Edudel, Directorate of Education Govt. of NCT of Delhi Class 8 Mental Maths Question Bank Chapter 13 Direct and Inverse Proportions Questions Solution. In this chapter, there are total 50 math problems. We have given each questions solution step by step.
Edudel Class 8 Mental Maths Chapter 13 Direct and Inverse Proportions:
1.) ‘x’ and ‘y’ are directly proportional to each other. If x1= 20, y1 = 8, x2 = 5 then find y2.
ANSWER:
Given,
‘x’ and ‘y’ are directly proportional to each other.
x1/x2= y1/y2 is constant.
x1= 20, y1 = 8, x2 = 5
20/5 = 8/y2
By cross multiplication,
y2 = 5 x 8 / 20 = 2
y2 = 2
2.) A person can build a wall in 10 days. What fraction of the wall will be completed in 2 days?
ANSWER:
Given,
A person can build a wall in 10 days.
We have to find what fraction of the wall will be completed in 2 days
In 2 days = 2/10 of the wall will be completed
2/10 = 1/5 wall will be completed
3.) A lady covers a distance of 75 m in 60 steps. What distance will she cover in 320 steps?
ANSWER:
Given,
A lady covers a distance of 75 m in 60 steps.
We have to find distance will she cover in 320 steps
75 m = 60 steps.
? = 320 steps
By cross multiplication,
320 x 75 / 60
= 75 x 6
= 450 m.
She cover 320 steps in 450 m.
4.) It takes 2 hours for 6 pipes to fill a tank. How much time will be needed to fill 10 such tanks if 12 pipes are used?
ANSWER:
2 hours for 6 pipes to fill a tank.
We have to find how much time will be needed to fill 10 such tanks if 12 pipes are used.
For 1 tank = 2 hours x 6 pipes
Time will be needed to fill 10 tanks = 10 tanks x 12 pipes / 2 hours x 6 pipes
Time will be needed to fill 10 tanks = 10 hours.
5.) A train is moving at 150 kilometer/hour. How far will it go in 20 minutes?
ANSWER:
Given, a train is moving at 150 kilometre/hour.
We have to find How far it will go in 20 minutes.
150 kilometre = 60 minute
? = 20 minutes.
By cross multiplication,
150 x 20 / 60
= 50 kilometre.
50 kilometre it will go in 20 minutes.
6.) The scale of a map is 1:200000. What is the actual distance of 5 cm on the map?
ANSWER:
Given,
The scale of a map is 1:200000.
We have to find the actual distance of 5 cm on the map
5 cm on the map = 5 x 200000. = 1000000.
We know,
1m = 100 cm
1 km = 100000 cm
1000000 cm = 10 km.
The actual distance of 5 cm on the map is 10 km.
7.) Four pipes can fill a tank in 1 hour 20 minutes. How long will it take to fill the tank if 8 pipes are used?
ANSWER:
Four pipes can fill a tank in 1 hour 20 minutes.
We have to find long will it take to fill the tank if 8 pipes are used.
This example is of inverse proportion.
X1y1= x2y2
4 x 80 minutes = 8x?
y2 = 40 minutes.
40 minutes it take to fill the tank if 8 pipes are used.
8.) If 15 tailors can stitch a dress in 24 days, how long will 9 tailors take to stitch the same dress?
ANSWER:
Given,
15 tailors can stitch a dress in 24 days
We have to find how long 9 tailors will take to stitch the same dress.
This example is of inverse proportion.
X1y1= x2y2
15 x 24 = 9 x y2
Y2 = 15 x 24 / 9
Y2 = 40 days.
9 tailors will take 40 days to stitch the same dress.
9.) Bus is travelling at an average speed of 55 km/ hour. How much distance would it cover in 12 minutes?
ANSWER:
Bus is travelling at an average speed of 55 km/ hour
We have to find how much distance it would cover in 12 minutes.
This example is of direct proportion.
55 km = 60 minutes
? = 12 minutes.
