✅ SOLUTIONS
Class 5
Chapter 8: Weight and Capacity
Math Mela · NCERT Solutions
Class 5Math Mela (NCERT)Chapter 8
📚 Jump to a Section
- Check! Check! & Reading Scales
- Different Units, Same Measure
- Let Us Find — g/kg Conversions
- Comparing Weights
- Milligram Section
- Quintal, Tonne & King's Weight
- Grocery Store — Adding/Subtracting
- Let Us Do — Weight Word Problems
- Multiplying & Dividing Weights
- Capacity — Big to Small
- Milkman's Delivery & Let Us Think
- Let Us Compare — Petrol Pump
- Let Us Solve — Final Capacity Problems
✅ Check! Check! & Reading Scales
Are Anu's recorded weights correct?
Solution
| Item | Recorded | Correct? | Why |
|---|---|---|---|
| 1. Iron Almirah | 40 g | ❌ NO | Should be ~40 kg — 40g is lighter than a spoon! |
| 2. Bed | 60 kg | ✅ Correct | Reasonable weight for a bed |
| 3. Rice Bag | 5 kg | ✅ Correct | Reasonable for a bag of rice |
| 4. Sofa | 30 g | ❌ NO | Should be ~30 kg — far too light as written |
| 5. Bucket | 1 kg 800 g | ✅ Correct | Reasonable for a full bucket |
| 6. Water Bottle | 650 g | ✅ Correct | Reasonable for a filled bottle |
| 7. Refrigerator | 50 g | ❌ NO | Should be ~50 kg or more — nowhere close as written |
Read the scales (a-f) and write the correct weights.
Solution
| Scale | Range | Reading |
|---|---|---|
| (a) | 0-4 kg dial | 900 g |
| (b) | 0-2 kg dial | 1 kg 800 g |
| (c) | 0-6 kg dial | 2 kg 800 g |
| (d) | 0-4 kg dial | 2 kg 600 g |
| (e) | 0-1 kg dial (250g marks) | 125 g |
| (f) | 0-1 kg dial (250g marks) | 625 g |
💡 How to read a dial scale: Find the maximum value (like 4kg), count how many small ticks are between each labelled number, and figure out what each tick represents. Then count how many ticks the pointer has moved past the last labelled number.
⚖️ Different Units but Same Measure
Match weights on the two balances; fill the double number line.
Solution
| Balance 1 (kg) | Balance 2 (g) |
|---|---|
| 3 kg | 3,000 g |
| 6 kg | 6,000 g |
| 5 kg | 5,000 g |
| 10 kg | 10,000 g |
| 25 kg | 25,000 g |
| 30 kg | 30,000 g |
Double number line completed:
kg: 1, 3, 8, 15, 20, 25, 30 | g: 1,000, 3,000, 8,000, 15,000, 20,000, 25,000, 30,000
🔢 Let Us Find — Conversions
Q1. 5 kg 50 g in grams — Shamim says 5,050g, Rehan says 5,500g. Who's right?
Solution
Shamim is correct: 5,050 g ✅. "50 g" simply means 50 grams — not 500! Rehan mistakenly treated "50" as if it meant "500."
Q2. Fill in the conversion blanks (a-f).
Solution
| Problem | Answer |
|---|---|
| (a) 7 kg 67 g | 7,067 g |
| (b) 3 kg 300 g | 3,300 g |
| (c) 8 kg 69 g | 8,069 g |
| (d) 10,760 g | 10 kg 760 g |
| (e) 4,080 g | 4 kg 80 g |
| (f) 12,042 g | 12 kg 42 g |
⚖️ Comparing Weights
Q1. Harpreet's fruits: Watermelon 3kg, Pineapple 1kg750g, Apples 1kg250g, Mangoes 2kg.
Solution
(a) Highest weight = Watermelon (3 kg)
(b) Least weight = Apples (1 kg 250 g)
(c) Descending order: Watermelon > Mangoes > Pineapple > Apples
Q2. Compare using <, =, >.
Solution
| Part | Comparison | Answer |
|---|---|---|
| (a) | 1kg600g(1600g) vs 1700g | < |
| (b) | 1kg600g(1600g) vs 1kg60g(1060g) | > |
| (c) | 10kg35g(10035g) vs 10,035g | = |
| (d) | 1kg600g(1600g) vs 2kg500g(2500g) | < |
| (e) | 5kg50g(5050g) vs 4kg500g(4500g) | > |
| (f) | 900g+7000g(7900g) vs 7kg+900g(7900g) | = |
🐜 Milligram Section
Q1. 5g sugar sachet in mg?
