Proportional Reasoning 2 — Class 8 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Proportional Reasoning 2" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Proportional Reasoning 2" — 8 important questions with detailed answers for CBSE bo…
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NCERT Solutions for Class 8 Mathematics — Proportional Reasoning 2. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Proportional Reasoning 2 — All 8 Questions Solved
Q1. If 25% of a number is 50, find the number.
Step 1: Let the number be x
Step 2: 25% of x = 50
Step 3: (25/100) × x = 50
Step 4: 0.25x = 50
Step 5: x = 50 ÷ 0.25 = 200
Step 6: The number is 200
Q2. A shopkeeper bought goods for Rs 400 and sold them for Rs 500. Find the profit percentage.
Step 1: Cost price (CP) = Rs 400
Step 2: Selling price (SP) = Rs 500
Step 3: Profit = SP − CP = 500 − 400 = Rs 100
Step 4: Profit % = (Profit/CP) × 100 = (100/400) × 100
Step 5: Profit % = (1/4) × 100 = 25%
Q3. A discount of 20% is given on an article marked at Rs 300. What is the selling price?
Step 1: Marked price (MP) = Rs 300
Step 2: Discount = 20% of 300 = (20/100) × 300 = Rs 60
Step 3: Selling price (SP) = MP − Discount
Step 4: SP = 300 − 60 = Rs 240
Q4. What is 15% of 200?
Step 1: To find 15% of 200
Step 2: 15% = 15/100
Step 3: 15% of 200 = (15/100) × 200
Step 4: = 15 × 2 = 30
Q5. Calculate simple interest on Rs 1000 at 8% per annum for 2 years.
Step 1: Principal (P) = Rs 1000
Step 2: Rate (R) = 8% per annum
Step 3: Time (T) = 2 years
Step 4: Simple Interest (SI) = (P × R × T)/100
Step 5: SI = (1000 × 8 × 2)/100 = 16000/100 = Rs 160
Q6. An article was sold at a loss of 10%. If the cost price was Rs 500, find the selling price.
Step 1: Cost price (CP) = Rs 500
Step 2: Loss = 10% of 500 = (10/100) × 500 = Rs 50
Step 3: Selling price (SP) = CP − Loss
Step 4: SP = 500 − 50 = Rs 450
Q7. If 40 is 50% of a number, find the number.
Step 1: Let the number be x
Step 2: 50% of x = 40
Step 3: (50/100) × x = 40
Step 4: 0.5x = 40
Step 5: x = 40 ÷ 0.5 = 80
Step 6: The number is 80
Q8. A shop gives a discount of 25% on articles marked at Rs 800. What is the final price?
Step 1: Marked price (MP) = Rs 800
Step 2: Discount = 25% of 800 = (25/100) × 800 = Rs 200
Step 3: Final price = MP − Discount
Step 4: Final price = 800 − 200 = Rs 600
Proportional Reasoning 2 — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. A car travels 120 km in 2 hours. How far will it travel in 5 hours if it maintains the same speed?
- A. 240 km
- B. 300 km
- C. 180 km
- D. 360 km
Answer: B. 300 km — This is a direct proportion problem. The speed is 120 km / 2 hours = 60 km/hour. In 5 hours, the distance covered will be 60 km/hour * 5 hours = 300 km.
MCQ 2. If 5 workers can complete a task in 10 days, how many days will 10 workers take to complete the same task?
- A. 20 days
- B. 15 days
- C. 5 days
- D. 8 days
Answer: C. 5 days — This is an inverse proportion problem. The total work units (workers × days) remain constant. So, 5 workers × 10 days = 10 workers × X days, which means X = 50 / 10 = 5 days.
MCQ 3. The cost of 7 kg of apples is ₹560. What is the cost of 12 kg of apples?
- A. ₹960
- B. ₹840
- C. ₹1080
- D. ₹720
Answer: A. ₹960 — First, find the cost of 1 kg of apples: ₹560 / 7 kg = ₹80/kg. Then, the cost of 12 kg of apples is ₹80/kg * 12 kg = ₹960.
MCQ 4. A train moving at 80 km/h covers a certain distance in 6 hours. How long will it take to cover the same distance if it moves at 60 km/h?
- A. 4 hours
- B. 8 hours
- C. 7 hours
- D. 9 hours
Answer: B. 8 hours — This is an inverse proportion problem. The total distance is Speed × Time = 80 km/h × 6 hours = 480 km. At 60 km/h, the time taken will be 480 km / 60 km/h = 8 hours.
MCQ 5. If 10 men can build a wall of 100 meters in 5 days, how many men are needed to build a wall of 144 meters in 6 days?
- A. 10 men
- B. 12 men
- C. 8 men
- D. 15 men
Answer: B. 12 men — Using the compound proportion formula (M1*D1)/W1 = (M2*D2)/W2, we have (10 * 5) / 100 = (M2 * 6) / 144. This simplifies to 50/100 = 6M2/144, or 1/2 = 6M2/144. Cross-multiplying gives 144 = 12M2, so M2 = 12 men.
MCQ 6. If 3 kg of sugar costs ₹120, what is the cost of 5 kg of sugar?
- A. ₹180
- B. ₹200
- C. ₹240
- D. ₹150
Answer: B. ₹200 — This is a direct proportion. The cost of 1 kg of sugar is ₹120 / 3 = ₹40. So, the cost of 5 kg of sugar is ₹40 * 5 = ₹200.
MCQ 7. A fort has enough food for 200 soldiers for 30 days. If 50 more soldiers join the fort, for how many days will the food last?
