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## Wednesday 24 February 2021

### CBSE Class 8 Maths - MCQ and Online Tests - Unit 13 - Direct and Indirect Proportions

#### 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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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) x1/y1 = x2/y2
(b) x1/x2 = y1/y2
(c) x1/x2 = y2/y1
(d) x1.x2 = y1.y2

Explanation:
x ?1/y
x = k (1/y)
xy = k
x1y1=x2y2
x1/x2=y2/y1

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

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

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

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

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

Explanation:
x ? 1/y
x = k/y
xy = k
Where k is a constant.

Question 36.
If x ? y and x1= 5, y1 = 210 and x2 = 2, then find y2 ?
(a) 200
(b) 84
(c) 99
(d) 70

Explanation:
x ? y
x = ky
x/y = k
x1/y1 = x2/y2
5/210 = 2/y2
y2 = 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

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.

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.

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.

Explanation:
18 Ũ 7 = 6 Ũ ? ? ? = 21.

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