Ch 13 Direct and Inverse Proportions mcqs & important questions mathematics | class 8th
MCQ Questions for Class 8 Maths: Ch 13 Direct and Inverse Proportions
1. A garrison of 500 persons had provisions for 27 days. After 3 days a reinforcement of 300 persons arrived. For how many more days will the remaining food last now?
(a) 12 days
(b) 14 days
(c) 16 days
(d) 15 days
► (d) 15 days
2. When one quantity is increased, the other quantity is also increased. This proportion is called _______
(a) Kally proportion
(b) Direct proportion
(c) Inverse proportion
(d) None of these
► (b) Direct proportion
3. 72 books are packed in 4 cartons of the same size. How many cartons are required for 360 books?
(a) 22
(b) 18
(c) 20
(d) None of these
► (c) 20
4. 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
► (d) Rs 50
5. The price of 357 mangoes is Rs.1517.25. What will be the approximate price of 49 dozens of such mangoes?
(a) Rs.3000
(b) Rs.3500
(c) Rs.4000
(d) Rs.2500
► (a) Rs.3000
6. 6 pipes are required to fill a tank in 1 hour 20 minutes. How long will it take if only 5 pipes of the same type are used?
(a) 56 minutes
(b) 72 minutes
(c) 96 minutes
(d) 80 minutes
► (c) 96 minutes
7. A van covers 432 km with 36 litres of diesel. How much distance would it cover with 25 litres of diesel?
(a) 200 km
(b) 300 km
(c) 100 km
(d) 350 km
► (b) 300 km
8. 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
► (b) Rs 2000
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
► (d) 6 minutes
10. 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.
(a) Rs 100
(b) Rs 84
(c) Rs 90
(d) Rs 60
► (b) Rs 84
11. An electric pole, 14 metres high, casts a shadow of 10 metres. Find the height of a tree that casts a shadow of 15 metres under similar conditions.
(a) 21 metres
(b) 30 metres
(c) 25 metres
(d) None of these
► (a) 21 metres
12. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
(a) 15 days
(b) 20 days
(c) 25 days
(d) 30 days
► (c) 25 days
13. The scale of a map is 1:3×107 Two cities are 5 cm apart on the map. Find the actual distance between them in kilometres.
(a) 1500 km
(b) 1000 km
(c) 1100 km
(d) 2000 km
► (a) 1500 km
14. A journey by bus takes 45 minutes at 40 km/hour. How fast must a car go to undertake the same journey in 25 minutes?
(a) 36 km/h
(b) 48 km/h
(c) 72 km/h
(d) None of these
► (c) 72 km/h
15. Raju earns Rs 1440, if he works for 12 days. If he works for 30 days, he will earn
(a) Rs 2400
(b) Rs 3600
(c) Rs 4800
(d) None of these
► (b) Rs 3600
16. x varies inversely as square of y. Given that y = 3 for x = 1.find the value of x for y = 4.
(a) 3
(b) 9
(c) 1/3
(d) 9/16
► (d) 9/16
17. If the cost of 27 bags of paddy is Rs.9450, what is the cost of 36 bags of paddy?
(a) Rs.12000
(b) Rs.12600
(c) Rs.16200
(d) Rs.10620
► (b) Rs.12600
18. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
(a) 24 days
(b) 28 days
(c) 34 days
(d) 35 days
► (a) 24 days
19. If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work?
(a) 4 days
(b) 5 days
(c) 3 days
(d) 2 days
► (c) 3 days
20. There is enough food to last for 40 people for 10 days. If 10 more people join them, the food will last for
(a) 10 days
(b) 12 days
(c) 8 days
(d) None of these
► (c) 8 days
21. A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. How many parts of base will be used in mixture by mixing 7 part of red pigment?
