Section A: Multiple Choice Questions (MCQs) (1 × 20 = 20 marks)
- If the cost of 8 kg of rice is ₹320, what is the cost of 5 kg of rice?
a) ₹180
b) ₹200
c) ₹220
d) ₹240 - Which of the following shows inverse proportion?
a) Cost and quantity
b) Speed and time for fixed distance
c) Distance and time
d) Wages and days - If 12 workers take 10 days to complete a work, how many days will 6 workers take?
a) 5
b) 10
c) 20
d) 30 - If x ∝ y, then which is constant?
a) x + y
b) x − y
c) x ÷ y
d) x × y - A car travels 240 km using 16 litres of petrol. How far will it travel using 10 litres?
a) 120 km
b) 140 km
c) 150 km
d) 160 km - If 4 pipes fill a tank in 12 hours, how long will 8 pipes take?
a) 24 hours
b) 12 hours
c) 6 hours
d) 4 hours - If 15 notebooks cost ₹225, find the cost of 4 notebooks.
a) ₹50
b) ₹55
c) ₹60
d) ₹65 - When the number of workers increases, the time taken to do the same work will:
a) Increase
b) Decrease
c) Remain same
d) Become zero - If 6 kg of apples cost ₹360, what is the cost of 9 kg?
a) ₹480
b) ₹510
c) ₹540
d) ₹600 - If x × y = constant, then x and y are in:
a) Direct proportion
b) Inverse proportion
c) No proportion
d) Equal proportion - A train covers 90 km in 2 hours. How much distance will it cover in 5 hours?
a) 180 km
b) 200 km
c) 225 km
d) 250 km - If 10 men can complete a job in 18 days, how many men are needed to finish it in 9 days?
a) 5
b) 10
c) 15
d) 20 - If 7 books weigh 2.1 kg, what is the weight of 10 such books?
a) 2.5 kg
b) 3 kg
c) 3.2 kg
d) 3.5 kg - Speed and time for the same distance are related by:
a) Direct proportion
b) Inverse proportion
c) Constant ratio
d) No relation - If the scale of a map is 1 : 50,000, what distance does 4 cm represent?
a) 2 km
b) 4 km
c) 8 km
d) 10 km - A worker earns ₹750 in 15 days. How much will he earn in 20 days?
a) ₹900
b) ₹950
c) ₹1,000
d) ₹1,050 - If 24 taps fill a tank in 5 hours, how many taps are required to fill it in 10 hours?
a) 6
b) 10
c) 12
d) 48 - If the cost of 12 pens is ₹180, what is the cost of 20 pens?
a) ₹250
b) ₹270
c) ₹300
d) ₹320 - Which quantity remains constant in inverse proportion?
a) Ratio
b) Difference
c) Sum
d) Product - A car travels 150 km in 3 hours. What is its speed?
a) 40 km/h
b) 45 km/h
c) 50 km/h
d) 60 km/h
Section B: Short Answer Numericals (2 × 10 = 20 marks)
- If 9 kg of wheat costs ₹270, find the cost of 14 kg.
- A train covers 360 km in 6 hours. How long will it take to cover 540 km at the same speed?
- If 15 workers complete a work in 16 days, how many days will 20 workers take?
- The cost of 18 chairs is ₹7,200. Find the cost of 25 chairs.
- 8 pumps can empty a tank in 12 hours. How long will 6 pumps take?
- If 5 litres of petrol allows a car to travel 80 km, how far will it travel using 9 litres?
- The scale of a map is 1 : 20,000. Find the actual distance represented by 7 cm.
- A worker is paid ₹960 for 12 days. How much will he earn for 20 days?
- If 16 machines manufacture 4,800 bolts in a day, how many bolts will 10 machines manufacture?
- If 30 students can finish food in 18 days, how long will the food last for 45 students?
Section C: Long Answer Numericals (4 × 5 = 20 marks)
- A bus travels at a speed of 60 km/h and takes 7 hours to reach its destination.
(a) Find the distance covered.
(b) How long will it take to cover the same distance at 75 km/h? - 24 workers can complete a work in 15 days.
(a) How many workers are needed to complete the work in 10 days?
(b) How many days will 30 workers take to complete the same work? - In a hostel, food is sufficient for 200 students for 25 days. After 5 days, 50 students leave the hostel.
For how many more days will the remaining food last? - The extension of a spring varies directly with the load applied.
If a load of 3 kg produces an extension of 5 cm, find:
(a) Extension produced by 7.5 kg
(b) Load required to produce an extension of 12 cm
Section D: Case-Based (5 × 4 = 20 marks)
- A factory produces goods using machines.
| Machines | 8 | 12 | 20 |
|---|---|---|---|
| Days | 15 | ? | 6 |
Answer the following:
(a) Identify the type of proportion
(b) Find the missing number of days
(c) Write the formula used
(d) What happens to time if machines increase further?
- A car covers a fixed distance.
| Speed (km/h) | 50 | 75 | ? |
|---|---|---|---|
| Time (h) | 6 | 4 | 3 |
Answer Key
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