NCERT Solutions for Class 5th Maths Chapter 6 Solve like Nida, like Kanti, like John; then word problems — Let Us Do

Book page 79–80 Updated on2026-09-19

Q1.

Solve the following problems like Nida did (using a grid). a) 78 × 4 b) 83 × 9 c) 67 × 28 d) 53 × 37

Answer

Nida's way is to draw a grid, split each number into its place values, multiply every box, then add.

a) 78 × 4 = 312

×	70	8
4	280	32
Total	280 + 32 = 312

b) 83 × 9 = 747

×	80	3
9	720	27
Total	720 + 27 = 747

c) 67 × 28 = 1,876

×	60	7	Row total
20	1,200	140	1,340
8	480	56	536
Total	1,340 + 536 = 1,876

d) 53 × 37 = 1,961

×	50	3	Row total
30	1,500	90	1,590
7	350	21	371
Total	1,590 + 371 = 1,961

How to fill a grid
Step 1. Split each number into its place values (67 → 60 + 7).
Step 2. Write one number across the top and the other down the side.
Step 3. Multiply each pair and write the answer in that box.
Step 4. Add every box.

Check c) another way: 67 × 28 = 67 × 30 − 67 × 2 = 2,010 − 134 = 1,876 ✓

Q2.

Solve the following problems like Kanti. a) 94 × 5 b) 49 × 6 c) 37 × 53 d) 28 × 79

Answer

Kanti's way is to write every small piece on its own line, smallest first, then add them all.

a) 94 × 5
94 (90 + 4) × 5
Step 1. 5 × 4 = 20
Step 2. 5 × 90 = 450
Step 3. 20 + 450 = 470

b) 49 × 6
49 (40 + 9) × 6
Step 1. 6 × 9 = 54
Step 2. 6 × 40 = 240
Step 3. 54 + 240 = 294

c) 37 × 53
37 (30 + 7) × 53 (50 + 3)
Step 1. 3 × 7 = 21
Step 2. 3 × 30 = 90
Step 3. 50 × 7 = 350
Step 4. 50 × 30 = 1,500
Step 5. 21 + 90 + 350 + 1,500 = 1,961

d) 28 × 79
28 (20 + 8) × 79 (70 + 9)
Step 1. 9 × 8 = 72
Step 2. 9 × 20 = 180
Step 3. 70 × 8 = 560
Step 4. 70 × 20 = 1,400
Step 5. 72 + 180 + 560 + 1,400 = 2,212

Why four lines for c) and d): Both numbers were split into two parts, so there are 2 × 2 = 4 pieces to multiply. For a) and b) only one number was split, so there are just 2 pieces.

Check d): 28 × 79 = 28 × 80 − 28 = 2,240 − 28 = 2,212 ✓

Q3.

Solve the following problems like John. a) 86 × 3 b) 72 × 7 c) 94 × 36 d) 66 × 22

Answer

John's way is one line for each digit of the second number, with the pieces of that line already added together.

a) 86 × 3
Step 1. 3 × 86 → 240 + 18 = 258

b) 72 × 7
Step 1. 7 × 72 → 490 + 14 = 504

c) 94 × 36
Step 1. 6 × 94 → 540 + 24 = 564
Step 2. 30 × 94 → 2,700 + 120 = 2,820
Step 3. 564 + 2,820 = 3,384

d) 66 × 22
Step 1. 2 × 66 → 120 + 12 = 132
Step 2. 20 × 66 → 1,200 + 120 = 1,320
Step 3. 132 + 1,320 = 1,452

Watch the second line. In c) the 3 of 36 is really 30, so the line is 30 × 94, not 3 × 94. That is why 2,820 is ten times bigger than 282.

Check d) with doubling and halving: 66 × 22 = 33 × 44. And 33 × 44 = 33 × 40 + 33 × 4 = 1,320 + 132 = 1,452 ✓

Q4.

(a) A movie theater has 8 rows of seats, and each row has 12 seats. If half the seats are filled, how many people are watching the movie? If 3 more rows get filled, how many total people will be there?

Answer

48 people are watching. After 3 more rows fill up, there will be 84 people.

First find how many seats the whole theatre has.