(a) 70
(b) 56
(c) 63
(d) 49
► (b) 56
22. Two quantities x and y are said to be in ___________ if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.
(a) inverse proportion
(b) mix proportion
(c) direct proportion
(d) None of these
► (c) direct proportion
important questions
Question 1:
Observe the tables given below and in each one find whether x and y are proportional:
(i)
| x | 3 | 5 | 8 | 11 | 26 |
| y | 9 | 15 | 24 | 33 | 78 |
(ii)
| x | 2.5 | 4 | 7.5 | 10 | 14 |
| y | 10 | 16 | 30 | 40 | 42 |
(iii)
| x | 5 | 7 | 9 | 15 | 18 | 25 |
| y | 15 | 21 | 27 | 60 | 72 | 75 |
ANSWER:
(i)
Clearly, xy=39=515=824=1133=2678=13(constant)Therefore, x and y are proportional.Clearly, xy=39=515=824=1133=2678=13(constant)Therefore, x and y are proportional.
(ii)
Clearly, xy=2.510=416=7.530=1040=14, while 1442=13i.e., 2.510=416=7.530=1040is not equal to 1442.Therefore, x and y are not proportional.Clearly, xy=2.510=416=7.530=1040=14, while 1442=13i.e., 2.510=416=7.530=1040is not equal to 1442.Therefore, x and y are not proportional.
(iii)
Clearly, xy=515=721=927=2575=13, while 1560=1872=14i.e., 515=721=927=2575is not equal to 1560 and1872.Therefore, x and y are not proportional.Clearly, xy=515=721=927=2575=13, while 1560=1872=14i.e., 515=721=927=2575is not equal to 1560 and1872.Therefore, x and y are not proportional.
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Question 2:
If x and y are directly proportional, find the values of x1 , x2 and y1 in the table given below:
| x | 3 | x1 | x2 | 10 |
| y | 72 | 120 | 192 | y1 |
ANSWER:
Since x and y are directly propotional, we have: 372=x1120=x2192=10y1Now, 372=x1120⇒x1=120×372 = 5Since x and y are directly propotional, we have: 372=x1120=x2192=10y1Now, 372=x1120⇒x1=120×372 = 5
And, 372 = x2192 ⇒ x2 = 3 × 19272 = 8And, 372 = x2192 ⇒ x2 = 3 × 19272 = 8
And, 372=10y1⇒y1=72×103=240And, 372=10y1⇒y1=72×103=240
Therefore, x1 = 5, x2 = 8 and y1 = 240Therefore, x1 = 5, x2 = 8 and y1 = 240
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Question 3:
A truck covers a distance of 510 km in 34 litres of diesel. How much distance would it cover in 20 litres of diesel?
ANSWER:
Let the required distance be x km. Then, we have:
| Quantity of diesel (in litres) | 34 | 20 |
| Distance (in km) | 510 | x |
Clearly, the less the quantity of diesel consumed, the less is the distance covered.
So, this is a case of direct proportion.
Now, 34510=20x⇒115=20x⇒x×1=20×15=300Now, 34510=20x⇒115=20x⇒x×1=20×15=300
Therefore, the required distance is 300 km.
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Question 4:
A taxi charges a fare of Rs 2550 for a journey of 150 km. How much would it charge for a journey of 124 km?
ANSWER:
Let the charge for a journey of 124 km be ₹x.
| Price(in ₹) | 2550 | x |
| Distance(in km) | 150 | 124 |
More is the distance travelled, more will be the price.
So, it is a case of direct proportion.
∴2550150=x124⇒x=2550×124150=2108∴2550150=x124⇒x=2550×124150=2108
Thus, the taxi charges ₹2,108 for the distance of 124 km.
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Question 5:
A loaded truck covers 16 km in 25 minutes. At the same speed, how far can it travel in 5 hours?
ANSWER:
Let the required distance be x km. Then, we have:
1 h=60 mini.e., 5 h=5×60=300 min1 h=60 mini.e., 5 h=5×60=300 min.
| Distance (in km) | 16 | x |
| Time (in min) | 25 | 300 |
Clearly, the more the time taken, the more will be the distance covered.
So, this is a case of direct proportion.
