NCERT Solutions for Class 5th Maths Chapter 6 Nida's, Kanti's and John's ways of multiplying — Waste and Composting

Book page 77–78 Updated on2026-09-19

Q1.

A family of 4 produces around 35 kg of kitchen waste in a month. How much waste will the family produce in a year? The family produces _____ kg of waste in a year.

Answer

The family produces 420 kg of kitchen waste in a year.

A year has 12 months. Each month brings 35 kg of waste.

Waste in a year = 12 × 35
Step 1. Split 35 into 30 and 5, and 12 into 10 and 2.
Step 2. 10 × 30 = 300
Step 3. 10 × 5 = 50
Step 4. 2 × 30 = 60
Step 5. 2 × 5 = 10
Step 6. 300 + 50 + 60 + 10 = 420 kg

Nida's grid shows the same four pieces in a box:

×	30 kg	5 kg
10	300	50
2	60	10
Column totals	360	60
Grand total	420 kg

Why the grid has four boxes: 12 was split into 2 parts and 35 was split into 2 parts. Two parts times two parts makes four small rectangles. Add all four and you get the whole rectangle back.

Did you know? Kitchen waste — vegetable peels, tea leaves, leftover rice — does not have to go to the dump. Buried in a pit it turns into compost, a rich brown food for plants.

Q2.

Kanti and John tried to solve it in the following ways. How are these solutions same or different? Discuss in class.

Answer

Both are the same idea; they only differ in how many lines they write. Both split 35 into 30 + 5 and 12 into 10 + 2, and both reach 420.

Kanti writes four lines	John writes two lines
10 (2 × 5)	60 + 10 = 70 (2 × 35)
60 (2 × 30)	60 + 10 = 70 (2 × 35)
50 (10 × 5)	300 + 50 = 350 (10 × 35)
300 (10 × 30)	300 + 50 = 350 (10 × 35)
Total 420	Total 420

Same pieces. Both use 10, 60, 50 and 300. Not one piece is missing from either.
Different grouping. Kanti keeps all four pieces apart. John joins the two pieces that came from the same row: he adds 60 + 10 straight away to make 70, and 300 + 50 to make 350.
Same answer. Kanti: 10 + 60 + 50 + 300 = 420. John: 70 + 350 = 420.

Which is better? Kanti's way shows every step, so it is easier to understand and easier to check. John's way is shorter, so it is faster once you are sure of yourself. Both are correct — pick the one you can do without slipping.

Sample answer for the class discussion: We said John's method is really Kanti's method with the pairs already added up. Nida's grid is the same again, drawn as a picture instead of a list. Three faces of one idea: break the numbers into place values, multiply the pieces, add them all back.

Q3.

The family regularly composts the collected waste. They get around 150 kg of compost each year, which they use in their garden. 1 kg of compost is often sold in the market at ₹24. By creating their own compost, how much money have they saved in a year?

Answer

The family saves ₹3,600 in a year.

They did not have to buy 150 kg of compost. Each kilogram would have cost ₹24.

Money saved = 24 × 150
Step 1. Split 150 into 100 + 50, and 24 into 20 + 4.
Step 2. 20 × 100 = 2,000
Step 3. 20 × 50 = 1,000
Step 4. 4 × 100 = 400
Step 5. 4 × 50 = 200
Step 6. 2,000 + 1,000 + 400 + 200 = ₹3,600

×	100	50
20	2,000	1,000
4	400	200
Column totals	2,400	1,200
Grand total	₹3,600

Check it a shorter way: 24 × 150 = 24 × 100 + 24 × 50 = 2,400 + 1,200 = ₹3,600 ✓

Why this counts as saving: Money saved is money you did not have to spend. By turning their own kitchen waste into compost, the family kept ₹3,600 in their pocket — and kept 420 kg of waste out of the rubbish heap.

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