Solution
5 g × 1,000 = 5,000 mg
Q2. Complete the double number line.
Solution
g: 1, 5, 12, 20, 25, 31 | mg: 1000, 5000, 12000, 20000, 25000, 31000
Q3 & Q4. Ornament weights in mg.
Solution
Q3: 4 g 100 mg = 4,100 mg
Q4: 10 g 500 mg = 10,500 mg
Q5. Compare using <, =, >.
Solution
| Part | Comparison | Answer |
|---|---|---|
| (a) | 20g(20000mg) vs 200mg | > |
| (b) | 16g50mg(16050mg) vs 50g16mg(50016mg) | < |
| (c) | 2010mg vs 2g100mg(2100mg) | < |
| (d) | 9000mg(9g) vs 90g | < |
| (e) | 5000g vs 7500g | < |
| (f) | 800+88=888mg vs 880+8=888mg | = |
🏋️ Quintal, Tonne & King's Weight
Q6 & Q7. Quintal/tonne conversions.
Solution
Q6: 5,000 kg × 40 = 200,000 kg = 2,000 quintals = 200 tonnes
| Problem | Answer |
|---|---|
| (a) 5,000 kg = ? quintals = ? tonnes | 50 quintals = 5 tonnes |
| (b) 9,000 kg = ? quintals | 90 quintals |
| (c) ? kg = 8 tonnes | 8,000 kg |
King's Weight: donates 10× his weight in wheat.
Solution
(a) 800 kg donated = 10 × weight → weight = 800÷10 = 80 kg
(b) 780 kg donated last year = 10 × last year's weight → 780÷10 = 78 kg
(c) Weight gained = 80 − 78 = 2 kg
🛒 Grocery Store
Rathna's rice: 2kg500g + 1kg750g. Extra rice for household vs Pongal?
Solution
Total rice = 4 kg 250 g (given/worked example)
Extra for household = 2kg500g − 1kg750g = 750 g more
✍️ Let Us Do — Weight Word Problems
Seven weight addition/subtraction word problems.
Solution
| # | Problem | Working | Answer |
|---|---|---|---|
| 1 | Onions: 5kg200g+8kg900g+12kg600g | 25kg+1700g | 26 kg 700 g |
| 2 | Apples: 2kg100g+3kg950g | 5kg+1050g | 6 kg 50 g |
| 3 | Sand: 10kg−4kg500g | 5 kg 500 g | |
| 4 | Rice: 9kg750g−3kg700g | 6 kg 50 g | |
| 5 | Delivery: 17kg900g+12kg700g | 29kg+1600g | 30 kg 600 g |
| 6 | Books: 14kg750g−10kg500g | 4 kg 250 g | |
| 7 | Flour: 65kg−42kg275g+52kg500g | 22kg725g+52kg500g | 75 kg 225 g |
✖️➗ Multiplying & Dividing Weights
Q1. Grocery table — find total cost for each item.
Solution
| Item | Weight | Rate/kg | Total Cost |
|---|---|---|---|
| Rice | 12 kg 500 g | ₹60 | ₹750 |
| Flour | 7 kg 250 g | ₹40 | ₹290 |
| Sugar | 5 kg | ₹45 | ₹225 |
| Chana dal | 3 kg 600 g | ₹70 | ₹252 |
| Besan | 4 kg | ₹60 | ₹240 |
| Jaggery | 1 kg 400 g | ₹50 | ₹70 |
Q2-4. Rice for 8 people, tomato cost, scrap dealer.
Solution
Q2: 4 people need 500g → 8 people (double) need 1,000 g = 1 kg
Q3: 5kg tomatoes=₹73 → 10kg (double) = ₹146
Q4(a): 16kg × ₹8/kg = ₹128
Q4(b): 20kg iron = 2×10kg → 2×₹200 = ₹400
Q4(c): 10kg plastic = 2×5kg → 2×₹30 = ₹60
🥤 Capacity — Big to Small
Measuring Capacity discussion questions.
Solution
1. For 2 cups of tea: roughly 300-400 ml of water+milk combined is typical — 1 litre would be WAY too much (that's more like 5-6 cups worth), and 500ml of water ALONE is also more than usually needed.