Now, 1625=x300⇒x=(16×30025)⇒x = 192Now, 1625=x300⇒x=16×30025⇒x = 192
Therefore, the required distance is 192 km.
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Question 6:
If 18 dolls cost Rs 630, how many dolls can be bought for Rs 455?
ANSWER:
Let the required number of dolls be x. Then, we have:
| No of dolls | 18 | x |
| Cost of dolls (in rupees) | 630 | 455 |
Clearly, the less the amount of money, the less will be the number of dolls bought.
So, this is a case of direct proportion.
Now, 18630=x455⇒135=x455⇒x=45535⇒x=13Now, 18630=x455⇒135=x455⇒x=45535⇒x=13
Therefore, 13 dolls can be bought for Rs 455.
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Question 7:
If 9 kg of sugar costs ₹ 238.50, how much sugar can be bought for ₹ 371?
ANSWER:
Let the quantity of sugar bought for ₹371 be x kg.
| Quantity(in kg) | 9 | x |
| Price(in ₹) | 238.50 | 371 |
The price increases as the quantity increases. Thus, this is a case of direct proportion.
∴9238.50=x371⇒x=9×371238.50=14∴9238.50=x371⇒x=9×371238.50=14
Thus, the quantity of sugar bought for ₹371 is 14 kg.
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Question 8:
The cost of 15 metres of a cloth is Rs 981. What length of this cloth can be purchased for Rs 1308?
ANSWER:
Let the length of cloth be x m. Then, we have:
| Length of cloth (in metres) | 15 | x |
| Cost of cloth (in rupees) | 981 | 1308 |
Clearly, more length of cloth can be bought by more amount of money.
So, this is a case of direct proportion.
Now, 15981=x1308⇒x=15×1308981⇒x=20Now, 15981=x1308⇒x=15×1308981⇒x=20
Therefore, 20 m of cloth can be bought for Rs 1,308.
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Question 9:
In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 15m high. If the length of the ship is 35 metres, how long is the model ship?
ANSWER:
Let x m be the length of the model of the ship. Then, we have:
1 m = 100 cmTherefore, 15 m= 1500 cm35 m= 3500 cm1 m = 100 cmTherefore, 15 m= 1500 cm35 m= 3500 cm
| Length of the mast (in cm) | Length of the ship (in cm) | |
| Actual ship | 1500 | 3500 |
| Model of the ship | 9 | x |
Clearly, if the length of the actual ship is more, then the length of the model ship will also be more.
So, this is a case of direct proportion.
Now, 15009=3500x⇒x=3500×91500⇒x=21 cmNow, 15009=3500x⇒x=3500×91500⇒x=21 cm
Therefore, the length of the model of the ship is 21 cm.
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Question 10:
In 8 days, the earth picks up (6.4 × 107) kg of dust from the atmosphere. How much dust will it pick up in 15 days?
ANSWER:
Let x kg be the required amount of dust. Then, we have:
| No. of days | 8 | 15 |
| Dust (in kg) | 6.4×1076.4×107 | x |
Clearly, more amount of dust will be collected in more number of days.
So, this is a case of direct proportion.
Now, 86.4×107=15x⇒x=15×6.4×1078⇒x=12×107Now, 86.4×107=15x⇒x=15×6.4×1078⇒x=12×107
Therefore, 12,00,00,000 kg of dust will be picked up in 15 days.
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Question 11:
A car is travelling at the average speed of 50 km/hr. How much distance would it travel in 1 hour 12 minutes?
ANSWER:
Let x km be the required distance. Then, we have:
1 h=60 mini.e., 1h 12 min=(60+12) min=72 min1 h=60 mini.e., 1h 12 min=(60+12) min=72 min
| Distance covered (in km) | 50 | x |
| Time (in min) | 60 | 72 |
Clearly, more distance will be covered in more time.
So, this is a case of direct proportion.
Now, 5060=x72⇒x=50×7260⇒x=60Now, 5060=x72⇒x=50×7260⇒x=60
Therefore, the distance travelled by the car in 1 h 12 min is 60 km.
