2

Explanation:

8 = 4k ? k = 2.

Question 5.

8 g of sandal wood cost Rs 40. What will 10 g cost ?

(a) Rs 30

(b) Rs 36

(c) Rs 48

(d) Rs 50.

## Answer

Answer: (d) Rs 50.

Explanation:

\(\frac{8}{10}\) = \(\frac{10}{?}\) ? ? = 50

Question 6.

20 trucks can hold 150 metric tonnes. How much will 12 trucks hold ?

(a) 80 metric tonnes

(b) 90 metric tonnes

(c) 60 metric tonnes

(d) 40 metric tonnes.

## Answer

Answer: (b) 90 metric tonnes

Explanation:

\(\frac{20}{150}\) = \(\frac{12}{?}\) ? ? = 90

Question 7.

120 copies of a book cost Rs 600. What will 400 copies cost ?

(a) Rs 1000

(b) Rs 2000

(c) Rs 3000

(d) Rs 2400.

## Answer

Answer: (b) Rs 2000

Explanation:

\(\frac{120}{600}\) = \(\frac{400}{?}\) ? ? = 2000

Question 8.

The rent of 7 hectares is Rs 875. What is the rent of 16 hectares ?

(a) Rs 2000

(b) Rs 1500

(c) Rs 1600

(d) Rs 1200.

## Answer

Answer: (a) Rs 2000

Explanation:

\(\frac{7}{875}\) = \(\frac{16}{?}\) ? ? = \(\frac{875Ũ16}{7}\) = 2000

Question 9.

A boy runs 1 km in 10 minutes. How long will he take to ran 600 m ?

(a) 2 minutes

(b) 3 minutes

(c) 4 minutes

(d) 6 minutes.

## Answer

Answer: (d) 6 minutes.

Explanation:

\(\frac{1000}{10}\) = \(\frac{600}{?}\) ? ? = 6

Question 10.

A shot travels 90 m in 1 second. How long will it take to go 225 m ?

(a) 2 seconds

(b) 2.5 seconds

(c) 4 seconds

(d) 3.5 seconds.

## Answer

Answer: (b) 2.5 seconds

Explanation:

\(\frac{90}{1}\) = \(\frac{225}{?}\) ? ? = 2.5

Question 11.

3 knives cost Rs 63. What will 17 knives cost ?

(a) Rs 357

(b) Rs 375

(c) Rs 537

(d) Rs 573.

## Answer

Answer: (a) Rs 357

Explanation:

\(\frac{3}{63}\) = \(\frac{17}{?}\) ? ? = 357

Question 12.

15 men can mow 40 hectares of land in 1 day. How much will 6 men mow in 1 day ?

(a) 16 hectares

(b) 12 hectares

(c) 20 hectares

(d) 24 hectares.

## Answer

Answer: (a) 16 hectares

Explanation:

\(\frac{15}{40}\) = \(\frac{6}{?}\) ? ? = \(\frac{40Ũ6}{15}\) = 16

Question 13.

A man walks 20 km in 5 hours. How long would he take in walking 32 km ?

(a) 3 hours

(b) 4 hours

(c) 6 hours

(d) 8 hours.

## Answer

Answer: (d) 8 hours.

Explanation:

\(\frac{20}{5}\) = \(\frac{32}{?}\) ? ? = 8

Question 14.

What is the cost of 50 sticks at Rs 24 per score ?

(a) Rs 30

(b) Rs 40

(c) Rs 50

(d) Rs 60.

## Answer

Answer: (d) Rs 60.

Explanation:

\(\frac{20}{24}\) = \(\frac{50}{?}\) ? ? = 60

Question 15.

A train travels 60 km in 1 hour. How long will it take to go 150 km ?

(a) 2 hours

(b) 3 hours

(c) 2.5 hours

(d) 4 hours.

## Answer

Answer: (c) 2.5 hours

Explanation:

\(\frac{60}{1}\) = \(\frac{150}{?}\) ? ? = 2.5

Question 16.

If 3 quintals of coal cost Rs 6000, what is the cost of 120 kg ?

(a) Rs 1200

(b) Rs 2400

(c) Rs 3600

(d) Rs 4800.

## Answer

Answer: (b) Rs 2400

Explanation:

\(\frac{300}{6000}\) = \(\frac{120}{?}\) ? ? = 2400

Question 17.