By cross multiplication,
55 x 12 / 60
11 km.
Bus travel 11 km in 12 minutes.
10.) 20 women can whitewash a building in 26 days. In how many days can 52 women whitewash the same building?
ANSWER:
20 women can whitewash a building in 26 days.
We have to find how many days can 52 women whitewash the same building
This example is of inverse proportion.
X1y1= x2y2
20 x 26 = 52 x y2
y2 = 20 x 26 / 52
y2 = 10 days.
In 10 days 52 women whitewash the same building.
11.) 72 chocolates are packed in 8 boxes of same size. How many boxes are required for 360 chocolates?
ANSWER:
72 chocolates are packed in 8 boxes of same size.
We have to find how many boxes are required for 360 chocolates.
This example is of direct proportion.
72 chocolates = 8 boxes
360 chocolates =?
By cross multiplication,
360 x 8 / 72
= 40 boxes.
40 boxes are required for 360 chocolates.
12.) 6 men can construct a wall in 5 days. If 10 men are employed, find the number of days in which the similar wall can be constructed?
ANSWER:
6 men can construct a wall in 5 days
We have to find If 10 men are employed, find the number of days for similar wall can be constructed
This example is of inverse proportion.
X1y1= x2y2
6 x 5 = 10 x y2
y2 = 3
10 men are employed in 3 days similar wall can be constructed
13.) A carpenter prepares 36 tables in 8 days. In how many days would he prepare 27 such tables?
ANSWER:
A carpenter prepares 36 tables in 8 days.
We have to find in how many days would he prepare 27 such tables.
This example is of direct proportion.
36 tables = 8 days.
27 tables =?
By cross multiplication,
27 x 8 / 36
= 6
In 6 days would he prepare 27 such tables.
14.) If 560 notebooks cost Rs.3920, find the cost of 6 dozen notebooks.
ANSWER:
560 notebooks cost Rs.3920
We have to find cost of 6 dozen notebooks
We know,
1 dozen = 12 notebooks
6 dozen = 72 notebooks
This example is of direct proportion.
560 notebooks = Rs.3920
72 notebooks = ?
By cross multiplication,
Rs.3920 x 72 / 560
Rs.504
Cost of 6 dozen notebooks is Rs.504
15.) 10 women can do a job in 20 days. In how many days can 20 women do the same job?
ANSWER:
10 women can do a job in 20 days.
We have to find in how many days can 20 women do the same job.
This example is of inverse proportion.
X1y1= x2y2
10 x 20 = 20 x y2
y2 = 10 days
In 10 days can 20 women do the same job.
16.) What will happen to the area of a square if the length of each side is doubled?
ANSWER:
If the length of each side of a square is doubled then the area of a square becomes 4 times.
17.) A scooter travels 44 kilometer on 4 litres of petrol. How far will it go in 13 litres of petrol?
ANSWER:
A scooter travels 44 kilometer on 4 litres of petrol.
We have to find how far it will go in 13 litres of petrol.
This example is of direct proportion.
44 kilometer = 4 litres
? = 13 litres
By cross multiplication,
44 x 13 / 4
11 x 13
143 kilometres.
143 kilometres it will go in 13 litres of petrol.
18.) In a fort, there is food for 240 soldiers that is enough for 10 days. If 40 soldiers left the fort, then for how many days the food will last?
ANSWER:
In a fort, there is food for 240 soldiers that is enough for 10 days.
We have to find If 40 soldiers left the fort, then for how many days the food will last
This example is of inverse proportion.
X1y1= x2y2
240 x 10 = 200 x y2
y2 = 240 x 10 / 200
y2 = 12 days.
40 soldiers left the fort, then for 12 days the food will last.
19.) Nine bags of fertilizers weigh 639 kilograms. What is the weight of 4 bags?
ANSWER:
Nine bags of fertilizers weigh 639 kilograms
We have to find weight of 4 bags
This example is of direct proportion.
9 bags = 639 kilograms.