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Question 12:
Ravi walks at the uniform rate of 5 km/hr. What distance would he cover in 2 hours 24 minutes?
ANSWER:
Let x km be the required distance covered by Ravi in 2 h 24 min.
Then, we have:
1 h=60mini.e., 2 h 24 min=(120+24) min=144 min1 h=60mini.e., 2 h 24 min=(120+24) min=144 min
| Distance covered (in km) | 5 | x |
| Time (in min) | 60 | 144 |
Clearly, more distance will be covered in more time.
So, this is a case of direct proportion.
Now,560=x144⇒x=5×14460⇒x=12Now,560=x144⇒x=5×14460⇒x=12
Therefore, the distance covered by Ravi in 2 h 24 min is 12 km.
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Question 13:
If the thickness of a pile of 12 cardboards is 65 mm, find the thickness of a pile of 312 such cardboards.
ANSWER:
Let x mm be the required thickness. Then, we have:
| Thickness of cardboard (in mm) | 65 | x |
| No. of cardboards | 12 | 312 |
Clearly, when the number of cardboard is more, the thickness will also be more.
So, it is a case of direct proportion.
Now, 6512=x312⇒x=65×31212⇒x=1690Now, 6512=x312⇒x=65×31212⇒x=1690
Therefore, the thickness of the pile of 312 cardboards is 1690 mm.
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Question 14:
11 men can dig 634634-metre-long trench in one day. How many men should be employed for digging 27-metre-long trench of the same type in one day?
ANSWER:
Let x be the required number of men.
Now, 634 m=274 mNow, 634 m=274 m
Then, we have:
| Number of men | 11 | x |
| Length of trench (in metres) | 274274 | 27 |
Clearly, the longer the trench, the greater will be the number of men required.
So, it is a case of direct proportion.
Now, 11274=x27⇒11×427=x27⇒x=44Now, 11274=x27⇒11×427=x27⇒x=44
Therefore, 44 men should be employed to dig a trench of length 27 m.
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Question 15:
Reenu types 540 words during half an hour. How many words would she type in 8 minutes?
ANSWER:
Let Reenu type x words in 8 minutes.
| No. of words | 540 | x |
| Time taken (in min) | 30 | 8 |
Clearly, less number of words will be typed in less time.
So, it is a case of direct proportion.
Now,54030=x8⇒x=540×830⇒x=144Now,54030=x8⇒x=540×830⇒x=144
Therefore, Reenu will type 144 words in 8 minutes.
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Question 1:
Observe the tables given below and in each case find whether x and y are inversely proportional:
(i)
| x | 6 | 10 | 14 | 16 |
| y | 9 | 15 | 21 | 24 |
(ii)
| x | 5 | 9 | 15 | 3 | 45 |
| y | 18 | 10 | 6 | 30 | 2 |
(iii)
| x | 9 | 3 | 6 | 36 |
| y | 4 | 12 | 9 | 1 |
ANSWER:
(i)
Clearly, 6×9≠ 10×15 ≠ 14×21≠ 16×24Therefore, x and y are not inversely proportional.Clearly, 6×9≠ 10×15 ≠ 14×21≠ 16×24Therefore, x and y are not inversely proportional.
(ii)
Clearly, 5×18= 9×10=15×6=3×30=45×2=90=(consant)Therefore, x and y are inversely proportional.Clearly, 5×18= 9×10=15×6=3×30=45×2=90=(consant)Therefore, x and y are inversely proportional.
(iii)
Clearly, 9×4=3×12=36×1=36, while 6×9=54i.e., 9×4=3×12=36×1≠6×9Therefore, x and y are not inversely proportional.Clearly, 9×4=3×12=36×1=36, while 6×9=54i.e., 9×4=3×12=36×1≠6×9Therefore, x and y are not inversely proportional.