2. "A bucket holds max 20 ml" is INCORRECT — 20ml is just a few spoonfuls! A bucket should be measured in litres (typically 10-20 litres), not millilitres.
Q1-2. Ramiz's water bottles; Muskaan's refills.
Solution
Ramiz: 500ml + 500ml = 1,000 ml = 1 litre at school
Muskaan: 3L = 3,000ml. Refills needed = 3,000÷500 = 6 times
🥛 Milkman's Delivery & Let Us Think
2L milk marked on ml-only vessel; complete family delivery table.
Solution
2 l = 2,000 ml mark
| Family | Litres | Millilitres |
|---|---|---|
| Arora's | 8 l | 8,000 ml |
| Nair's | 14 l | 14,000 ml |
| Shrivastava's | 12 l | 12,000 ml |
| Das's | 20 l | 20,000 ml |
| Rao's | 25 l | 25,000 ml |
Q1. Bottle capacity: Mary says 1,400ml, Daisy says 1,040ml for 1l400ml. Who's right?
Solution
1,400 ml is correct ✅. 1 litre = 1,000ml, plus 400ml more = 1,400ml. The "1,040ml" answer wrongly treats "400" as if it were "40."
Q2. Convert (a-f).
Solution
| Problem | Answer |
|---|---|
| (a) 3l 8ml | 3,008 ml |
| (b) 9l 90ml | 9,090 ml |
| (c) 14,075 ml | 14 l 75 ml |
| (d) 8l 86ml | 8,086 ml |
| (e) 12,200 ml | 12 l 200 ml |
| (f) 18,350 ml | 18 l 350 ml |
⛽ Let Us Compare — Petrol Pump
Complete the fuel table; answer (a) and (b).
Solution
| Vehicle | No. | Fuel each (L) | Total Fuel (L) |
|---|---|---|---|
| Truck | 3 | 500 | 1,500 |
| Bus | 6 | 300 | 1,800 |
| Car | 10 | 50 | 500 |
| Auto Rickshaw | 12 | 8 | 96 |
| Two-wheeler | 25 | 5 | 125 |
(a) Buses − Trucks = 1,800 − 1,500 = 300 L more for buses
(b) Total fuel = 1500+1800+500+96+125 = 4,021 L
Q3. Compare using <, =, >.
Solution
| Part | Comparison | Answer |
|---|---|---|
| (a) | 5l600ml(5600ml) vs 5400ml | > |
| (b) | 10l100ml(10100ml) vs 1l600ml(1600ml) | > |
| (c) | 190+800=990ml vs 800+109=909ml | > |
| (d) | 3l600ml(3600ml) vs 3600ml | = |
| (e) | 4l50ml(4050ml) vs 4l500ml(4500ml) | < |
Q4. Sam & Tina's petrol; fuel before refuelling.
Solution
Sam bought = 2l500ml + 2l800ml = 5 l 300 ml(worked example)
Fuel before refuelling = 9l − 5l300ml = 3 l 700 ml(worked example)
✏️ Let Us Solve — Final Capacity Problems
Q1. Riya: 1×2l + 4×500ml. Aarav: 3×750ml. Who filled more?
Solution
Riya: 2,000 + 4×500 = 2,000+2,000 = 4,000 ml = 4 l
Aarav: 3×750 = 2,250 ml = 2 l 250 ml
Riya filled more, by 4,000−2,250 = 1,750 ml (1 l 750 ml) more
Q2. Milk bottle → 8 glasses of 360ml, 120ml left. Initial milk? Cost of 3L at ₹40/L?
Solution
(a) 8 × 360 = 2,880 ml (capacity of 8 glasses)
(b) Initial milk = 2,880 + 120 = 3,000 ml = 3 L
(c) 3L × ₹40 = ₹120
Q3. 5L juice container, 250ml glasses.
Solution
(a) Full glasses = 5,000÷250 = 20 glasses
(b) After 10 served: 5,000−2,500 = 2,500 ml (2.5 L) left
(c) 20 glasses × ₹25 = ₹500
Q4 & Q5. Oil into containers; buttermilk containers.
Solution
Q4: 8l400ml ÷ 7 = 8,400÷7 = 1,200 ml = 1 l 200 ml each
Q5: 8 × (1l75ml) = 8l + 600ml = 8 l 600 ml total