Question Check 1
Check the recorded weight: Iron almirah, 40 g.
Steps only
Think about whether the object is light enough for grams or heavy enough for kilograms.
Answer
Incorrect; a metal almirah would be measured in kilograms.
CLASS 5 · MATHS MELA · CHAPTER 8
Weight and Capacity
Convert and compare measures from milligrams to tonnes and millilitres to litres, then solve practical weight, cost and capacity problems.
114 worked answersAll 6 exercise sets
What you will learn
- Choose and convert appropriate weight and capacity units.
- Add, subtract, multiply and divide mixed measurements.
- Use unit rates and estimates in everyday situations.
114 worked answers · short steps first, explanations when you need them
Reading and Converting Weights
Textbook pages 104–106
Question Check 2
Check the recorded weight: Bed, 60 kg.
Steps only
Think about whether the object is light enough for grams or heavy enough for kilograms.
Answer
Reasonable.
Question Check 3
Check the recorded weight: Rice bag, 5 kg.
Steps only
Think about whether the object is light enough for grams or heavy enough for kilograms.
Answer
Reasonable.
Question Check 4
Check the recorded weight: Sofa, 30 g.
Steps only
Think about whether the object is light enough for grams or heavy enough for kilograms.
Answer
Incorrect; a sofa would be measured in kilograms.
Question Check 5
Check the recorded weight: Bucket, 1 kg 800 g.
Steps only
Think about whether the object is light enough for grams or heavy enough for kilograms.
Answer
Reasonable for a bucket of that size.
Question Check 6
Check the recorded weight: Water bottle, 650 g.
Steps only
Think about whether the object is light enough for grams or heavy enough for kilograms.
Answer
Reasonable for a filled small bottle.
Question Check 7
Check the recorded weight: Refrigerator, 50 g.
Steps only
Think about whether the object is light enough for grams or heavy enough for kilograms.
Answer
Incorrect; a refrigerator would be measured in kilograms.
Question Scales
How should the six dial scales be read?
Steps only
Find the value between labelled marks, count equal intervals, and calculate the value of one interval.
Start at 0 and follow the pointer; write kilograms and remaining grams.
Answer
Read each pointer from its own zero mark; the pointer value equals labelled start plus counted intervals.
Question Match 3 kg
Match 3 kg to grams.
Steps only
Multiply kilograms by 1,000: 3 kg=3,000 g.
Answer
3,000 g.
Question Match 5 kg
Match 5 kg to grams.
Steps only
Multiply kilograms by 1,000: 5 kg=5,000 g.
Answer
5,000 g.
Question Match 6 kg
Match 6 kg to grams.
Steps only
Multiply kilograms by 1,000: 6 kg=6,000 g.
Answer
6,000 g.
Question Match 10 kg
Match 10 kg to grams.
Steps only
Multiply kilograms by 1,000: 10 kg=10,000 g.
Answer
10,000 g.
Question Match 25 kg
Match 25 kg to grams.
Steps only
Multiply kilograms by 1,000: 25 kg=25,000 g.
Answer
25,000 g.
Question Match 30 kg
Match 30 kg to grams.
Steps only
Multiply kilograms by 1,000: 30 kg=30,000 g.
Answer
30,000 g.
Question Double line
Complete the kg–g number line.
Steps only
Multiply every kilogram value by 1,000.
Answer
1, 3, 8, 15, 20, 25, 30 kg correspond to 1,000, 3,000, 8,000, 15,000, 20,000, 25,000, 30,000 g.
Question Flour 1
Convert 3 kg 500 g.
Steps only
3,500 g.
Answer
3,500 g.
Question Flour 2
Convert 2 kg 250 g.
Steps only
2,250 g.
Answer
2,250 g.
Question 1
Is 5 kg 50 g equal to 5,050 g or 5,500 g?
Steps only
5 kg=5,000 g; add 50 g.
Answer
5,050 g.
Question 2(a)
Convert 7 kg 67 g.
Steps only
7,067 g.
Answer
7,067 g.