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Question 2:
If x and y are inversely proportional, find the values of x1, x2, y1 and y2 in the table given below:
| x | 8 | x1 | 16 | x2 | 80 |
| y | y1 | 4 | 5 | 2 | y2 |
ANSWER:
Since x and y are inversely proportional, xy must be a constant.Since x and y are inversely proportional, xy must be a constant.
Therefore, 8×y1=x1×4=16×5=x2×2=80×y2Now, 16×5=8×y1⇒808=y1∴ y1=1016×5=x1×4⇒804=x1∴ x1=2016×5=x2×2⇒802=x2∴ x2=4016×5=80×y2⇒8080=y2∴ y2=1Hence, y1=10, x1=20, x2=40 and y2=1Therefore, 8×y1=x1×4=16×5=x2×2=80×y2Now, 16×5=8×y1⇒808=y1∴ y1=1016×5=x1×4⇒804=x1∴ x1=2016×5=x2×2⇒802=x2∴ x2=4016×5=80×y2⇒8080=y2∴ y2=1Hence, y1=10, x1=20, x2=40 and y2=1
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Question 3:
If 35 men can reap a field in 8 days, in how many days can 20 men reap the same field?
ANSWER:
Let x be the required number of days. Then, we have:
| No. of days | 8 | x |
| No. of men | 35 | 20 |
Clearly, less men will take more days to reap the field.
So, it is a case of inverse proportion.
Now, 8 × 35=x × 20⇒8 × 3520=x⇒14=xNow, 8 × 35=x × 20⇒8 × 3520=x⇒14=x
Therefore, 20 men can reap the same field in 14 days.
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Question 4:
12 men can dig a pond in 8 days. How many men can dig it in 6 days?
ANSWER:
Let x be the required number of men. Then, we have:
| No. of days | 8 | 6 |
| No. of men | 12 | x |
Clearly, more men will require less number of days to dig the pond.
So, it is a case of inverse proportion.
Now, 8 × 12 = 6 × x⇒x=8 × 126 ⇒x=16Now, 8 × 12 = 6 × x⇒x=8 × 126 ⇒x=16
Therefore, 16 men can dig the pond in 6 days.
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Question 5:
6 cows can graze a field in 28 days. How long would 14 cows take to graze the same field?
ANSWER:
Let x be the number of days. Then, we have:
| No. of days | 28 | x |
| No. of cows | 6 | 14 |
Clearly, more number of cows will take less number of days to graze the field.
So, it is a case of inverse proportion.
Now, 28 × 6 = x × 14⇒x=28 × 614 ⇒x=12Now, 28 × 6 = x × 14⇒x=28 × 614 ⇒x=12
Therefore, 14 cows will take 12 days to graze the field.
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Question 6:
A car takes 5 hours to reach a destination by travelling at the speed of 60 km/hr. How long will it take when the car travels at the speed of 75 km/hr?
ANSWER:
Let x h be the required time taken. Then, we have:
| Speed (in km/h) | 60 | 75 |
| Time (in h) | 5 | x |
Clearly, the higher the speed, the lesser will be the the time taken.
So, it is a case of inverse proportion.
Now, 60×5=75×x⇒x=60×575⇒x=4Now, 60×5=75×x⇒x=60×575⇒x=4
Therefore, the car will reach its destination in 4 h if it travels at a speed of 75 km/h.
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Question 7:
A factory requires 42 machines to produce a given number of articles in 56 days. How many machines would be required to produce the same number of articles in 48 days?
ANSWER:
Let x be the number of machines required to produce same number of articles in 48.
Then, we have:
| No. of machines | 42 | x |
| No. of days | 56 | 48 |
Clearly, less number of days will require more number of machines.
So, it is a case of inverse proportion.
Now, 42×56=x×48⇒x=42×5648⇒x=49Now, 42×56=x×48⇒x=42×5648⇒x=49
Therefore, 49 machines would be required to produce the same number of articles in 48 days.
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Question 8:
7 teps of the same size fill a tank in 1 hour 36 minutes. How long will 8 taps of the same size take to fill the tank?
