Class 8th Mathematics MCQ

Q1. Mark againts the correct answer in the following:

A pump can fill a cistern in 2 hours. Due to a leak in the tank it takes hours to fill it. The leak can empty the full

tank in:

1. 7 hours.

2. 14 hours.

3. 8 hours.

4. 3 hours.

Ans: 2. 14 hours.

Solution:

A pump fills a tank in 2 hours.

Part of tank filled by the pump in one hour

Let x hours be the time required for water to leak from the cistern.

Part of tank drained by the leak in one hour

ime required to fill the leaking cistern hours.

Part of tank stored with water in one hour

hours.

Q2. 3 lambs finish eating turnips in 8 days. In how many days will 2 lambs finish them?

1. 6

2. 8

3. 10

4. 12

Ans: 4. 12

Solution:

3 × 8 = 2 × ? ⇒ ? = 12

Q3. Tick the correct answer in the following:

A does 20% less work than B. If A can finish a piece of work in hours, then B can finish it in:

1.

2.

3.

4.

Ans: 3.

Solution:

A’s hour’s work

A and B’s ratio in work

Let ratio be, x and x, then,

B can finish the work in 6 hours.

Q4. 14 workers can build a wall in 42 days. One worker can build it in:

1. 3 days.

2. 147 days.

3. 294 days.

4. 588 days.

Ans: 4. 588 days.

Solution:

Let one worker take x days to build the wall.

No. of workers 14 1

No. of days 42 xx

Clearly, one worker will take more days to finish the work.

So, it is a case of inverse proportion.

Now, 14 × 42 = 1 × x

⇒ x = 14 × 42

⇒ x = 588

One worker can build the wall in 588 days.

Q5. If x and y are inversely proportional, then:

1. x + y = constant

2. xy = constant

3. x – y = constant

4.

Ans: 2. xy = constant

Solution:

Where k is a constant.

Q6. Tick the correct answer in the following:

Two pipes can fill a tank in 20 minutes and 30 minutes respectively. If both the pipes are opened simultaneously,

then hte tank will be filled in:

1. 10 minutes.

2. 12 minutes.

3. 15 minutes.

4. 25 minutes.

Ans: 2. 12 minutes.

Solution:

Frist pipe 1 minutes work

Second pipe 1 minutes work

Both’s 1 minutes work

Both’s 1 will do the work in = 12 minutes.

Q7. A photograph of a type of bacteria enlarged 50000 times attains a length of 5cm. What is the actual length of

bacteria?

1. 1000cm

2. 10 cm

3. 10 cm

4. 10 cm

Ans: 3. 10 cm

Q8. If and and then find 

1. 200

2. 99

3. 84

4. 70

Ans: 3. 84

Solution:

Q9. Assuming land to be uniformly fertile, the area of land and the yield on it vary

1. Directly with each other.

2. Inversely with each other.

3. Neither directly nor inversely with each other.

4. Sometimes directly and sometimes inversely with each other.

Ans: 1. Directly with each other.

Solution:

If land to be uniformly fertie,then the area of land and the yield on vary directly with each other.

Q10. The price of 357 mangoes is Rs. 1517.25 What will be the approximate price of 49 dozens of such mangoes?

1. Rs. 2500

2. Rs. 3500

3. Rs. 4000

4. Rs. 3000

Ans: 1. Rs. 2500

Q11. x and y vary inversely. When x = 15, then y = 6. What will be the value of y when x = 9?

1. 10

2. 15

3. 54

4. 135

Ans: 1. 10

Solution:

x 15 9

y 6 y

Since x and y vary inversely, xy = constant.

Now, 15 × 6 = 9 × y

Value of y = 10, when x = 9.

Q12. Apala types 200 words in half an hour. How many words will she type in 12 minutes?

1. 80

2. 50

3. 100

4. 60

Ans: 1. 80

Solution:

x ∝ y

x = ky

x = k

Q13. If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?

1. 15

2. 14

3. 24

4. 30

Ans: 3. 24

Q14. A bus covers 432km with 36 litres of diesel. How much distance would it cover with 25 litres of diesel?

1. 200km

2. 300km

3. 100km

4. 350km

Ans: 2. 300km

Q15. 72 books are packed in 4 cartons of the same size. How many cartons are required for 360 books?

1. 22

2. 18

3. 20

4. None of these.

Ans: 3. 20

Q16. The cost of 5 metres of a particular quality of cloth is Rs. 210. Find the cost of 2 metres of cloth of the same type.

1. Rs. 100

2. Rs. 84

3. Rs. 90

4. Rs. 60

Ans: 2. Rs. 84

Q17. If 5 people can do a piece of work in 20 days, how many people can do the same work in 2 days?

