myhelper: RS Aggarwal solution class 8 chapter 12 Direct and Inverse Proportions Test Paper 12

Test Paper 12

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Q1 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 1:

350 boxes can be placed in 25 cartons. How many boxes can be placed in 16 cartons?

Answer 1:

Let x be the required number of boxes.

No. of boxes	350	$x$
No. of cartons	25	16

Less number of boxes will require less number of cartons.
So, it is a case of direct proportion.

Now, \frac{350}{25} = \frac{x}{16} \Rightarrow x = \frac{350 \times 16}{25} \Rightarrow x = 224

∴ 224 boxes can be placed in 16 cartoons.

Q2 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 2:

The cost of 140 tennis balls is Rs 4900. Find the cost of 2 dozen such balls.

Answer 2:

Let Rs x be the cost of 24 tennis balls.

No. of balls	140	24
Cost of balls	4900	$x$

More tennis balls will cost more.

Now, \frac{140}{4900} = \frac{24}{x} \Rightarrow x = \frac{24 \times 4900}{140} \Rightarrow x = 840

∴ The cost of 2 dozen tennis balls is Rs 840.

Q3 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 3:

The railway fare for 61 km is Rs 183. Find the fare for 53 km.

Answer 3:

Let Rs x be the railway fare for a journey of distance 53 km.

Distance (in km)	61	53
Railway fare (in rupees)	183	$x$

The lesser the distance, the lesser will be the fare.
So, it is a case of direct proportion .

Now, \frac{61}{183} = \frac{53}{x} \Rightarrow x = \frac{53 \times 183}{61} \Rightarrow x = 159

The railway fare for a journey of distance 53 km is Rs 159.

Q4 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 4:

10 people can dig a trench in 6 days. How many people can dig it in 4 days?

Answer 4:

Let x people dig the trench in 4 days.

No. of people	10	$x$
No. of days	6	4

More people will take less number of days to dig the trench. Hence, this is a case of inverse proportion.

Now, 10 \times 6 = x \times 4 \Rightarrow x = \frac{60}{4} \Rightarrow x = 15

∴ 15 people can dig the trench in 4 days.

Q5 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 5:

30 men can finish a piece of work in 28 days. How many days will be taken by 21 men to finish it?

Answer 5:

Let x be the number of days taken by 21 men to finish the piece of work.

No. of men	30	21
No. of days	28	$x$

More men will take less time to complete the work.
So, this is a case of inverse proportion.

Now, 30 \times 28 = 21 \times x \Rightarrow x = \frac{30 \times 28}{21} \Rightarrow x = 40

∴ 21 men will take 40 days to finish the piece of work.

Q6 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 6:

A garrison of 200 men had provisions for 45 days. After 15 days, 40 more men join the garrison. Find the number of days for which the remaining food will last.

Answer 6:

Clearly, the remaining food is sufficient for 200 men for (45 − 15), i.e., 30 days.
Total number of men = 200 + 40 = 240
Let the remaining food last for x days.

No. of men	200	240
No. of days	30	$x$

Clearly, more men will take less number of days to finish the food.
So, it is a case of inverse proportion.

Now, 200 \times 30 = 240 \times x \Rightarrow x = \frac{200 \times 30}{240} \Rightarrow x = 25

∴ The remaining food will last for 25 days.

Q7 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 7:

Mark (✓) against the correct answer:
6 pipes can fill a tank in 24 minutes. One pipe can fill it in
(a) 4 minutes
(b) 30 minutes
(c) 72 minutes
(d) 144 minutes

Answer 7:

(d) 144 minutes

Let one pipe take x min to fill the tank.

No. of pipe	6	1
Time(in min)	24	$x$

Clearly, one pipe will take more time to fill the tank.
So, it is a case of inverse proportion.

Now, 6 \times 24 = 1 \times x \Rightarrow x = 6 \times 24 \Rightarrow x = 144

∴ One pipe can fill the tank in 144 minutes.

Q8 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 8:

Mark (✓) against the correct answer:
14 workers can build a wall in 42 days. One worker can build it in
(a) 3 days
(b) 147 days
(c) 294 days
(d) 588 days

Answer 8:

(d) 588 days
Let one worker take x days to build the wall.

No. of workers	14	1
No. of days	42	$x$

Clearly, one worker will take more days to finish the work.
So, it is a case of inverse proportion.

Now, 14 \times 42 = 1 \times x \Rightarrow x = 14 \times 42 \Rightarrow x = 588

∴ One worker can build the wall in 588 days.

Q9 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 9:

Mark (✓) against the correct answer:
35 men can reap a field in 8 days. In how many days can 20 men reap it?
(a) 14 days
(b) 28 days
(c) $87 \frac{1}{2}$ days
(d) none of these

Answer 9:

(a) 14 days
Let 20 men take x days to reap the field.

No. of days	8	$x$
No. of men	35	20

Clearly, less number of men will take more days.
So, it is a case of inverse proportion.

Now, 8 \times 35 = x \times 20 \Rightarrow x = \frac{8 \times 35}{20} \Rightarrow x = 14

∴ 20 men can reap the field in 14 days.

