Direct and Inverse Proportions Class 8 Worksheet 1 with Answers
1. A and B together finishes a work in 20 days.
They work at it for 10 days, then A left. If the remaining work was done by B
alone in 15 days, in how many days can B alone finish the whole work?
2.
A cistern can be filled by a tap in 18 minutes
and emptied by an outlet in 24 minutes. How long will it take to fill the
cistern, if both the tap and outlet are opened together?
3.
If 10 men bind 600 books in 8 days, then in
how many days will 16 men bind 440 books?
4. If 15 men working together can finish a work
in 84 days, then in how many days will 12 men finish the same work?
5.
The ratio of men to women in the party was 4 :
1. If there were 20 women, then find the number of people at the party.
6.
A can do a piece of work in 15 days and B can
do it in 10 days. Together they work for 5 days and B left. How long will A
alone finish the remaining work?
7. The cost of transporting 1500 kg wheat for 120
km is ₹ 800. What will be the cost of transporting 1200 kg of wheat for 80 km?
8.
5 bags of rice weigh 250 kg. What is the
weight of 14 such bags?
9. A mess in a hostel has enough food for 100
students for 30 days. How long will the food last if 50 more students join
them?
10. Mayank takes 6 hours to type 30 pages while Nisha
takes 4 hours to type 42 pages. How much time will they take together to type
124 pages?
11.
Two taps A and B can fill a cistern in 12
minutes and 15 minutes respectively. Both the taps are opened together but
after 5 minutes tap A is closed. Find the total time required to fill the
cistern.
12.
₹ x is divided among Raju, Ritu and Joya in the ratio 2 : 3 : 4
respectively. If Joya gets ₹ 20 more than Raju, then find the share of each of
them.
13.
A train crosses a tunnel which is 120 m long
in 18 seconds and a man sitting at the platform in 8 seconds. At what speed the
train is running?
14.
A car runs at a speed of 48 km/h and covers a
certain distance in 2 h 40 min. Find the speed at which the train must travel
to reduce the time of the journey to 2 hours.
15.
How long will a train 160 m long take to cross
a pole if it is running at a speed of 60 km/h?
16.
A train running at a speed of 54 km/h crosses
a bridge which is 260 m long in 30 seconds. Find the length of the train.
Direct and Inverse Proportions Class 8 Worksheet 2 with Answers
1. Manisha has enough money to send 14 parcels
each weighing 500 grams. Find the weight of each parcel, if she can send 20
parcels for the same money.
2. Nitesh completes cleaning of the house in 6
hours. What part of the house will he clean in 4 hours?
3. A school librarian has enough money to order 10 paperback books at ₹ 7.50 per paperback book. If he decides to order hard core
books at ₹ 15 per book instead of paperback books, how many books can he buy?
4. 12 persons can dig 324 cubic metres
earth in a day. How many persons will be required to dig 270 cubic metres
earth?
5. On a birthday party, an average of 5 bottles
of cold drinks are served among a group of 6 children. How many friends were
present at Nilu’s birthday party if 15 bottles of cold drinks were used in the
party.
6.
An aeroplane flies 4535 km in 5 hours 30
minutes. How long will it take to fly a distance of 2310 km?
7.
If the sum of ₹ 11205 is divided in the ratio
4 : 5 among Raj and Priya, then what is the share of each of them?
8.
The ratio of three sides of a triangle is 2 :
3 : 5. If the perimeter of the triangle is 40 cm, then find the measure of the
smallest side.
9. A and B can do a piece of work in 10 days, B
and C can do it in 15 days and C and A can do it in 12 days.
a. In how many
days will A, B and C finish it working together?
b. In how many
days will each of them take to finish it working alone?
10. Rohan had enough money to buy 15 notebooks
each containing 280 pages. How many pages will each notebook contain, if he
buys 10 notebooks with the same money?
11.
The ratio of three numbers is 5 : 3 : 1. If
their product is 7680, then find the numbers.
12. The ages of Pramod, Anuj and Pallavi are in the ratio 7 : 5 : 3. If the age of Anuj is 15 years, then find the ages of Pramod and Pallavi.
13.
Due to festive season, the price of a washing
machine is decreased in the ratio 9 : 7. If the original price was ₹ 11304,
then find the new price.
14.
Ria bought bananas, oranges and apples. The
ratio of bananas to oranges was 3 : 1 and the ratio of oranges to apples was 2
: 5. If she bought 18 bananas, how many apples and oranges did she buy?