Question 2(b)
Convert 3 kg 300 g.
Steps only
3,300 g.
Answer
3,300 g.
Question 2(c)
Convert 8 kg 69 g.
Steps only
8,069 g.
Answer
8,069 g.
Question 2(d)
Convert 10,760 g.
Steps only
10 kg 760 g.
Answer
10 kg 760 g.
Question 2(e)
Convert 4,080 g.
Steps only
4 kg 80 g.
Answer
4 kg 80 g.
Question 2(f)
Convert 12,042 g.
Steps only
12 kg 42 g.
Answer
12 kg 42 g.
Comparing Weights and Milligrams
Textbook pages 107–109
Question Fruits (a)
Which fruit group is heaviest?
Steps only
Compare 3 kg, 1 kg 750 g, 1 kg 250 g and 2 kg.
Answer
Watermelon, 3 kg.
Question Fruits (b)
Which fruit group is lightest?
Steps only
The smallest is 1 kg 250 g.
Answer
Apples, 1 kg 250 g.
Question Fruits (c)
Order the fruit weights from greatest to least.
Steps only
3 kg>2 kg>1 kg 750 g>1 kg 250 g.
Answer
Watermelon, mangoes, pineapple, apples.
Question Compare (a)
Compare 1 kg 600 g and 1,700 g.
Steps only
Convert both sides to grams.
Answer
1 kg 600 g < 1,700 g.
Question Compare (b)
Compare 1 kg 600 g and 1 kg 60 g.
Steps only
Convert both sides to grams.
Answer
1 kg 600 g > 1 kg 60 g.
Question Compare (c)
Compare 10 kg 35 g and 10,035 g.
Steps only
Convert both sides to grams.
Answer
10 kg 35 g = 10,035 g.
Question Compare (d)
Compare 1 kg 600 g and 2 kg 500 g.
Steps only
Convert both sides to grams.
Answer
1 kg 600 g < 2 kg 500 g.
Question Compare (e)
Compare 5 kg 50 g and 4 kg 500 g.
Steps only
Convert both sides to grams.
Answer
5 kg 50 g > 4 kg 500 g.
Question Compare (f)
Compare 900 g+7,000 g and 7 kg+900 g.
Steps only
Convert both sides to grams.
Answer
900 g+7,000 g = 7 kg+900 g.
Question Milligram 1
Convert 5 g.
Steps only
5,000 mg.
Answer
5,000 mg.
Question Milligram line
Complete the g–mg line.
Steps only
Multiply grams by 1,000.
Answer
1, 5, 12, 20, 25, 31 g correspond to 1,000, 5,000, 12,000, 20,000, 25,000, 31,000 mg.
Question Milligram 3
Convert 4 g 100 mg.
Steps only
4,100 mg.
Answer
4,100 mg.
Question Milligram 4
Convert 10 g 500 mg.
Steps only
10,500 mg.
Answer
10,500 mg.
Question 5(a)
Compare 20 g and 200 mg.
Steps only
Convert grams to milligrams and add each side.
Answer
20 g > 200 mg.
Question 5(b)
Compare 16 g 50 mg and 50 g 16 mg.
Steps only
Convert grams to milligrams and add each side.
Answer
16 g 50 mg < 50 g 16 mg.
Question 5(c)
Compare 2,010 mg and 2 g 100 mg.
Steps only
Convert grams to milligrams and add each side.
Answer
2,010 mg < 2 g 100 mg.
Question 5(d)
Compare 9,000 mg and 90 g.
Steps only
Convert grams to milligrams and add each side.
Answer
9,000 mg < 90 g.
Question 5(e)
Compare 5,000 g and 7,500 g.
Steps only
Convert grams to milligrams and add each side.
Answer
5,000 g < 7,500 g.
Question 5(f)
Compare 800 mg+88 mg and 880 mg+8 mg.
Steps only
Convert grams to milligrams and add each side.
Answer
800 mg+88 mg = 880 mg+8 mg.
Quintals, Tonnes and Weight Operations
Textbook pages 109–111
Question 6
A picture shows 40 groups of 5,000 kg. Find the total.