- A. 24 days
- B. 20 days
- C. 28 days
- D. 25 days
Answer: A. 24 days — This is an inverse proportion problem. Total food units = 200 soldiers × 30 days = 6000 units. New number of soldiers = 200 + 50 = 250. The food will last for 6000 / 250 = 24 days.
MCQ 8. A bus covers a distance of 360 km in 6 hours. How much distance will it cover in 9 hours at the same speed?
- A. 480 km
- B. 540 km
- C. 600 km
- D. 450 km
Answer: B. 540 km — The speed of the bus is 360 km / 6 hours = 60 km/hour. In 9 hours, the distance covered will be 60 km/hour × 9 hours = 540 km.
MCQ 9. A and B together can complete a work in 12 days. If A alone can complete the same work in 20 days, how many days will B alone take to complete the work?
- A. 25 days
- B. 30 days
- C. 15 days
- D. 24 days
Answer: B. 30 days — A and B's combined work rate is 1/12 per day. A's work rate is 1/20 per day. B's work rate = 1/12 - 1/20 = 5/60 - 3/60 = 2/60 = 1/30. So, B alone will take 30 days.
MCQ 10. If 8 pencils cost ₹40, how many pencils can be bought for ₹60?
- A. 10 pencils
- B. 12 pencils
- C. 15 pencils
- D. 8 pencils
Answer: B. 12 pencils — The cost per pencil is ₹40 / 8 = ₹5. For ₹60, you can buy ₹60 / ₹5 per pencil = 12 pencils.
MCQ 11. 3 taps can fill a tank in 100 minutes. How many taps of the same rate are needed to fill the tank in 60 minutes?
- A. 4 taps
- B. 5 taps
- C. 6 taps
- D. 7 taps
Answer: B. 5 taps — This is an inverse proportion problem. The total work (taps × minutes) remains constant. So, 3 taps × 100 minutes = X taps × 60 minutes, which means X = 300 / 60 = 5 taps.
MCQ 12. If 15 women can weave 100 baskets in 10 days, how many baskets can 12 women weave in 8 days?
- A. 64 baskets
- B. 72 baskets
- C. 60 baskets
- D. 56 baskets
Answer: A. 64 baskets — Using the compound proportion formula W1/(M1*D1) = W2/(M2*D2), we have 100 / (15 * 10) = X / (12 * 8). This simplifies to 100/150 = X/96, or 2/3 = X/96. Cross-multiplying gives 3X = 2 * 96 = 192, so X = 64 baskets.
MCQ 13. The ratio of boys to girls in a class is 4:5. If there are 20 boys, what is the total number of students in the class?
- A. 40
- B. 45
- C. 50
- D. 36
Answer: B. 45 — If 4 parts of the ratio represent 20 boys, then 1 part = 20/4 = 5 students. The number of girls is 5 parts = 5 * 5 = 25 girls. Total students = 20 boys + 25 girls = 45 students.
MCQ 14. If 1 USD is equal to ₹75, how many Indian Rupees will 15 USD be worth?
- A. ₹1000
- B. ₹1125
- C. ₹1250
- D. ₹1050
Answer: B. ₹1125 — This is a direct proportion. If 1 USD = ₹75, then 15 USD = 15 × ₹75 = ₹1125.
MCQ 15. A can do a piece of work in 10 days, and B can do the same work in 15 days. If they work together, in how many days will they complete the work?
- A. 6 days
- B. 8 days
- C. 5 days
- D. 12 days
Answer: A. 6 days — A's 1-day work is 1/10. B's 1-day work is 1/15. Together, their 1-day work = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. So, they will complete the work together in 6 days.
MCQ 16. If 6 meters of cloth costs ₹180, what is the cost of 4 meters of cloth?
- A. ₹120
- B. ₹100
- C. ₹90
- D. ₹150
Answer: A. ₹120 — The cost of 1 meter of cloth is ₹180 / 6 = ₹30. So, the cost of 4 meters of cloth is ₹30 × 4 = ₹120.
MCQ 17. A cyclist covers a distance in 3 hours at a speed of 20 km/h. If he increases his speed to 30 km/h, how much time will he take to cover the same distance?
- A. 2 hours
- B. 4 hours
- C. 1.5 hours
- D. 2.5 hours
Answer: A. 2 hours — The total distance covered is 20 km/h × 3 hours = 60 km. If the speed is increased to 30 km/h, the time taken will be 60 km / 30 km/h = 2 hours.
MCQ 18. A factory uses 10 machines to produce 500 units in 5 days. How many units can 12 machines produce in 7 days?
- A. 840 units
- B. 700 units
- C. 600 units
- D. 900 units
Answer: A. 840 units — Units per machine-day = 500 units / (10 machines × 5 days) = 10 units/machine-day. For 12 machines in 7 days, total units = 12 machines × 7 days × 10 units/machine-day = 840 units.
MCQ 19. The weight of 5 identical books is 1.5 kg. What is the weight of 10 such books?
- A. 2 kg
- B. 3 kg
- C. 2.5 kg
- D. 3.5 kg
Answer: B. 3 kg — This is a direct proportion. If 5 books weigh 1.5 kg, then 10 books (double the number) will weigh double the weight, which is 1.5 kg × 2 = 3 kg.
MCQ 20. A sum of money can support 40 students for 20 days. If 8 students leave, for how many days can the remaining sum support the students?
- A. 25 days
- B. 28 days
- C. 30 days
- D. 24 days
Answer: A. 25 days — This is an inverse proportion problem. Initial support units = 40 students × 20 days = 800 units. If 8 students leave, 40 - 8 = 32 students remain. The sum can support them for 800 / 32 = 25 days.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.