4 bags = ?
By cross multiplication,
4 x 639 / 9
284 kilograms.
The weight of 4 bags is 284 kilograms.
20.) Ravi takes 40 minutes to reach the school with a speed of 4 km/hr. If he walks with a speed of 5 km/hr., how much time will he now take to reach the school?
ANSWER:
. Ravi takes 40 minutes to reach the school with a speed of 4 km/hr.
4 km = 60 minutes
? = 40 minutes
By cross multiplication,
4 x 40 / 60
2.66 km.
Now,
5 km = 60 minutes
2.66 =? Minutes
By cross multiplication,
2.66 x 60 / 5
= 32 minutes
He walks with a speed of 5 km/hr, 32 minutes take to reach the school.
21.) If the cost of 20 m cloth is Rs.420, how much cloth can be bought for Rs.105?
ANSWER:
The cost of 20 m cloth is Rs.420
We have to find how much cloth can be bought for Rs.105.
This example is of direct proportion.
20 m cloth = Rs.420
? cloth = Rs.105.
By cross multiplication,
20 x 105 / 420
= 5m
5m cloth can be bought for Rs.105.
22.) Out of 45 students, 9 are absent. What is the ratio of present students to absent ones?
ANSWER:
Out of 45 students, 9 are absent.
We have to find ratio of present students to absent ones
Present student = 45 – 9
Present student = 36 students
Ratio of present students to absent = 36 / 9
Ratio of present students to absent = 4:1
23.) The weekly consumption of potatoes in a hostel with 640 students is 160 kilogram. Find the consumption if the number of students become 800.
ANSWER:
The weekly consumption of potatoes in a hostel with 640 students is 160 kilogram.
We have to find the consumption if the number of students become 800.
This example is of direct proportion.
640 students = 160 kilogram.
800 students = ?
By cross multiplication,
800 x 160 / 640 = 200 kilogram.
200 kilogram the consumption if the number of students become 800.
24.) If the cost of two dozen pens is Rs.60, what will be the cost of 60 pens?
ANSWER:
The cost of two dozen pens is Rs.60
We have to find the cost of 60 pens
1 dozen = 12 pens
2 dozen = 24 pens
This example is of direct proportion.
24 pens = Rs.60
60 pens = ?
By cross multiplication,
60 x 60 / 24
= Rs.150
The cost of 60 pens is Rs.150
25.) 6 taps can fill a water tank in 90 minutes. How many taps can fill the same water tank in 30 minutes?
ANSWER:
6 taps can fill a water tank in 90 minutes.
We have to find how many taps can fill the same water tank in 30 minutes
This example is of inverse proportion.
X1y1= x2y2
6 taps x 90 minutes.= x2 x 30 minutes
x2 = 6 taps x 90 minutes./ 30 minutes
x2 = 18 taps
18 taps can fill the same water tank in 30 minutes.
26.) If Aman reads 12 pages daily, he can complete a book in 15 days. How many days will it take to complete the book, if he reads 30 pages daily?
ANSWER:
Aman reads 12 pages daily, he can complete a book in 15 days.
We have to find how many days it will take to complete the book, if he reads 30 pages daily
This example is of inverse proportion.
X1y1= x2y2
12 pages x 15 days. = 30 pages x y2
y2 = 12 pages x 15 days. / 30 pages
y2 = 6 days.
6 days will it take to complete the book, if he reads 30 pages daily.
27.) A stock of food grains is enough for 600 students for 10 weeks. How long will the same stock last for 240 students?
ANSWER:
A stock of food grains is enough for 600 students for 10 weeks.
We have to find how long the same stock last will for 240 students.
This example is of inverse proportion.
X1y1= x2y2
600 students x 10 weeks. = 240 students x y2
y2 = 600 students x 10 weeks. / 240 students
y2 = 25 weeks
25 weeks the same stock last will for 240 students.
28.) If the length of a rectangle is halved, what change should be made in its breadth so that its area remains the same?