Steps only
5,000×40=200,000.
Answer
200,000 kg.
Question 7(a)
Convert 5,000 kg to quintals and tonnes.
Steps only
5,000÷100=50 quintals; 5,000÷1,000=5 tonnes.
Answer
50 quintals=5 tonnes.
Question 7(b)
Convert 9,000 kg to quintals.
Steps only
9,000÷100=90.
Answer
90 quintals.
Question 7(c)
How many kilograms are 8 tonnes?
Steps only
8×1,000=8,000.
Answer
8,000 kg.
Question King (a)
The king donates 10 times his weight: 800 kg. Find his weight.
Steps only
800÷10=80.
Answer
80 kg.
Question King (b)
Last year the donation was 780 kg. Find his weight.
Steps only
780÷10=78.
Answer
78 kg.
Question King (c)
How much weight did the king gain?
Steps only
80−78=2.
Answer
2 kg.
Question Grocery total
Add 2 kg 500 g and 1 kg 750 g rice.
Steps only
500+750=1,250 g=1 kg 250 g.
2+1+1=4 kg.
Answer
4 kg 250 g.
Question Grocery difference
How much more is 2 kg 500 g than 1 kg 750 g?
Steps only
2,500−1,750=750.
Answer
750 g.
Question Let Us Do 1
Calculate 5 kg 200 g+8 kg 900 g+12 kg 600 g.
Steps only
5,200+8,900+12,600=26,700 g.
Answer
26 kg 700 g.
Question Let Us Do 2
Calculate 2 kg 100 g+3 kg 950 g.
Steps only
2,100+3,950=6,050 g.
Answer
6 kg 50 g.
Question Let Us Do 3
Calculate 10 kg−4 kg 500 g.
Steps only
10,000−4,500=5,500 g.
Answer
5 kg 500 g.
Question Let Us Do 4
Calculate 9 kg 750 g−3 kg 700 g.
Steps only
9,750−3,700=6,050 g.
Answer
6 kg 50 g.
Question Let Us Do 5
Calculate 17 kg 900 g+12 kg 700 g.
Steps only
17,900+12,700=30,600 g.
Answer
30 kg 600 g.
Question Let Us Do 6
Calculate 14 kg 750 g−10 kg 500 g.
Steps only
14,750−10,500=4,250 g.
Answer
4 kg 250 g.
Question Let Us Do 7
Calculate 65 kg−42 kg 275 g+52 kg 500 g.
Steps only
65,000−42,275=22,725 g; add 52,500 g.
Answer
75 kg 225 g.
Grocery Costs and Unit Rates
Textbook pages 112–113
Question Potatoes
Four sacks weigh 10 kg 500 g each. Find total.
Steps only
10,500×4=42,000 g.
Answer
42 kg.
Question Nuts
Share 4 kg 800 g equally among four boxes.
Steps only
4,800÷4=1,200 g.
Answer
1 kg 200 g per box.
Question Cost rice
Find the total cost of 12 kg 500 g at ₹60/kg.
Steps only
Multiply whole kilograms by the rate and the fractional kilogram by the same rate.
Answer
₹750.
Question Cost flour
Find the total cost of 7 kg 250 g at ₹40/kg.
Steps only
Multiply whole kilograms by the rate and the fractional kilogram by the same rate.
Answer
₹290.
Question Cost sugar
Find the total cost of 5 kg at ₹45/kg.
Steps only
Multiply whole kilograms by the rate and the fractional kilogram by the same rate.
Answer
₹225.
Question Cost chana
Find the total cost of 3 kg 600 g at ₹70/kg.
Steps only
Multiply whole kilograms by the rate and the fractional kilogram by the same rate.
Answer
₹252.
Question Cost besan
Find the total cost of 4 kg at ₹60/kg.
Steps only
Multiply whole kilograms by the rate and the fractional kilogram by the same rate.
Answer
₹240.
Question Cost jaggery
Find the total cost of 1 kg 400 g at ₹50/kg.