ANSWER:
Let x be the required number of taps. Then, we have:
1 h = 60 min
i.e., 1 h 36 min = (60+36) min = 96 min
| No. of taps | 7 | 8 |
| Time (in min) | 96 | x |
Clearly, more number of taps will require less time to fill the tank.
So, it is a case of inverse proportion.
Now, 7×96=8×x⇒x=7×968⇒x=84Now, 7×96=8×x⇒x=7×968⇒x=84
Therefore, 8 taps of the same size will take 84 min or 1 h 24 min to fill the tank.
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Question 9:
8 taps of the same size fill a tank in 27 minutes. If two taps go out of order, how long would the remaining taps take to fill the tank?
ANSWER:
Let x min be the required number of time. Then, we have:
| No. of taps | 8 | 6 |
| Time (in min) | 27 | xx |
Clearly, less number of taps will take more time to fill the tank .
So, it is a case of inverse proportion.
Now, 8×27=6×x⇒x=8×276⇒x=36Now, 8×27=6×x⇒x=8×276⇒x=36
Therefore, it will take 36 min to fill the tank.
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Question 10:
A farmer has enough food to feed 28 animals in his cattle for 9 days. How long would the food last, if there were 8 more animals in his cattle?
ANSWER:
Let x be the required number of days. Then, we have:
| No. of days | 9 | x |
| No. of animals | 28 | 36 |
Clearly, more number of animals will take less number of days to finish the food.
So, it is a case of inverse proportion.
Now, 9×28=x×36⇒x=9×2836⇒x=7Now, 9×28=x×36⇒x=9×2836⇒x=7
Therefore, the food will last for 7 days.
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Question 11:
A garrison of 900 men had provisions for 42 days. However, a reinforcement of 500 men arrived. For how many days will the food last now?
ANSWER:
Let x be the required number of days. Then, we have:
| No. of men | 900 | 1400 |
| No. of days | 42 | x |
Clearly, more men will take less number of days to finish the food.
So, it is a case of inverse proportion.
Now, 900×42=1400×x⇒x=900×421400⇒x=27Now, 900×42=1400×x⇒x=900×421400⇒x=27
Therefore, the food will now last for 27 days.
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Question 12:
In a hostel, 75 students had food provision for 24 days. If 15 students leave the hostel, for how many days would the food provision last?
ANSWER:
Let x be the required number of days. Then, we have:
| No. of students | 75 | 60 |
| No. of days | 24 | x |
Clearly, less number of students will take more days to finish the food.
So, it is a case of inverse proportion.
Now, 75×24=60×x⇒x=75×2460⇒x=30Now, 75×24=60×x⇒x=75×2460⇒x=30
Therefore, the food will now last for 30 days.
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Question 13:
A school has 9 periods a day each of 40 minutes duration. How long would each period be, if the school has 8 periods a day, assuming the number of school hours to be the same?
ANSWER:
Let x min be the duration of each period when the school has 8 periods a day.
| No. of periods | 9 | 8 |
| Time (in min) | 40 | x |
Clearly, if the number of periods reduces, the duration of each period will increase.
So, it is a case of inverse proportion.
Now, 9×40=8×x⇒x=9×408⇒x=45Now, 9×40=8×x⇒x=9×408⇒x=45
Therefore, the duration of each period will be 45 min if there were eight periods a day.
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Question 14:
If x and y vary inversely and x = 15 when y = 6, find y when x = 9.
ANSWER:
| xx | 15 | 9 |
| yy | 6 | y1y1 |
x and y vary inversely.i.e. xy = constantNow, 15×6=9×y1⇒y1=15×69⇒y1=10x and y vary inversely.i.e. xy = constantNow, 15×6=9×y1⇒y1=15×69⇒y1=10
∴ Value of y=10y=10, when x =9
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Question 15:
If x and y vary inversely and x = 18 when y = 8, find x when y = 16.