1. 8

2. 50

3. 100

4. 200

Ans: 1. 8

Q18. Tick the correct answer in the following:

A works twice as fast as B. If both of them can together finish a piece of work in 12 days, then B alone can do it in:

1. 24 days.

2. 27 days.

3. 36 days.

4. 48 days.

Ans: 3. 36 days.

Solution:

Let B’s 1 day’s work = x

Then A’s 1 day’s work = 2x

A and B’s 1 day’s work

B can do the work in 36 days.

Q19. 3 knives cost Rs. 63 What will 17 knives cost?

1. Rs. 357

2. Rs. 375

3. Rs. 537

4. Rs. 573

Ans: 1. Rs. 357

Solution:

Q20. Suppose 2kg of sugar contains 9 × 106 crystals. How many sugar crystals are there in 1.2kg of sugar?

1. 10 crystals

2. 5.4 × 10 crystals

3. 5.4 crystals

4. None of these.

Ans: 2. 5.4 × 10 crystals

Q21. If 11.25m of a uniform iron rod weighs 42.75kg, what will be the weight of 6m of the same rod?

1. 22.8kg

2. 25.6kg

3. 28kg

4. 26.5kg

Ans: 1. 22.8kg

Q22. Tick the correct answer in the following:

A alone can do a piece of work in 10 days and B alone can do it in 15 days. In how many days will A and B

together do the same work?

1. 5 days.

2. 6 days.

3. 8 days.

4. 9 days.

Ans: 2. 6 days.

Solution:

A’s 1 day’s work

B’s 1 day’s work

Both A and B’s 1 day’s work,

A and B can do the work in 6 days.

Q23. If an increase in one quantity brings about a corresponding decrease in the other and ice versa, then the two

quantities vary:

1. Directly.

2. Inversely.

3. Sometimes directly and sometimes inversely.

4. None of these.

Ans: 2. Inversely.

Solution:

The Two Quantities are inversely proportional.

One quantity increases and the other decreases in a related manner.

Therefore,

Q24. Tick the correct answer in the folllowing:

If 14kg of pulses cost Rs. 882, what is the cost of 22kg of pulses?

1. Rs. 1254

2. Rs. 1298

3. Rs. 1342

4. Rs. 1386

Ans: 4. Rs. 1386

Solution:

Let 22kg of pulses cost Rs. x

Quantity(in kg) 14 22

Price(in Rs.) 882 x

As the quantity increases, the price also increases. So, it is a case of direct proportion.

Thus the cost of 22kg of pilses is Rs. 1,386

Q25. If x = ky and when y = 4, x = 8 then k =

1. 1

2. 2

3. 3

4. 4

Ans: 2. 2

Solution:

8 = 4k ⇒ k = 2

Q26. Tick the correct answer in the following:

To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how

much time shall B take to do it?

1. 30 days.

2. 35 days.

3. 40 days.

4. 45 days.

Ans: 1. 30 days.

Solution:

Let B can do a work in = x days,

Then A can do the work,

A and B 1 days work

A’s 1 days’s work

And B’s 1 days work

B can do the work in = 30 days.

Q27. There is enough food to last for 40 people for 10 days. If 10 more people join them, the food will last for.

1. 10 days

2. 12 days

3. 8 days

4. None of these.

Ans: 3. 8 days

Q28. A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is 14cm How many times can

it go round a cylinder with radius 20cm?

1. 40

2. 49

3. 100

4. 54

Ans: 2. 49

Q29. 10 men can dig a trench in 15 days. How long will 3 men take?

1. 50 days

2. 60 days

3. 100 days

4. 75 days

Ans: 1. 50 days

Solution:

10 × 15 = 3 × ? ⇒ ? = 50.

Q30. If 18 women can reap a field in 7 days, in what time can 6 women reap the same field?

1. 15 days

2. 21 days

3. 30 days

4. 36 days

Ans: 2. 21 days

Solution:

18 × 7 = 6 × ? ⇒ ? = 21

Q31. If an amount of food last for 40 days for 120 men, how long will it last for 80 men at the same rate?

1. 50 days

2. 60 days

3. 80 days

4. 100 days

Ans: 2. 60 days

Solution:

40 × 120 = 80 × ? ⇒ ? = 60

Q32. 6 pipes are required to fill a tank in 1 hr 20 minutes. How long will it take if only 5 pipes of the same type are

used?

1. 2 hr 36 minutes.

2. 1 hr 36 minutes.

3. 2 hours.

4. 1 hr 30 minutes.

Ans: 2. 1 hr 36 minutes.

Q33. Tick the correct answer in the following:

A pump can fill a tank in 2 hours. Due to a leak in the tank it takes hours to fill the tank. The leak can empty

the full tank in:

1. hours.