Steps only
Multiply whole kilograms by the rate and the fractional kilogram by the same rate.
Answer
₹70.
Question Rice for 8
Four people need 500 g rice. How much do 8 need?
Steps only
Eight is twice four; 500×2=1,000 g.
Answer
1,000 g=1 kg.
Question Tomatoes
Five kilograms cost ₹73. Find the cost of 10 kg.
Steps only
Ten kilograms is twice five; 73×2=146.
Answer
₹146.
Question Scrap (a)
Find payment for 16 kg newspaper at ₹8/kg.
Steps only
16×8=128.
Answer
₹128.
Question Scrap (b)
Find payment for 20 kg iron at ₹200 per 10 kg.
Steps only
20 kg is two groups of 10 kg; 2×200=400.
Answer
₹400.
Question Scrap (c)
Find payment for 10 kg plastic at ₹30 per 5 kg.
Steps only
10 kg is two groups of 5 kg; 2×30=60.
Answer
₹60.
Capacity Units and Conversions
Textbook pages 113–115
Question Tea
How much liquid is suitable for two cups of tea?
Steps only
Measure one cup, then double it.
For ordinary cups the total is usually well below 1 L; 500 ml is often enough.
Answer
Use twice the capacity of one cup; 500 ml is a reasonable estimate for two small cups.
Question Bucket
Can a bucket hold only 20 ml?
Steps only
20 ml is about four teaspoons.
Answer
No; a bucket capacity should be about 20 L, not 20 ml.
Question Ramiz
Ramiz drinks two 500 ml bottles.
Steps only
500+500=1,000 ml.
Answer
1,000 ml=1 L.
Question Muskaan
How many 500 ml bottles make 3 L?
Steps only
3 L=3,000 ml; 3,000÷500=6.
Answer
6 refills; 3,000 ml total.
Question Container sets
How should each pictured group of containers be totalled?
Steps only
Convert every litre label to millilitres.
Add all labels in a group, then divide by 1,000 to write litres and remaining millilitres.
Answer
For each group: total ml=(1,000×number of litres)+all labelled ml; report quotient litres and remainder ml.
Question Milk line
Complete the milk-delivery double number line.
Steps only
Multiply litres by 1,000.
Answer
1, 2, 6, 8, 12, 14, 20, 25 L correspond to 1,000, 2,000, 6,000, 8,000, 12,000, 14,000, 20,000, 25,000 ml.
Question Family Arora
Convert 8 L.
Steps only
8,000 ml.
Answer
8,000 ml.
Question Family Nair
Convert 14 L.
Steps only
14,000 ml.
Answer
14,000 ml.
Question Family Shrivastava
Convert 12,000 ml.
Steps only
12 L.
Answer
12 L.
Question Family Das
Convert 20,000 ml.
Steps only
20 L.
Answer
20 L.
Question Family Rao
Convert 25,000 ml.
Steps only
25 L.
Answer
25 L.
Question Sunday
Dev needs 1 L milk plus 500 ml on Sunday.
Steps only
1,000+500=1,500 ml.
Answer
1 L 500 ml=1,500 ml.
Question Think 1
Is 1 L 400 ml equal to 1,400 ml or 1,040 ml?
Steps only
1 L=1,000 ml; 1,000+400=1,400.
Answer
1,400 ml.
Question 2(a)
Convert 3 L 8 ml.
Steps only
3,008 ml.
Answer
3,008 ml.
Question 2(b)
Convert 9 L 90 ml.
Steps only
9,090 ml.
Answer
9,090 ml.
Question 2(c)
Convert 14,075 ml.
Steps only
14 L 75 ml.
Answer
14 L 75 ml.
Question 2(d)
Convert 8 L 86 ml.
Steps only
8,086 ml.
Answer
8,086 ml.
Question 2(e)
Convert 12,200 ml.
Steps only
12 L 200 ml.
Answer
12 L 200 ml.
Question 2(f)
Convert 18,350 ml.