If 20 cows eat as much as 15 oxen, how many cows will eat at much as 36 oxen ?

(a) 40

(b) 44

(c) 45

(d) 48

## Answer

Answer: (d) 48

Explanation:

\(\frac{15}{20}\) = \(\frac{36}{?}\) ? ? = \(\frac{20Ũ36}{15}\) = 48

Question 18.

The fare for a journey of 40 km is Rs 25. How much can be travelled for Rs40 ?

(a) 32 km

(b) 64 km

(c) 50 km

(d) 60 km.

## Answer

Answer: (b) 64 km

Explanation:

\(\frac{25}{40}\) = \(\frac{40}{?}\) ? ? = \(\frac{40Ũ40}{25}\) = 64

Question 19.

Apala types 200 words in half an hour. How many words will she type in 12 minutes ?

(a) 80

(b) 50

(c) 100

(d) 60.

## Answer

Answer: (a) 80

Explanation:

\(\frac{30}{200}\) = \(\frac{12}{?}\) ? ? = 80

Question 20.

A labourer is paid Rs 400 for 2 days work. If he works for 5 days, how much will he get ?

(a) Rs 1000

(b) Rs 800

(c) Rs 750

(d) Rs 900.

## Answer

Answer: (a) Rs 1000

Explanation:

\(\frac{2}{400}\) = \(\frac{5}{?}\) ? ? = 1000

Question 21.

A machine in a soft drink factory fills 600 bottles in 5 hours. How many bottles will it fill in 2 hours ?

(a) 120

(b) 180

(c) 150

(d) 240.

## Answer

Answer: (d) 240

Explanation:

\(\frac{5}{600}\) = \(\frac{2}{?}\) ? ? = 240

Question 22.

10 men can dig a trench in 15 days. How long will 3 men take ?

(a) 50 days

(b) 60 days

(c) 100 days

(d) 75 days.

## Answer

Answer: (a) 50 days

Explanation:

10 Ũ 15 = 3 Ũ ? ? ? = 50.

Question 23.

3 lambs finish eating turnips in 8 days. In how many days will 2 lambs finish them ?

(a) 6

(b) 8

(c) 10

(d) 12.

## Answer

Answer: (d) 12

Explanation:

3 Ũ 8 = 2 Ũ ? ? ? = 12.

Question 24.

The constant of variation, if x ? y, from the following table is

(a ) 1

(b) 2

(c) 3

(d) 4.

## Answer

Answer: (c) 3

Explanation:

2 Ũ 3 = 6, 4 Ũ 3 = 12,

5 Ũ 3 = 15, 7 Ũ 3 = 21.

Question 25.

10 metres of cloth cost Rs 1000. What will 4 metres cost ?

(a) Rs 400

(b) Rs 800

(c) Rs 200

(d) Rs 100.

## Answer

Answer: (a) Rs 400

Explanation:

\(\frac{10}{1000}\) = \(\frac{4}{?}\) ? ? = 400

Question 26.

15 books weigh 6 kg. What will 6 books weigh ?

(a) 1.2 kg

(b) 2.4 kg

(c) 3.8 kg

(d) 3 kg.

## Answer

Answer: (b) 2.4 kg

Explanation:

\(\frac{15}{6}\) = \(\frac{6}{?}\) ? ? = 2.4

Question 27.

A horse eats 18 kg of com in 12 days ? How much does he eat in 9 days ?

(a) 11.5 kg

(b) 12.5 kg

(c) 13.5 kg

(d) 14.5 kg.

## Answer

Answer: (c) 13.5 kg

Explanation:

\(\frac{12}{18}\) = \(\frac{9}{?}\) ? ? = \(\frac{18Ũ9}{12}\) = 13.5

Question 28.

x and y vary inversely with each other. If x – 15 when y = 6, then the value of x when y = 15 is

(a) 2

(b) 4

(c) 5

(d) 6.

## Answer

Answer: (d) 6

Explanation:

15 Ũ 6 = ? Ũ 15 ? ? = 6.

Question 29.

If x = 20 and y = 40, then x and y are:

(a) Directly proportional

(b) Inversely proportional

(c) Neither directly nor inversely proportional

(d) Cannot be determined

## Answer

Answer: (a) Directly proportional

Explanation:

x = 20 and y = 40

Clearly, 40 = 2 Ũ 20

y = 2x

y ? x, where 2 is the proportionality constant.