Step 1. Total seats = 8 × 12 = 96 seats
Step 2. Half the seats = 96 ÷ 2 = 48 people
Step 3. Seats in 3 more rows = 3 × 12 = 36 seats
Step 4. New total = 48 + 36 = 84 people

Why 3 rows is 36 people: Every row holds 12 seats. Three full rows means three lots of 12, which is 36.

Check it yourself: 84 people out of 96 seats leaves 96 − 84 = 12 seats empty — exactly one row. That fits: half of 8 rows is 4 rows, plus 3 more rows makes 7 rows full and 1 row empty ✓

Q5.

(b) In a test match between India and West Indies, the Indian team hit twenty-four 4s and eighteen 6s across the two innings. How many runs were scored in 4s and 6s each? 234 runs were made by running between the wickets. If 23 runs were extras, how many runs were scored by Indian team in the two innings?

Answer

Runs in 4s = 96. Runs in 6s = 108. Total runs in the two innings = 461.

Runs from fours
Step 1. 24 fours = 24 × 4
Step 2. 24 × 4 = 96 runs

Runs from sixes
Step 1. 18 sixes = 18 × 6
Step 2. 18 × 6 = 108 runs

Total for the team
Step 1. Boundaries = 96 + 108 = 204 runs
Step 2. Add the running between wickets: 204 + 234 = 438 runs
Step 3. Add the extras: 438 + 23 = 461 runs

Why we add all three: A team's score is made of every run it gets — runs hit to the boundary, runs made by running, and extras given away by the other team. Nothing is counted twice, because a four is never also a run between the wickets.

Did you know? A four means the ball reaches the boundary rope along the ground. A six means it clears the rope in the air. Eighteen sixes across a test match is a big-hitting side.

Q6.

(c) Anjali buys 15 bulbs and 12 tube lights from Sudha Electricals. Each bulb costs ₹25 and each tube light costs ₹34. How much money should Anjali give to the shopkeeper?

Answer

Anjali should give ₹783 to the shopkeeper.

There are two different things being bought, so find each cost and then add.

Cost of bulbs
Step 1. 15 bulbs × ₹25 each
Step 2. Use doubling and halving: 15 × 25 = 30 × 12.5 — messy. Try place values instead.
Step 3. 15 × 25 = 10 × 25 + 5 × 25 = 250 + 125 = ₹375

Cost of tube lights
Step 1. 12 tube lights × ₹34 each
Step 2. 12 × 34 = 10 × 34 + 2 × 34
Step 3. 340 + 68 = ₹408

Total to pay
₹375 + ₹408 = ₹783

Check the bulbs a second way: 15 × 25 = 15 × 100 ÷ 4 = 1,500 ÷ 4 = 375 ✓ (because 25 is one quarter of 100).

Q7.

(d) A shopkeeper sold 28 bags of rice. Each bag costs ₹350. How much money did he earn by selling rice bags?

Answer

He earned ₹9,800.

Money earned = 28 × 350
Step 1. Set the zero of 350 aside: 28 × 35
Step 2. 28 × 35 = 28 × 30 + 28 × 5
Step 3. 28 × 30 = 840
Step 4. 28 × 5 = 140
Step 5. 840 + 140 = 980
Step 6. Put the zero back: ₹9,800

Check it with doubling and halving: 28 × 350 = 14 × 700 = 14 × 7 × 100 = 98 × 100 = ₹9,800 ✓

Q8.

(e) A school library has 86 shelves and each shelf has 162 books. Find the number of books in the library.

Answer

The library has 13,932 books.

Total books = 86 × 162
Step 1. Split 162 into 100 + 60 + 2.
Step 2. 86 × 100 = 8,600
Step 3. 86 × 60 = 5,160
Step 4. 86 × 2 = 172
Step 5. 8,600 + 5,160 + 172 = 13,932 books

Why 86 × 60 is 5,160: 86 × 6 = 516. Then 60 is ten times 6, so the answer is ten times 516, which is 5,160.

Check it yourself: Estimate first. 86 is close to 90 and 162 is close to 160, so the answer should be near 90 × 160 = 14,400. Our answer 13,932 is close to that, so it looks right ✓

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