2. 7 hours.

3. 8 hours.

4. 14 hours.

Ans: 4. 14 hours.

Solution:

Frist pump’s 1 hours work to fill

Due to leakage, tank is filled in hours,

hours,

Both its one hour work

Leakage’s 1 hour work to empty the tank,

Leak will empty the tank in 14 hours.

Q34. If x and y vary inversely. Then using the following table?

x 5

y 30

The value of x for y = 10 is:

1. 10

2. 40

3. 15

4. 20

Ans: 3. 15

Solution:

We have,

Given,

[Where, k = constant]

For,

Q35. There were 25 rooms in a hotel which were booked by a school for 80 students. How many more rooms would be

required if 20 more students joined?

1. 31 rooms

2. 20 rooms

3. 16 rooms

4. 6 rooms

Ans: 2. 20 rooms

Solution:

Let x rooms were required for 100 students (80 – 20)

As number of students is more so more rooms would be required. It is a case of inverse proportion which follows

Q36. By travelling at a speed of 48 kilometres per hour, a car can finish a certain journey in 10 hours. To cover the same

distance in 8 hours, the speed of the car should be

1. 60km/ h

2. 80km/ h

3. 30km/ h

4. 40km/ h

Ans: 1. 60km/ h

Solution:

speed of the car = 48km/ h & times teken by car = 10h

Distence = speed × times

If car need to car 480km in 8h, then

Requierd speed

Q37. x and y vary inversely with each other. If x – 15, when y = 6, then the value of x when y = 15 is.

1. 2

2. 4

3. 5

4. 6

Ans: 4. 6

Solution:

x = 5, y = 30

x × 1

y

⇒ x = k. 1

y

⇒ xy = k

⇒ k = (30 × 5)

y = 10, xy = k

⇒ x × 10 = 30 × 5

⇒ x = 15

= x1

x2

y2

y1

80 =

100

x

25

80 × 25 = 100 × x

y = 80×25

100

y = 20 rooms

= 48 × 10 = 480Km/ h

= = 60Km/ h 480

8

15 × 6 = ? × 15 ⇒ ? = 6.

Q38. Rohan runs at a speed of 5m/ min to cover a running track. He covers the distance in 12 hours. How much time

would be required if he triples his speed.

1. 4hours

2. 36hours

3. 8hours

4. 15hours

Ans: 1. 4hours

Solution:

Al a speed of Sm/min, the running track is covered in 12 hours. If the speed is tripled then less time would be required to cover the

same distance. It is a case of inverse proportion which follows.

Q39. A train travels a distance of 18km in 30 minutes. At same speed, how much distance can be covered by the train

in 3 hours?

1. 1.8km

2. 108km

3. 3km

4. 10.8km

Ans: 2. 108km

Solution:

Distance covered = 18km

Times required = 30 minutes

If the time is increased then more distance will be covered will be covered it is a case of direct proportion which follows,

Substituting the values, we get

Q40. Tick the correct answer in the following:

A tap can fill a cistern in 8 hours and another tap can empty the full cistern in 16 hours. If both the taps are open,

the time taken to fill the cistern is:

1. hours.

2. 10 hours.

3. 16 hours.

4. 20 hours.

Ans: 3. 16 hours.

Solution:

Frist tap’s 1 hours work to fill

Second tap’s 1 hours work to empty

Both 1 hour can fill the cistern

The cistern will fill up in 16 hours.

Q41. A shot travels 90m in 1 second. How long will it take to go 225m?

1. 2 seconds

2. 2.5 seconds

3. 4 seconds

4. 3.5 seconds

Ans: 2. 2.5 seconds

Solution:

Q42. The constant of variation, if from the following table is.

x 6 12 15 21

y 2 4 5 7

1. 1

2. 2

3. 3

4. 4

Ans: 3. 3

Solution:

2 × 3 = 6, 4 × 3 = 12,

5 × 3 = 15, 7 × 3 = 21

Q43. 12 men can dig 8 meters long trench in a day. How many men should be employed for digging 50 meter long

trench of the same type in one day?

1. 75

2. 50

3. 25

4. None of these.

Ans: 1. 75

Q44. If 12 workers can build a wall in 50 hours, how many workers will be required to do the same work in 40 hours?

1. 15

2. 10

3. 13

4. 14

Ans: 1. 15

Solution:

12 × 50 = x × 40

Q45. A boy runs 1km in 10 minutes. How long will he take to ran 600m?

1. 2 minutes

2. 3 minutes

3. 4 minutes

4. 6 minutes.

Ans: 4. 6 minutes.

Solution:

Q46. 120 copies of a book cost Rs. 600 What will 400 copies cost?