ANSWER:
We know,
Area of rectangle = Length x Breadth
Length x Breadth= Length / 2 x ?
Breadth= 2 times
29.) 12 workers can construct a room in 7 hours. How many workers will be needed in all for constructing the same sized room in 2 hours?
ANSWER:
12 workers can construct a room in 7 hours.
We have to find how many workers will be needed in all for constructing the same sized room in 2 hours.
This example is of inverse proportion.
X1y1= x2y2
12 x 7 = 2 x y2
Y2= 12 x 7 / 2
Y2= 42 workers
42 workers will be needed in all for constructing the same sized room in 2 hours.
30.) Aman and Abhinav can complete a project in 24 days. Aman alone can do the same task in 36 days. How much time will Abhinav take alone to complete the same project?
ANSWER:
Aman and Abhinav can complete a project in 24 days. Aman alone can do the same task in 36 days
We have to find how much time Abhinav will take alone to complete the same project.
Aman + Abhinav = 24 days.
Aman = 36 days
Abhinav =?
We take LCM of 24 and 36 is 72.
Aman + Abhinav = 72 / 24 = 3
Aman = 72/36 = 2
Aman + Abhinav = 3
But Aman= 2
Abhinav = 3 – 2 = 1
Abhinav will take alone to complete the same project = 72/1 = 72 days.
31.) In a library, 189 copies of a certain book require a shelf length of 3.78 meter. How many copies of the same book would occupy shelf length of 0.42 meter?
ANSWER:
189 copies of a certain book require a shelf length of 3.78 meter.
We have to find how many copies of the same book would occupy shelf length of 0.42 meter
This example is of direct proportion.
189 copies = 3.78 meter.
? = 0.42 meter
By cross multiplication,
189 x 0.42 / 3.78
21 copies.
21 copies of the same book would occupy shelf length of 0.42 meter.
32.) Mohan is paid Rs.2720 on working for eight days. If his total wages during a month is Rs.6800, for how many days did he work?
ANSWER:
Mohan is paid Rs.2720 on working for eight days
His total wages during a month is Rs.6800
We have to findhow many days did he work.
This example is of direct proportion.
Rs.2720 = 8 days
Rs.6800= ?
By cross multiplication,
6800 x 8 / 2720
= 20 days.
Mohan work for 20 days.
33.) A train running at the speed of 108 kilometer/ hr. passes a signal post in 10 seconds. Find the length of the train in meters.
ANSWER:
A train running at the speed of 108 kilometer/ hr.
Passes a signal post in 10 seconds.
We have to find length of the train in meters
We know,
Length of the train in meters = 5/18 x 108 x 10
Length of the train in meters = 5 x 6 x 10
Length of the train in meters = 300 meter.
34.) If 30 stamps occupy an area of 75 cm2, how much area of paper is required for putting 330 stamps assuming that no area is wasted in between two stamps?
ANSWER:
30 stamps occupy an area of 75 cm2
We have to findarea of paper is required for putting 330 stamps
This example is of direct proportion.
30 stamps = 75 cm2
330 stamps = ?
By cross multiplication,
330 x 75 / 30
= 11 x 75
= 825 cm2
825 cm2is required for putting 330 stamps.
35.) Geet, Meet and Reet can do a work in 15, 6 and 10 days respectively. All the three together canfinish four times of that work in how many days?
ANSWER:
Geet, Meet and Reet can do a work in 15, 6 and 10 days respectively.
We have to find all the three together can finish four times of that work in how many days.
We take LCM of 15, 6 and 10 days respectively. Which is 30.
Geet, Meet and Reet can do a work in 1 day is 2, 5 and 3.
All the three together = (2 + 5 + 3) = 10
Four times of work = 30 x 4 = 120 work.
No. of days = 120 work / 10
No. of days = 12
36.) If2x=3y=4z, then find x: y: z
ANSWER:
2x=3y=4z
We take LCM of 2, 3 and 4.
