Solved Questions on Direct and Indirect Proportions
1. A lamborghini car consumes 5.6 litres of petrol to travel a distance of 786 kilometres. How much distance will it cover in 8.4 litres of petrol?
a) 979 km
b) 1079 km
c) 1179 km
d) 1279 km
Answer: c) 1179 km
Explanation: According to the question,
|
Consumption of Petrol
|
5.6 Litres (x1)
|
8.4 Litres (x2)
|
|
Distance Covered
|
786 Kilometres (y1)
|
y2
|
If the consumption of petrol increases, then distance covered increases. Hence, a direct proportion relationship is established.
Using direct proportion formula,
A distance of 1179 km will be covered in 8.4 litres of petrol.
2. All the pipes used are of the same size. 17 pipes fill a cistern in 2 hours 22 minutes. How long will it take to fill the same cistern if 71 pipes are used?
a) 30 minutes
b) 34 minutes
c) 38 minutes
d) 42 minutes
Answer: b) 34 minutes
Explanation: A cistern means a tank for storing water.
According to the question,
|
Number of Pipes
|
17 pipes (x1)
|
71 pipes (x2)
|
|
Time to fill a Cistern
|
2 hours 22 minutes
= 142 minutes (y1)
|
y2
|
If number of pipes increases, then time to fill a cistern decreases. Hence, an inverse proportion relationship is established.
Using inverse proportion formula,
x1 × y1 = x2 × y2
⇒ 17 × 142 = 71 × y2
⇒ y2 = (17 × 142)/71
∴ y2 = 34
71 pipes can fill the same cistern in 34 minutes.
3. Bosch takes 27 minutes to reach from town A to B if he goes by bus on a highway at a speed of 173.5 kilometres per hour. What should be his speed on a bicycle if he wants to cover the same distance in 5 hours and 47 minutes?
a) 7.5 km/h
b) 9.5 km/h
c) 11.5 km/h
d) 13.5 km/h
Answer: d) 13.5 km/h
Explanation: Time in minutes to reach from town A to B by bicycle
= 5 hours 47 minutes
= 5 hours + 47 minutes
= (5 × 60) minutes + 47 minutes
= 300 minutes + 47 minutes
= 347 minutes
Using unitary method,
To reach from town A to B in 27 minutes, speed = 173.5 km/h
If time to travel decreases, then speed increases. Thus, multiplication is performed.
To reach from town A to B in 1 minute, speed = (27 × 173.5) km/h
If time to travel increases, then speed decreases. Thus, division is performed.
To reach from town A to B in 347 minutes, speed = (27 × 173.5)/347
= 27/2
= 13.5 km/h
4. A contractor makes a contract to build an underground canal in the months of September and November and employs 75 labourers to work for 8 hours daily. After 35 days, he found that two-thirds of the total work was complete and a smaller amount was left. So, he decided to decrease some labour. How many labourers should be decreased by him to complete the remaining work in time if they work for 10 hours daily?
a) 31 labours
b) 33 labours
c) 35 labours
d) 37 labours
Answer: b) 33 labours
Explanation: The months of September and November have 30 days each.
According to the question,
|
M1
|
75 labours
|
M2
|
x labours
|
|
D1
|
35 days
|
D2
|
2 months − 35 days
= (60 − 35) days
= 25 days
|
|
T1
|
8 hours
|
T2
|
10 hours
|
|
W1
|
2⁄3
|
W2
|
1 − 2⁄3 = 1⁄3
(Total work is taken as whole i.e. 1)
|
Using time and work relationships,
42 labourers can complete the remaining work in time.
Number of labourers should be decreased by him to complete the remaining work
= 75 − 42 = 33 labours
5. If 33 stallions consume 28 quintals of barley in 30 days, how long will one-fifth of barley last for 12 stallions?
a) 6 ½ days
b) 16 ½ days
c) 26 ½ days
d) 36 ½ days
Answer: b) 16 ½ days
Explanation: According to the question,
|
Number of stallions or horses
|
M1
|
33 stallions
|
M2
|
12 stallions
|
|
Time in days
|
T1
|
30 days
|
T2
|
x days
|
|
Quantity of barley
in quintal
|
W1
|
28 quintal
|
W2
|
1⁄5 × 28 = 5.6 quintal
|
Using time and work relationships,