1. Rs. 1000

2. Rs. 2000

3. Rs. 3000

4. Rs. 2400

Ans: 2. Rs. 2000

Solution:

= ⇒? = 2.5 90

1

225

?

x ∝ y,

x = = 15

(12×50)

40

= ⇒? = 6 1000

10

600

?

Q47. The cost of 5 books is Rs. 620 Find the cost of 12 books.

1. Rs. 1488

2. Rs. 7440

3. Rs. 3250

4. Rs. 258

Ans: 1. Rs. 1488

Solution:

As the number of books increases, cost of books increases.

Using relation,

Here, and

Therefore, gives

Q48. If and then x and y are:

1. Inversely proportional.

2. Directly proportional.

3. Neither directly nor inversely proportional.

4. Cannot be determined.

Ans: 1. Inversely proportional.

Solution:

Hence, where is the proportionality constant.

Q49. If x and y are in inverse proportion then which of the following is correct:

1. x – y = constant

2. x + y = constant

3. xy = constant

4.

Ans: 3. xy = constant

Solution:

Given: x and y are in inverse proportion.

To Find: The correct option to the given statement.

Given that x and y are in inverse proportion.

Since x is inversely proportional to y,

It can be written as,

It means that where k is a constant.

Also y is inversely proportional to x can be written as.

It means that where k is a constant.

Then we can have that

xy = k

xy equals to constant.

I.e, xy = k(constant).

Q50. The cost of 8 meters cloth is Rs. 350. Calculate the cost of 15 meters cloth.

1. Rs. 186.67

2. Rs. 656.25

3. Rs. 5250

4. Rs. 2800

Ans: 2. Rs. 656.25

Solution:

It is case of direct proportion which folloes,

Substituting the values,

we get,

Q51. Tick the correct answer in the folllowing:

A car takes 2 hours to reach a destination by travelling at 60km/hr. How long will it take while travelling at

80km/hr

1. 1hr 30min

2. 1hr 40 min

3. 2hrs 40min

4. None of these

Ans: 1. 1hr 30min

Solution:

Let x h be the time taken by the car travelling at 80km/hr.

Speed (km/h) 60 80

Time (in h) 2 x

The greater the speed, the lesser will be the time taken.

So, it is a case of inverse proportion.

Now, 60 × 2 = 80 × x

⇒ x = 12080

⇒ x = 1.5

Therefore, the car will take 1h 30min to reach its destination if it travelsat a speed of 80km.

Q52. 35 men can reap a field in 8 days. In how many days can 20 men reap it?

1. 14 days.

2. 28 days.

3.

4. None of these.

Ans: 1. 14 days.

Solution:

Let 20 men take x days to reap the field.

No. of days 8 xx

No. of men 35 20

Clearly, less number of men will take more days.

So, it is a case of inverse proportion.

Now, 8 × 35 = x × 20

20 men can reap the field in 14 days.

Q53. If the cost of 18 pens is Rs. 234, a dozen pen will cost.

1. Rs. 144

2. Rs. 156

3. Rs. 192

4. Rs. 180

Ans: 2. Rs. 156

Q54. 

= x1

y1

x2

y2

8 =

350

15

y2

8y2 = 350 × 15

y2 = 350×15

8

y2 = 656.25

(✓)

87 . 1

2

⇒ x = 8×35

20

⇒ x = 14

∴

In an army camp, there are 320 soldiers. They have sufficient food for 80 days. If after 20 days, 20 soldiers left the

camp, for how many more days will the food last?

1. 56

2. 64

3. 32

4. 48

Ans: 2. 64

Q55. An electric pole 5m 60cm high would cast a shadow of length 4m. Find the length of the pole whose shadow is of

length 8m 20cm under similar conditions.

1. 11m 48cm

2. 10m 50cm

3. 5m 85cm

4. 114800cm

Ans: 1. 11m 48cm

Solution:

Length of electric pole = 5m 60cm = 560cm

Length of the shadow of the pole = 4m = 400cm

Length of the pole whose shadow ts of length 820cm

Q56. Tick the correct answer in the following:

A man can do a piece of work in 5 days. He and his son working together can finish it in 3 days. In how many days

can the son do it alone?

1.

2.

3.

4.

Ans: 3.

Solution:

A man’s 1 day work

Man and his son’s 1 days work

Son’s 1 days work

His son will finish the work,

Q57. Tick the correct answer in the following:

The rates of working of A and B are in the ratio 3 : 4. The number of days taken by them to finish the work are in

the ratio:

1. 3 : 4

2. 9 : 16

3. 4 : 3

4. 16 : 9

Ans: 3. 4 : 3

Solution:

Ratio in the rates of working of A and B = 3 : 4

Ratio in time =