LCM of 2, 3 and 4 is 12.
x: y: z = 6: 4 : 3
37.) If 75 goats can graze a field in 13 days, how many goats will graze the same field in 25 days?
ANSWER:
75 goats can graze a field in 13 days
We have to findhow many goats will graze the same field in 25 days.
This example is of inverse proportion.
X1y1= x2y2
75 x 13 = x2 x 25
x2 = 75 x 13 / 25
x2 = 39 goats.
39 goats will graze the same field in 25 days.
38.) Kavita can type a given assignment in 1 hour 30 minutes at a speed of 50 words per minute. Her friend Kareem can type the same assignment in 60 minutes. What would be Kareem’s typing speed?
ANSWER:
Kavita can type a given assignment in 1 hour 30 minutes at a speed of 50 words per minute.
Her friend Kareem can type the same assignment in 60 minutes.
We have to findKareem’s typing speed.
This example is of inverse proportion.
X1y1= x2y2
1 hour 30 minutes x 50 words per minute = 60 minutes. X y2
y2 = 90 x 50 / 60
y2 = 75 words per minute.
Kareem’s typing speed is 75 words per minute.
39.) If 40 square metres of a carpet cost Rs.241.60, find the cost of 50 square metres of carpet.
ANSWER:
40 square metres of a carpet cost Rs.241.60
We have to findcost of 50 square metres of carpet
This example is of direct proportion.
40 square metres = Rs.241.60
50 square metres = ?
By cross multiplication,
Rs.241.60 x 50 / 40
Rs.302
The cost of 50 square metres of carpet is Rs.302
40.) Reena, Meena and Teena can complete a job in 10, 12 and 15 days respectively. In how many days will they complete the work together?
ANSWER:
. Reena, Meena and Teena can complete a job in 10, 12 and 15 days respectively
We take LCM of 10, 12 and 15 days
LCM of 10, 12 and 15 days is 60.
Reena, Meena and Teena 1 day work are 60/10, 60/12 and 60/15.
Reena, Meena and Teena 1 day work are 6, 5 and 4.
All work together = ( 6 + 5 + 4) = 15
No. of days = LCM / All work together
No. of days = 60 / 15
No. of days = 4
Reena, Meena and Teena all together complete the work in 4 days.
41.) A journey by car takes 45 minutes at 40 kilometer/ hour. How fast must a car go to undertake the same journey in 25 minutes?
ANSWER:
A journey by car takes 45 minutes at 40 kilometer/ hour.
We have to find how fast a car must go to undertake the same journey in 25 minutes.
This example is of inverse proportion.
X1y1= x2y2
45 minutes x 40 kilometer/ hour. = 25 minutes x y2.
y2 = 45 minutes x 40 kilometer/ hour. / 25 minutes
y2 = 72 kilometer/ hour
72 kilometer/ hourcar must go to undertake the same journey in 25 minutes.
42.) If 30 women can repair a road in 48 days, how long will 18 women take to repair the same road?
ANSWER:
30 women can repair a road in 48 days
We have to findhow long 18 women will take to repair the same road.
This example is of inverse proportion.
X1y1= x2y2
30 women x 48 days = 18 women x y2
y2 = 30 x 48 / 18
y2 = 80 days
In 80 days, 18 women will take to repair the same road
43.) Rekha can drive to Gwalior in eight hours at 60 kilometer per hour. How long will Ravi take to drive to Gwalior if his speed is 40 kilometer per hour?
ANSWER:
Rekha can drive to Gwalior in eight hours at 60 kilometer per hour.
We have to findRavi take to drive to Gwalior if his speed is 40 kilometer per hour
This example is of inverse proportion.
X1y1= x2 y2
60 kilometer per hour x 8 hour = 40 kilometer per hour x y2
y2 = 60 kilometer per hour x 8 hour / 40 kilometer per hour
y2 = 12 hours
Ravi take to drive to Gwalior if his speed is 40 kilometer per hour in 12 hours.
