Namrata Das Exams Prep Master
Exams Prep Master
Direct and inverse proportions suggest a relationship between quantities and amount. It also helps to understand how the inter-relationship of two quantities can affect an equation or a problem. At times we see that while calculating something when we change one quantity, it affects the other quantity and the other also changes. For example, you can buy more amount of grocery with more amount of money. This is an example of direct proportionality. However, if you increase the speed of your vehicle, you shall cover your distance in lesser time. This is an example of inverse proportionality.
In this article, based on the complexity, importance, and weightage of the respective chapters MCQs are carefully selected. Students can secure more marks in their exams if they practice these MCQs. Here is sample Multiple Choice Questions to help you understand the concept better.
Ques: Ankita types 540 words in half an hour. How many words she can type in 120 seconds.
- 3
- 12
- 36
- 28
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Ans: c.
Explanation: By unitary method
No. Of words Ankita types: 540
Time taken : 1/2hr= 30 minutes
= 30X60= 1800 seconds
Therefore, No. Of words in 1 sec= 540/1800
= 0.3 word
No. Of words in 120 seconds = 120 X 0.3
= 36 words
Hence option c is correct.
| x | 540 | a |
|---|---|---|
| y | 30 | 120 |
Let the word be x term
Let the time taken in seconds be y term
By using direct inverse formula
x/y= K
540/1800=a/120
540 x 120=1800xa
= 36
Hence Ankita will write 36 words in 120 seconds.
Option c is correct.
Ques: 11 labours can dig 27/4m long trench in one day. How many labours should be employed for digging 47m long trench in one day?
- 69 labours
- 39 labours
- 78 labours
- 77 labours
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Ans: d.
Explanation: No. Of labours required to dig 27/4m= 11
No. Of labours required to dig 1m= 11/6.75
= 11÷6.75
= 1.63 Labours for 1 m
No. Of labours required for 47m= 1.63x47
= 76.61
I.e. = 77 labours
Hence option d is correct.
Ques: Cost of 5m carpet is Rs 270/- . Then what will be the cost of a 12m carpets?
- 624
- 684
- 6228
- 648
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Ans: d.
Explanation: By unitary method
Cost of 5m carpet: Rs 270
So, Cost of 1m carpet: 270÷5
= Rs 54 for 1m carpet
Therefore 12m carpet will cost:
= 54X12
= Rs 648
Hence option d is correct.
Ques: A train covers the distance in 2 hrs at the speed of 80 km/hr. Then how much time will it take to cover the same distance at speed the speed of 90 km/hr.
- 1 hour 46 minutes
- 1 hour 30 minutes
- 1 hour 50 minutes
- 1 hour 40 minutes
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Ans: a.
Explanation: Case 1
Let the distance be x
Speed of train , S= 80km/hr
Time taken, t= 2 hours
Therefore distance traveled by train = S x t
= 80 x 2
= 160 km
Case 2
Speed of train , S = 90km/hr
Distance travelled, d = 160km
Time taken by train, t = d/S
t= 160/90
t= 1.77 hr
To change the time value in Hour and minutes
1.77x60
= 106.6
= 1 hour 46 minutes (approx)
Hence option a is correct.
Ques: A machine at petrol pump fills 500L in 60 minutes. How much time will it take to fill 750L?
- 88 minutes
- 82 minutes
- 89 minutes
- 90 minutes
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Ans: d.
Explanation: Time taken by machine to fill 500L: 60 minutes
Let the time taken by machine to fill 1L be x
x = 60÷500
x = 0.12 minutes
Therefore,
Time taken by machine to fill 750L= 0.12 x 750
= 90 minutes
Hence option d correct.
Ques: If 52 men can do work in 5 days. In how many days 26 men will do the same work?
- 16 days
- 10 days
- 12days
- 18 days
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Ans: b.
Explanation: This is the question of the inverse.
Solving by Unitary method
Time taken by 52 men: 5 days
Time taken by 1 man to complete same work
= 5 x 52
= 260 days
Total work is of 260 days for 1 man
Therefore, time taken by 26 men to complete the work of 260 days,
= 260 ÷ 26
= 10 days
Hence option b is correct.
Ques: The scale of map is given as 1:500. Two cities are 7km apart on the map. The actual distance b/w them is?
- 3500km
- 35km
- 35000km
- None of above
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Ans: a.
Explanation: Scale of map = 1:500
That means 1km is map denotes 500km in actual distance.
Distance between two cities on map = 7km
Actual distance between them = 7 x 500
= 3500 km.
Hence the distance between two cities are 3500km
Option a is correct.
Ques: If the weight of 10 sheets of thick paper is 40gm. How many sheets of the same paper would weigh 1700gm?
- 42.5 sheets
- 425 sheets
- 325 sheets
- 300 sheets
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Ans: b.
Explanation: By unitary method
No. Of sheets: 10
Weight of 10 sheets: 40gm
No. Of sheets in 1gm: 10/40
No. Of sheets in 1700gm = 10/40(1700)
= 1/4 (1700)
= 425 sheets
Therefore, 425 sheets will weigh 1700gm
Hence option b is correct.
Ques: If x and y are inversely proportional, then which one is true?
- x1/y1 =x2/y2
- x1/x2=y1/y2
- x1/x2=y2/y1
- x1/y2=x2/y1
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Ans: d.
Explanation: Given: x is inversely proportional to y
x ∝ 1/y
x= K(1/y)
xy=K
Where K is the constant.
Hence, x1y1=x2y2
x1/y2=x2/y1
Therefore option d is correct.
Ques: 6 pipes required to fill a tank in 1hr.20min. If we use 8 pipes of same type then how much time will it take to fill the same tank.
- 60 min
- 30 min
- 140 min
- 160 min
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Ans: b.
Explanation: No of pipes given: 6
Time taken to fill the tank from given pipes: 1hr 20 min Or 80 min
Time taken to fill the tank by one pipe: 80 x 6
= 240 min Or 4 hours
8 pipes will take: 240÷8
= 30 minutes or half an hour.
Hence option b is correct.
Ques: A man walks 20 km in 5 hours. Find out the time it will take for him to walk 32 km?
- 3 hours
- 4 hours
- 6 hours
- 8 hours
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Ans: d.
Explanation: Man walks 20 km in = 5 hours
Which means it will take more time to walk 32 km. This is the case of direct proportion.
Therefore, 20/5 = 32/x
x = 32/4 = 8
Ques: If 300 Kg of coal cost 6000?, then what is the cost of 120 kg of coal?
- 1200\(\Box\)
- 2400\(\Box\)
- 3200\(\Box\)
- 4200\(\Box\)
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Ans: b.
Explanation:
300/6000 = 120/x
x = 2400
Ques: Manvi types 200 words in 30 minutes. Find how many words she will type in 12 minutes?
- 100
- 80
- 60
- 50
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Ans: b.
Explanation:
30/200 = 12/x
x = 12 x 200/30
x = 80
Ques: It takes 40 days for 120 men to complete a work. How long will it take for 80 men to complete the same work?
- 50 days
- 60 days
- 80 days
Click here for the answer
d.100 days
Ans: b.
Explanation: 60 days
40 × 120 = 80 × x
⇒ x = 60
Ques: If 6 pipes are required to fill a tank in 80 minutes. Then find how long will it take if only 5 pipes of the same type are used?
- 96 minutes
- 102 minutes
- 106 minutes
- 108 minutes
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Ans: a.
Explanation: 96 minutes
80 × 6 = x × 5
x = 96
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