ANSWER:
| xx | 18 | x1x1 |
| yy | 8 | 16 |
x and y vary inversely.i.e. xy = constantNow, 18×8=x1×16⇒18×816=x1⇒9=x1x and y vary inversely.i.e. xy = constantNow, 18×8=x1×16⇒18×816=x1⇒9=x1
∴ Value of x=9x=9
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Question 1:
If 14 kg of pulses cost ₹ 882, what is the cost of 22 kg of pulses?
(a) ₹ 1254
(b) ₹ 1298
(c) ₹ 1342
(d) ₹ 1386
ANSWER:
Let 22 kg of pulses cost ₹x.
| Quantity(in kg) | 14 | 22 |
| Price(in ₹) | 882 | x |
As the quantity increases, the price also increases. So, it is a case of direct proportion.
∴14882=22x⇒x=22×88214=1386∴14882=22x⇒x=22×88214=1386
Thus, the cost of 22 kg of pulses is ₹1,386.
Hence, the correct answer is option (d).
Page No 166:
Question 2:
If 8 oranges cost ₹ 52, how many oranges can be bought for ₹ 169?
(a) 13
(b) 18
(c) 26
(d) 24
ANSWER:
Let the number of oranges that can be bought for ₹169 be x.
| Quantity | 8 | x |
| Price(in ₹) | 52 | 169 |
As the quantity increases the price also increases. So, this is a case of direct proportion.
∴852=x169⇒x=8×16952=26∴852=x169⇒x=8×16952=26
Thus, 26 oranges can be bought for ₹169.
Hence, the correct answer is option (c).
Page No 166:
Question 3:
Tick (✓) the correct answer:
A machine fills 420 bottles in 3 hours. How many bottles will it fill in 5 hours?
(a) 252
(b) 700
(c) 504
(d) 300
ANSWER:
(b) 700
Let x be the number of bottles filled in 5 hours.
| No. of bottles | 420 | xx |
| Time (h) | 3 | 5 |
More number of bottles will be filled in more time.
Now, 4203=x5⇒x=420×53⇒x=700Now, 4203=x5⇒x=420×53⇒x=700
Therefore, 700 bottles would be filled in 5 h.
Page No 166:
Question 4:
Tick (✓) the correct answer:
A car is travelling at a uniform speed of 75 km/hr. How much distance will it cover in 20 minutes?
(a) 25 km
(b) 15 km
(c) 30 km
(d) 20 km
ANSWER:
(a) 25 km
Let x km be the required distance.
Now, 1 h = 60 min
| Distance (in km) | 75 | xx |
| Time (in min) | 60 | 20 |
Less distance will be covered in less time.
Now, 7560=x20⇒x=75×2060⇒x=25 kmNow, 7560=x20⇒x=75×2060⇒x=25 km
Page No 166:
Question 5:
Tick (✓) the correct answer:
The weight of 12 sheets of a thick paper is 40 grams. How many sheets would weight 1 kg?
(a) 480
(b) 360
(c) 300
(d) none of these
ANSWER:
(c) 300
Let x sheets weigh 1 kg.
Now, 1 kg = 1000 g
| No. of sheets | 12 | xx |
| Weight (in g) | 40 | 1000 |
Now, 1240=x1000⇒x=12×100040⇒x=300Now, 1240=x1000⇒x=12×100040⇒x=300
Page No 166:
Question 6:
Tick (✓) the correct answer:
A pole 14 m high casts a shadow of 10 m. At the same time, what will be the height of a tree, the length of whose shadow is 7 metres?
(a) 20 m
(b) 9.8 m
(c) 5 m
(d) none of these
ANSWER:
(b) 9.8 m
Let x m be the height of the tree.
| Height of object | 14 | xx |
| Length of shadow | 10 | 7 |
The more the length of the shadow, the more will be the height of the tree.
Now, 1410=x7⇒x=14×710⇒x=9.8Now, 1410=x7⇒x=14×710⇒x=9.8
Therefore, a 9.8 m tall tree will cast a shadow of length 7 m.