44.) The speed of a train 125 m long is 45 kilometer/hr. How much time will it take to pass a platform 1375m long?
ANSWER:
The speed of a train 125 m long is 45 kilometer/hr.
We have to findhow much time it will take to pass a platform 1375m long
We know,
5/18 x speed x time = Length of train + Length of platform
5/18 x 45 x time = 125 + 1375
5 x 5 / 2 x time = 1500
Time = 3000 / 25
Time = 120 seconds
45.) 6 monkeys take 6 minutes to eat 6 bananas. How many minutes would 10 monkeys will take to eat 10 bananas if their speed of eating is equal?
ANSWER:
6 monkeys take 6 minutes to eat 6 bananas.
We have to find how many minutes would 10 monkeys will take to eat 10 bananas if their speed of eating is equal
This example is of inverse proportion.
X1y1= x2 y2
6 monkeys x 6 minutes / 6 bananas. = 10 monkeys x y2 /10 bananas
Y2 = 36 / 6 = 1
Y2 = 6 minute.
6minutes would 10 monkeys will take to eat 10 bananas.
46.) How long will an athlete take to run around a rectangular park measuring50m x 40m,if she runs at a speed of 3 m/sec?
ANSWER:
Rectangular park measuring 50 m x 40 m. She runs at a speed of 3 m/sec
We have to find how long an athlete will take to run around a rectangular park.
Perimeter of rectangle = 2 x (50m + 40m)
Perimeter of rectangle = 180 m.
Time taken = Perimeter of rectangle / speed of 3 m/sec
Time taken = 180 / 3
Time taken = 60 second.
47.) Two bus drivers start from same place in opposite directions. One goes towards north at 36 kilometer/ hour and other goes towards south at a speed of 40 kilometer/ hour. What time did they to be 190 kilometer apart?
ANSWER:
Two bus drivers start from same place in opposite directions.
One goes towards north at 36 kilometer/ hour and other goes towards south at a speed of 40 kilometer/ hour.
When bus are in opposite directions we add their speeds.
36 kilometer/ hour + 40 kilometer/ hour. = 76 kilometer/ hour.
Time did they to be 190 kilometer apart = 190 kilometer / 76 kilometer/ hour
Time did they to be 190 kilometer apart = 2 hours 30 minute.
48.) Satyam has enough money to buy 60 oranges at Rs.5 per orange. How many oranges can he buy if the price is increased by rupees 1 per orange?
ANSWER:
. Satyam has enough money to buy 60 oranges at Rs.5 per orange.
Price of 60 oranges =60 oranges x Rs.5 per orange = Rs. 300
Now the price is increased by rupees 1 per orange.
New price = Rs. 5 + 1 = 6
New number of oranges = Rs. 300 / 6
New number of oranges = 50
- )The cost of 32 packets of Vim each weighing 900 gram is Rs.56. What will be the cost of 27 packets if each packet weighs 1 kilogram?
ANSWER:
The cost of 32 packets of Vim each weighing 900 gram is Rs.56.
This example is of direct proportion.
32 x 900 = Rs.56.
27 x 1000 =?
By cross multiplication,
27 x 1000 x 56 / 32 x 900
Rs. 52.50
The cost of 27 packets if each packet weighs 1 kilogram is Rs. 52.50
50.) Abha cycles to her school at an average speed of 15 kilometer per hour. It takes 20 minutes to reach the school in time. At what speed should she cycle if she has to reach 5 minutes earlier?
ANSWER:
Abha cycles to her school at an average speed of 15 kilometer per hour. It takes 20 minutes to reach the school in time.
We have to find at what speed she should cycle if she has to reach 5 minutes earlier.
15 kilometer = 60 minute
? = 20 minutes
By cross multiplication,
15 x 20 / 60
= 5 km
Abhaschool is 5 km.
Now,
We know,
Speed = (distance / Time)
Speed = 5 km / (1/4)
Speed =20 kilometer per hour.