15.
The price of a TV and a microwave are in the
ratio of 5 : 3. If the difference of their cost is ₹ 6,000, then find the
price of a TV and a microwave.
16. A car travels 80 km in 4 hours. Find the
distance covered by the car in 5 hours.
Direct and Inverse Proportions Class 8 Worksheet 3 with Answers
1. A farmer has enough food to feed 20 animals at
his farm for 6 days. How long will the food last, if there were 10 more animals
at his farm?
2. A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time
a. the length of the shadow cast by
another pole 10 m 50 cm high.
b. the height of
the pole which casts a shadow 5 m long.
3.
Two trains 50 m and 110 m long are running at
a speed of 36 km/h and 54 km/h respectively in opposite directions approaching
the same railway station. How long would it take them to pass each other?
4.
Hemant travelled the first 2 hours of his
journey at 40 km/h and the remaining 3 hours of his journey at 80 km/h. What is
his average speed for the entire journey?
5.
The speed of a boat in still water is 10 km/h.
It can travel 20 km downstream and in the same time it can travel 12 km
upstream. What is the speed of the water current?
6.
Heena travelled 36 km at a speed of 8 km/h and
Dilip travelled 48 km at a speed of 10 km/h. Whose journey was quickest?
7.
A car covers a distance of 60 km at a speed of
80 km/h and another car covers a distance of 125 km at a speed of 75 km/h. Find
the average speed of the car for the whole journey.
8. A boat running downstream covers a distance of
16 km in 2 hours while for covering the same distance upstream it takes 4
hours. What is the speed of the boat in still water?
9.
Aman walks at a speed of 3 km/h to catch the
school bus and he missed the bus by 6 minutes. If he walks at a speed of 5 km/h,
he reaches the bus stop 10 minutes before. Find the distance between his house
and the bus stop.
10. A train left a station towards its destination at a speed of 60 km/h. After a few hours, another train left the same station travelling in the opposite direction of the first train at the speed of 80 km/h. After the first train had travelled for 20 hours, it was 2000 km apart from the second train. After how many hours of the first train, the second train started travelling?
11.
A train starts from A at 6:00 a.m. and travels towards B at a speed of 50 km/h. Another train starts from A at 8:00 a.m. and
travels towards B at a speed of 70 km/h. At what time will it catch the slower
train?
12.
The speed of a boat in still water is 4.5 km/h
and the speed of the stream is 3 km/h. The boat is rowed upstream for a certain
distance and then rowed back to the starting point. Find the average speed of
the boat for the whole journey.
13. If the cost of 8 kg of tomatoes is ₹ 88, find
a. the weight of
tomatoes bought for ₹ 60.50.
b. the cost of 17
kg of tomatoes.
14. A school has 8 periods a day each of 45
minutes duration. How long would each period be, if the school has 9 periods a
day, assuming the number of school hours is same?
15.
How much time will a train 178 m long running
at a speed of 36 km/h, take to pass 162 m long tunnel?
16. Find the least number which must be subtracted
from each of the numbers 3, 1, 5 and 4 so that the new numbers may be proportional.
ANSWERS
Worksheet
1
1. 30
days 2. 72 minutes
3. 32/3
days 4. 105 days
5. 100
people 6. 21/2
days
7. ₹
426.67 8. 700 kg
9. 20
days 10. 8 hours
11. 83/4
days
12. ₹ 20,
₹ 30, ₹ 40
13. 43.2
km/h
14. 64
km/h
15. 9.6
sec
16. 190 m
Worksheet
2
1. 350
grams 2. 2/3
3. 5 books 4. 10 persons
5. 18
friends 6. 2.8 hours
7. ₹ 4980,
₹ 6225
8. 8
cm
9. a. 8
days
b. 171/7 days, 24
days, 40 days
10. 420
pages
11. 40,
24, 8
12. 21
years; 9 years
13. ₹ 8792
14. 15
apples, 6 oranges
15. ₹
15,000; ₹ 9000
16. 100 km
Worksheet
3
1. 4
days
2. a. 6
m b. 8 m 75 cm
3. 6.4
sec 4. 64 km/h
5. 2.5
km/h 6. Heena
7. 76.55
km/h
8. 6
km/h 9. 2 km
10. 10 hours 11. 1 p.m.
12. 2.5
km/h
13. a. 5.5
kg b. ₹ 187
14. 40
minutes
15. 34
seconds
16. 7
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