Page No 167:
Question 7:
Tick (✓) the correct answer:
A photograph of a bacteria enlarged 50000 times attains a length of 5 cm. The actual length of bacteria is
(a) 1000 cm
(b) 10−3 cm
(c) 10−4 cm
(d) 10−2 cm
ANSWER:
(c) 10−4 cm10-4 cm
Let x cm be the actual length of the bacteria.
The larger the object, the larger its image will be.
Now, x1=550000=10−4 cmNow, x1=550000=10-4 cm
Hence, the actual length of the bacteria is 10−4 cm10-4 cm.
Page No 167:
Question 8:
Tick (✓) the correct answer:
6 pipes fill a tank in 120 minutes, then 5 pipes will fill it in
(a) 100 min
(b) 144 min
(c) 140 min
(d) 108 min
ANSWER:
(b) 144 min
Let x min be the time taken by 5 pipes to fill the tank.
| No. of pipes | 6 | 5 |
| Time (in min) | 120 | xx |
Now, 6×120=5×x⇒x=144 Now, 6×120=5×x⇒x=144
Therefore, 5 pipes will take 144 min to fill the tank.
Page No 167:
Question 9:
Tick (✓) the correct answer:
3 persons can build a wall in 4 days, then 4 persons can build it in
(a) 513513 days
(b) 3 days
(c) 413413 days
(d) none of these
ANSWER:
(b) 3 days
Let x be number of days taken by 4 persons to build the wall.
| No. of persons | 3 | 4 |
| No. of days | 4 | xx |
More number of persons will take less time to build the wall.
So, it is a case of inverse proportion.
Now, 3×4=4×x⇒x=3 Now, 3×4=4×x⇒x=3
Therefore, 4 persons can build the wall in 3 days.
Page No 167:
Question 10:
Tick (✓) the correct answer:
A car takes 2 hours to reach a destination by travelling at 60 km/hr. How long will it take while travelling at 80 km/hr?
(a) 1 hr 30 min
(b) 1 hr 40 min
(c) 2 hrs 40 min
(d) none of these
ANSWER:
(a) 1 h 30 min
Let x h be the time taken by the car travelling at 80 km/hr.
| Speed (km/h) | 60 | 80 |
| Time (in h) | 2 | xx |
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= 1.5Therefore, the car will take 1 h 30 min to reach its destination if it travels at a speed of 80 km/h.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= 1.5Therefore, the car will take 1 h 30 min to reach its destination if it travels at a speed of 80 km/h.
Page No 168:
Question 1:
350 boxes can be placed in 25 cartons. How many boxes can be placed in 16 cartons?
ANSWER:
Let x be the required number of boxes.
| No. of boxes | 350 | xx |
| No. of cartons | 25 | 16 |
Less number of boxes will require less number of cartons.
So, it is a case of direct proportion.
Now, 35025=x16⇒x=350×1625⇒x=224Now, 35025=x16⇒x=350×1625⇒x=224
∴ 224 boxes can be placed in 16 cartoons.
Page No 168:
Question 2:
The cost of 140 tennis balls is Rs 4900. Find the cost of 2 dozen such balls.
ANSWER:
Let Rs x be the cost of 24 tennis balls.
| No. of balls | 140 | 24 |
| Cost of balls | 4900 | xx |
More tennis balls will cost more.
Now, 1404900=24x⇒x=24×4900140⇒x=840Now, 1404900=24x⇒x=24×4900140⇒x=840
∴ The cost of 2 dozen tennis balls is Rs 840.
Page No 168:
Question 3:
The railway fare for 61 km is Rs 183. Find the fare for 53 km.
ANSWER:
Let Rs x be the railway fare for a journey of distance 53 km.
| Distance (in km) | 61 | 53 |
| Railway fare (in rupees) | 183 | xx |
The lesser the distance, the lesser will be the fare.
So, it is a case of direct proportion .
Now, 61183=53x⇒x=53×18361⇒x=159Now, 61183=53x⇒x=53×18361⇒x=159
The railway fare for a journey of distance 53 km is Rs 159.
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