Question 30.

If x and y are inversely proportional, then which one is true?

(a) x_{1}/y_{1} = x_{2}/y_{2}

(b) x_{1}/x_{2} = y_{1}/y_{2}

(c) x_{1}/x_{2} = y_{2}/y_{1}

(d) x_{1}.x_{2} = y_{1}.y_{2}

## Answer

Answer: (c) x_{1}/x_{2} = y_{2}/y_{1}

Explanation:

x ?1/y

x = k (1/y)

xy = k

x_{1}y_{1}=x_{2}y_{2}

x_{1}/x_{2}=y_{2}/y_{1}

Question 31.

6 pipes are required to fill a tank in 1 hour 20 minutes. If we use 5 such types of pipes, how much time it will take to fill the tank?

(a) 120 minutes

(b) 96 minutes

(c) 80 minutes

(d) 85 minutes

## Answer

Answer: (b) 96 minutes

Explanation:

For 6 pipes, it takes 1 hour 20 minutes

1 hour 20 minutes = 60 + 20 = 80 minutes

For 5 pipes, let the time taken be x.

This is inverse proportion case:

80 Ũ 6 = x Ũ 5

x = 480/5 = 96

Question 32.

If 12 workers can build a wall in 50 hours, how many workers will be required to do the same work in 40 hours?

(a) 10

(b) 13

(c) 14

(d) 15

## Answer

Answer: (d) 15

Explanation:

12 Ũ 50 = x Ũ 40

x = (12Ũ50)/40 = 15

Question 33.

If x = 15 and y = 1/30, then x and y are:

(a) Directly proportional

(b) Inversely proportional

(c) Neither directly nor inversely proportional

(d) Cannot be determined

## Answer

Answer: (a) Directly proportional

Explanation:

x = 15, y = 1/30

1/30 = 1/(2 Ũ 15)

y = 1/2x

Hence, y ? 1/x, where 1/2 is the proportionality constant.

Question 34.

If x and y are directly proportional, then which of the following is correct?

(a) x + y = constant

(b) x – y = constant

(c) xy = constant

(d) x/y = constant

## Answer

Answer: (d) x/y = constant

Explanation:

x ? y

x = ky

k = x/y, where k is a constant.

Question 35.

If x and y are inversely proportional, then:

(a) x + y = constant

(b) x – y = constant

(c) xy = constant

(d) x/y = constant

## Answer

Answer: (c) xy = constant

Explanation:

x ? 1/y

x = k/y

xy = k

Where k is a constant.

Question 36.

If x ? y and x_{1}= 5, y_{1} = 210 and x_{2} = 2, then find y_{2} ?

(a) 200

(b) 84

(c) 99

(d) 70

## Answer

Answer: (b) 84

Explanation:

x ? y

x = ky

x/y = k

x_{1}/y_{1} = x_{2}/y_{2}

5/210 = 2/y_{2}

y_{2} = 84

Question 37.

If the weight of 12 sheets of thick paper is 40 grams, how many sheets of the same paper would weigh 2500 grams?

(a) 750

(b) 800

(c) 850

(d) 950

## Answer

Answer: (a) 750

Explanation:

For 12 sheets, weight of paper is 40 grams

Let number of sheets for 2500 is x.

Using direct proportion concept:

12/40 = x/2500

x = (12 Ũ 2500)/40

x = 750

Question 38.

If 8 men can do a piece of work in 20 days, in how many days could 20 men do the same work ?

(a) 6 days

(b) 8 days

(c) 4 days

(d) 10 days.

## Answer

Answer: (b) 8 days

Explanation:

8 Ũ 20 = 20 Ũ ? ? ? = 8.

Question 39.

If an amount of food last for 40 days for 120 men, how long will it last for 80 men at the same rate ?

(a) 50 days

(b) 60 days

(c) 80 days

(d) 100 days.

## Answer

Answer: (b) 60 days

Explanation:

40 Ũ 120 = 80 Ũ ? ? ? = 60.

Question 40.

If 18 women can reap a field in 7 days, in what time can 6 women reap the same field ?

(a) 15 days

(b) 21 days

(c) 30 days

(d) 36 days.

## Answer

Answer: (b) 21 days

Explanation:

18 Ũ 7 = 6 Ũ ? ? ? = 21.

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