Class 8 Maths - Direct and Inverse Proportions CBSE Worksheets Solutions

Q1: The cost of 7m of a particular quality of pipe is ₹200 tabulate the cost of 4 meter of pipe of the same type.
(a) 114.28
(b) 28.114
(c) 11.42
(d) 1.428
Ans: (a)

Q2: A train is moving at a uniform speed of 60 km/hr. How far will it travel in 30 minutes?
(a) 20
(b) 25
(c) 30
(d) 40
Ans: (c)
Sol:
Speed = 60 km/h = 60 km in 60 minutes.
Distance in 30 minutes = 60 × (30 ÷ 60) = 60 × 0.5 = 30 km.

Q3: The scale of map is given as 1:40000000 two cities are 3cm apart on the map. Find the actual distance between them?
(a) 1400
(b) 1300
(c) 1200
(d) 1100
Ans: (c)
Sol:
Scale 1 : 40,000,000 means 1 cm on map = 40,000,000 cm in reality.
Convert to km: 1 km = 100,000 cm, so 40,000,000 cm = 40,000,000 ÷ 100,000 = 400 km.
Therefore 3 cm → 3 × 400 = 1200 km.

Q4: A train is moving at uniform speed of 60km/hr. Find the time required to cover a distance 200 km?
(a) 200 min
(b) 300 min
(c) 60 min
(d) 250 min
Ans: (a)
Sol:
Time = Distance ÷ Speed = 200 ÷ 60 = 10/3 hours = 3 1/3 hours.
Convert hours to minutes: 3 1/3 hours = 3 hours 20 minutes = 3×60 + 20 = 200 minutes.

Q5: A machine in Cocacola factory fills 640 bottles in 4 hours. How many bottles will it fill in 5 hours?
(a) 700
(b) 1000
(c) 900
(d) 800
Ans: (d)
Sol:
Rate = 640 bottles ÷ 4 hours = 160 bottles per hour.
In 5 hours → 160 × 5 = 800 bottles.

Q6: 5 pipes are required to fill a tank in 1 hour 20 minute. How long will it take if only 4 pipes of the same type are used?
(a) 200 min
(b) 100 min
(c) 60 min
(d) 40 min
Ans: (b)
Sol:
5 pipes → 1 h 20 min = 80 minutes.
Let time with 4 pipes = x minutes. For the same work, Number of pipes × Time is constant (inverse proportion).
5 × 80 = 4 × x → x = (5 × 80) ÷ 4 = 400 ÷ 4 = 100 minutes.

Q7: If 10 workers can build a wall in 40 hours how many workers will be required to do the same work in 20 hours?
(a) 10
(b) 30
(c) 20
(d) 40
Ans: (c)
Sol:
Work = constant. Workers × Time = constant.
10 × 40 = y × 20 → y = (10 × 40) ÷ 20 = 400 ÷ 20 = 20 workers.

Q8: Observe the following tables and find which pair of variables are in inverse proportion.
(a)

Q9: There are 50 students in hostel. Food provision for them is for 20 days. How long will these provision last 50 more students join the group?
(a) 15
(b) 20
(c) 30
(d) 10
Ans: (d)
Sol:
Initial: 50 students for 20 days → total student‐days = 50 × 20 = 1000 student‐days.
Now students = 50 + 50 = 100.
Days = 1000 ÷ 100 = 10 days.

Q10: A batch of mango were packed in 25 boxes with 20 mangoes in each box if the same batch is packed using 25 mangoes in each box, how many boxes would be filed?
(a) 10
(b) 30
(c) 40
(d) 20
Ans: (d)
Sol:
Total mangoes = 25 boxes × 20 mangoes = 500 mangoes.
With 25 mangoes per box → boxes = 500 ÷ 25 = 20 boxes.

Q11: A farmer has enough food to feed 30 animals in his cattle for 6 days. How long would the food last if there were 12 animals in his cattle?
(a) 14
(b) 12
(c) 15
(d) 13
Ans: (c)
Sol:
Total animal‐days = 30 × 6 = 180 animal‐days.
With 12 animals → days = 180 ÷ 12 = 15 days.

Q12: Motorcycles takes 2 hour to reach a destination by travelling at the speed of 40km/hr. How long will it take when the motor travels at the speed of 80 km/hr?
(a) 1hr
(b) 2hr
(c) 1.30hr
(d) 2.30hr
Ans: (a)
Sol:
Distance = Speed × Time = 40 km/h × 2 h = 80 km.
At 80 km/h, Time = Distance ÷ Speed = 80 ÷ 80 = 1 hour.

Q13: A loaded train travels 28km in 30 minutes. If the speed remains the same, how far can it travel in 5 hours?
(a) 100
(b) 210
(c) 240
(d) 280
Ans: (d)
Sol:
30 minutes = 0.5 hour.
Speed = 28 ÷ 0.5 = 56 km/h.
Distance in 5 hours = 56 × 5 = 280 km.

Q14: The cost of 10 meters of particular quality of cloth ₹200 tabulate the cost of 8 meters of cloth the same type.
(a) 120
(b) 140
(c) 160
(d) 180
Ans: (c)

Q15: An electric pole 18 meters high castle shadow of 10 meters. Find the height of electric pole that cost a shadow of 20 meters under similar condition?
(a) 32
(b) 36
(c) 34
(d) 40
Ans: (b)
Sol:
Height ∝ Shadow length (similar triangles): 18 ÷ 10 = x ÷ 20.
x = 18 × 20 ÷ 10 = 18 × 2 = 36 m.