Q10 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 10:

Mark (✓) against the correct answer:
A car is travelling at an average speed of 60 km per hour. How much distance will it cover in 1 hour 12 minutes?
(a) 50 km
(b) 72 km
(c) 63 km
(d) 67.2 km

Answer 10:

(b) 72 km
Let x km be the distance covered in 1 h 12 min.
Now, 1 h 12 min = (60+12) min = 72 min

Distance(in km)	60	$x$
Time(in min)	60	72

More distance will be covered in more time.
So, it is a cas of direct proportion.

Now, \frac{60}{60} = \frac{x}{72} \Rightarrow x = 72 km

∴ The car will cover a distance of 72

km

in 1 h 12 min.

Q11 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 11:

Mark (✓) against the correct answer:
Rashmi types 510 words in half an hour. How many words would she type in 10 minutes?
(a) 85
(b) 150
(c) 170
(d) 153

Answer 11:

No. of words	510	$x$
Time(in min)	30	10

Less time will be taken to type less number of words.
So, it is a case of direct variation.

Now, \frac{510}{30} = \frac{x}{10} \Rightarrow x = 170

∴ Rashmi will type 170 words in 10 minutes.

Q12 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 12:

Mark (✓) against the correct answer:
x and y vary directly. When x = 3, then y = 36. What will be the value of x when y = 96?
(a) 18
(b) 12
(c) 8
(d) 4

Answer 12:

$x$	3	$x_{1}$
$y$	36	96

x and y var y directly . Then x = k y, where k is the constant of proportionality . \Rightarrow k = \frac{x}{y} Now, \frac{3}{36} = \frac{x_{1}}{96} \Rightarrow \frac{96 \times 3}{36} = x_{1} \Rightarrow 8 = x_{1}

∴ Value of

x = 8

Q13 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 13:

Mark (✓) against the correct answer:
x and y vary inversely. When x = 15, then y = 6. What will be the value of y when x = 9?
(a) 10
(b) 15
(c) 54
(d) 135

Answer 13:

(a) 10

$x$	15	9
$y$	6	$y_{1}$

Since x and y var y inversely, x y = constant . Now, 15 \times 6 = 9 \times y_{1} \Rightarrow \frac{90}{9} = y_{1} \Rightarrow 10 = y_{1}

∴ Value of y = 10, when x = 9.

Q14 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 14:

Fill in the blanks.
(i) If 3 persons can do a piece of work in 4 days, then 4 persons can do it in ......... days.
(ii) If 5 pipes can fill tank in 144 minutes, then 6 pipes can fill it in ......... minutes.
(iii) A car covers a certain distance in 1 hr 30 minutes at 60 km per hour. If it moves at 45 km per hour, it will take ......... hours.
(iv) If 8 oranges cost Rs 20.80, the cost of 5 oranges is Rs .........
(v) The weight of 12 sheets of a paper is 50 grams. How many sheets will weigh 500 grams?

Answer 14:

(i)
Let x be the number of days taken by 4 persons to complete the work.

No. of days	4	$x$
No. of persons	3	4

Clearly, more workers will take less number of days.
So, it is a case of inverse proportion.

Now, 4 \times 3 = x \times 4 \Rightarrow x = 3

Therefore, 4 persons can do the piece of work in 3 days.

(ii)
Let x min be the time taken by 6 pipes to fill the tank.

No. of pipes	5	6
Time (in min)	144	$x$

Clearly, more number of pipes will take less time to fill the tank.
So, it is a case of inverse proportion.

Now, 5 \times 144 = 6 \times x \Rightarrow x = \frac{5 \times 144}{6} \Rightarrow x = 120 \min

∴ 6 pipes can fill the tank in 120 min.

(iii)
Let x min be the time taken by the car travelling at 45 km/h.
Now, 1 h 30 min = (60+30) min

Speed(in km/hr)	60	45
Time(in min)	90	$x$

Clearly, a car travelling at a less speed will take more time.
So, it is a case of inverse proportion.

Now, 60 \times 90 = 45 \times x \Rightarrow x = \frac{60 \times 90}{45} \Rightarrow x = 120 \min = 2 h

∴ The car will take 2 h if it travels at a speed of 45 km/h.

(iv)
Let Rs x be the cost of 5 oranges.

No. of oranges	8	5
Cost of oranges	20.80	$x$

Clearly, less number of oranges will cost less.
So, it is a case of direct variation.

Now, \frac{8}{20.80} = \frac{5}{x} \Rightarrow x = \frac{5 \times 20.80}{8} \Rightarrow x = 13

∴ The cost of 5 oranges is Rs 13.

(v)
Let x be the number of sheets that weigh 500 g.

No. of sheets	12	$x$
Weight(in grams)	50	500

More number of sheets will weigh more.
So, it is a case of direct variation.

Now, \frac{12}{50} = \frac{x}{500} \Rightarrow x = \frac{12 \times 500}{50} \Rightarrow x = 120

∴ 120 sheets will weigh 500 g.

RS Aggarwal solution class 8 chapter 12 Direct and Inverse Proportions Test Paper 12

Test Paper 12

Page-168

Q1 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Question 1:

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Q2 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q3 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q4 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q5 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q6 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q7 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q8 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q9 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q10 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q11 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q12 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q13 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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Q14 | Test Paper 12 | Class 8 | RS AGGARWAL | chapter 12 | Direct and Inverse Proportions

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