Steps only
18 L 350 ml.
Answer
18 L 350 ml.
Comparing and Operating on Capacity
Textbook pages 115–118
Question Fuel truck
Calculate 3 trucks×500 L.
Steps only
Multiply vehicles by litres in each vehicle.
Answer
1,500 L.
Question Fuel bus
Calculate 6 buses×300 L.
Steps only
Multiply vehicles by litres in each vehicle.
Answer
1,800 L.
Question Fuel car
Calculate 10 cars×50 L.
Steps only
Multiply vehicles by litres in each vehicle.
Answer
500 L.
Question Fuel auto
Calculate 12 autos×8 L.
Steps only
Multiply vehicles by litres in each vehicle.
Answer
96 L.
Question Fuel two-wheeler
Calculate 25 two-wheelers×5 L.
Steps only
Multiply vehicles by litres in each vehicle.
Answer
125 L.
Question Fuel (a)
How much more fuel did buses buy than trucks?
Steps only
1,800−1,500=300.
Answer
300 L.
Question Fuel (b)
Find all fuel sold that day.
Steps only
1,500+1,800+500+96+125=4,021.
Answer
4,021 L.
Question Compare (a)
Compare 5 L 600 ml and 5,400 ml.
Steps only
Convert both sides to millilitres.
Answer
5 L 600 ml > 5,400 ml.
Question Compare (b)
Compare 10 L 100 ml and 1 L 600 ml.
Steps only
Convert both sides to millilitres.
Answer
10 L 100 ml > 1 L 600 ml.
Question Compare (c)
Compare 190 ml+800 ml and 800 ml+109 ml.
Steps only
Convert both sides to millilitres.
Answer
190 ml+800 ml > 800 ml+109 ml.
Question Compare (d)
Compare 3 L 600 ml and 3,600 ml.
Steps only
Convert both sides to millilitres.
Answer
3 L 600 ml = 3,600 ml.
Question Compare (e)
Compare 4 L 50 ml and 4 L 500 ml.
Steps only
Convert both sides to millilitres.
Answer
4 L 50 ml < 4 L 500 ml.
Question Sam bought
Tina bought 2 L 500 ml; Sam bought 2 L 800 ml more. Find Sam’s amount.
Steps only
2,500+2,800=5,300 ml.
Answer
5 L 300 ml.
Question Sam before
After adding 5 L 300 ml, Sam’s tank reads 9 L. What was there before?
Steps only
9,000−5,300=3,700 ml.
Answer
3 L 700 ml.
Question Final 1
Riya fills 2 L plus four 500 ml bottles; Aarav fills three 750 ml bottles.
Steps only
Riya=2,000+4×500=4,000 ml.
Aarav=3×750=2,250 ml; difference=1,750 ml.
Answer
Riya filled 1 L 750 ml more.
Question Final 2(a)
Eight glasses hold 360 ml each.
Steps only
8×360=2,880.
Answer
2,880 ml.
Question Final 2(b)
The eight glasses are full and 120 ml remains. Find original milk.
Steps only
2,880+120=3,000 ml.
Answer
3 L.
Question Final 2(c)
One litre milk costs ₹40. Find 3 L.
Steps only
3×40=120.
Answer
₹120.
Question Final 3(a)
How many 250 ml glasses fill from 5 L?
Steps only
5 L=5,000 ml; 5,000÷250=20.
Answer
20 glasses.
Question Final 3(b)
After serving ten 250 ml glasses from 5 L, how much remains?
Steps only
Served=10×250=2,500 ml.
5,000−2,500=2,500 ml.
Answer
2 L 500 ml.
Question Final 3(c)
At ₹25 per 250 ml, find revenue from 5 L.
Steps only
There are 20 glasses; 20×25=500.
Answer
₹500.
Question Final 4
Share 8 L 400 ml equally into 7 containers.
Steps only
8,400÷7=1,200 ml.
Answer
1 L 200 ml each.
Question Final 5
Eight containers hold 1 L 75 ml each.
Steps only
1,075×8=8,600 ml.
Answer
8 L 600 ml.