NCERT Solutions for Class 5th Maths Chapter 9 Shows, ice cream, biscuits, remainders, relations, the cycle rally and the carpenter — Let Us Solve

Book page 132–133 Updated on2026-09-19

Q1.

1. A theatre company can accommodate 45 people during one show. (a) A total of 475 people bought tickets for a puppet show. How many shows are needed to seat all the people who bought tickets? (b) There are 2 shows in a day. How many days will be needed to accommodate all the people?

Answer

(a) 11 shows. (b) 6 days.

(a) How many shows? Each show seats 45 people, and 475 people have tickets.

Step 1: 475 ÷ 45
Step 2: 45 × 10 = 450, which fits
Step 3: 475 − 450 = 25 people still without a seat
Step 4: Those 25 need one more show

Shows = 10 full + 1 more = 11 shows

(b) How many days? There are 2 shows in a day, and 11 shows are needed.

Step 1: 11 ÷ 2
Step 2: 2 × 5 = 10, and 11 − 10 = 1
Step 3: After 5 days, 10 shows are done and 1 show is still left
Step 4: That last show needs one more day

Days = 5 + 1 = 6 days

Why we round up twice: You cannot run 10 and a half shows, and you cannot use half a day. Whenever people or events are left over, you need one more whole show, one more whole day.

Check by a second route: 11 shows × 45 seats = 495 seats, enough for 475 people ✓ And 6 days × 2 shows = 12 shows, enough for 11 ✓

Q2.

2. Naina bought 5 kg of ice cream as a birthday treat for her 23 friends. 400 g ice cream was left after everyone had an equal share. How much ice cream did each of her friends eat?

Answer

Each friend ate 200 g of ice cream.

Be careful: the ice cream is in kilograms but the leftover is in grams. Change everything to grams first.

Step 1 — change the units:
1 kg = 1000 g
5 kg = 5 × 1000 = 5000 g

Step 2 — take away what was left:
5000 g − 400 g = 4600 g was eaten

Step 3 — share it among 23 friends:
4600 ÷ 23
23 × 200 = 4600
So each friend ate 200 g

Why we subtract first: The 400 g was never eaten. Only the 4,600 g was actually shared, so only that amount should be divided.

Check by a second route: 23 friends × 200 g = 4,600 g, and 4,600 g + 400 g left over = 5,000 g = 5 kg ✓
Answer: 200 g each.

Q3.

3. Megha packs 15 packets of ragi-oats biscuits for a 4-day group trip. Each packet contains 8 biscuits. There are 6 people in the group. If distributed evenly, how many biscuits can one person have each day?

Answer

Each person can have 5 biscuits each day.

There are two things to work out first: how many biscuits there are altogether, and how many shares must be made.

Step 1 — total biscuits:
15 packets × 8 biscuits = 120 biscuits

Step 2 — how many shares?
6 people × 4 days = 24 shares
(one share is what one person eats on one day)

Step 3 — divide:
120 ÷ 24 = 5 biscuits

The same answer another way, one step at a time:

Share 120 biscuits among 6 people: 120 ÷ 6 = 20 biscuits per person for the whole trip.
Spread those 20 over 4 days: 20 ÷ 4 = 5 biscuits a day.

Check by a second route: 5 biscuits × 6 people = 30 biscuits a day. Over 4 days that is 30 × 4 = 120 biscuits — exactly what she packed ✓
Answer: 5 biscuits per person per day.

Q4.

4. Solve the following and identify the remainder, if any. Check whether N = D × Q + R in each case. (a) 9,045 ÷ 5 (b) 1,034 ÷ 4 (c) 2,504 ÷ 7 (d) 8,900 ÷ 15 (e) 9,876 ÷ 32 (f) 7,506 ÷ 24

Answer

Part	Division	Quotient (Q)	Remainder (R)	Check: N = D × Q + R
(a)	9,045 ÷ 5	1,809	0	5 × 1809 = 9,045 ✓
(b)	1,034 ÷ 4	258	2	4 × 258 + 2 = 1032 + 2 = 1,034 ✓
(c)	2,504 ÷ 7	357	5	7 × 357 + 5 = 2499 + 5 = 2,504 ✓
(d)	8,900 ÷ 15	593	5	15 × 593 + 5 = 8895 + 5 = 8,900 ✓
(e)	9,876 ÷ 32	308	20	32 × 308 + 20 = 9856 + 20 = 9,876 ✓
(f)	7,506 ÷ 24	312	18	24 × 312 + 18 = 7488 + 18 = 7,506 ✓

(a) 9,045 ÷ 5 — split it:

9045 = 9000 + 45
9000 ÷ 5 = 1800
45 ÷ 5 = 9
1800 + 9 = 1,809, remainder 0

(d) 8,900 ÷ 15 — partial quotients:

15) 8900 ( 500 + 90 + 3
−7500 → 1400 (15 × 500)
−1350 → 50 (15 × 90)
−45 → 5 (15 × 3)

Q = 500 + 90 + 3 = 593, R = 5

(e) 9,876 ÷ 32 — partial quotients:

32) 9876 ( 300 + 8
−9600 → 276 (32 × 300)
−256 → 20 (32 × 8)

Q = 300 + 8 = 308, R = 20

Every remainder is smaller than its divisor: 0 < 5, 2 < 4, 5 < 7, 5 < 15, 20 < 32, 18 < 24. That is your first quick test that an answer is sensible.

Q5.

5. Find the solutions for part A. Observe the relations between the quotient, divisor and dividend and use it to answer parts B and C. A. (a) 340 ÷ 34 = 10 (b) 340 ÷ 17 = ___ (c) 680 ÷ 17 = ___ (d) 680 ÷ 34 = ___ (e) 170 ÷ 17 = ___ (f) 680 ÷ 68 = ___

Answer

Part	Division	Answer	How it follows from the one above
(a)	340 ÷ 34	10	given in the book
(b)	340 ÷ 17	20	17 is half of 34 → the answer doubles: 10 × 2
(c)	680 ÷ 17	40	680 is double 340 → the answer doubles again: 20 × 2
(d)	680 ÷ 34	20	both doubled from (a) → answer unchanged … no: dividend doubled, divisor same as (a) → 10 × 2
(e)	170 ÷ 17	10	170 is half of 340 and 17 is half of 34 → answer unchanged
(f)	680 ÷ 68	10	both doubled from (a) → answer unchanged

The two relations you are meant to notice:

Halve the divisor and the quotient doubles. 340 ÷ 34 = 10, so 340 ÷ 17 = 20. Sharing the same amount among half as many groups gives each group twice as much.
Double the dividend and the quotient doubles. 340 ÷ 17 = 20, so 680 ÷ 17 = 40. Twice as much to share among the same groups gives each group twice as much.
Double both and the quotient stays the same. 340 ÷ 34 = 10 and 680 ÷ 68 = 10.

Check them all by multiplying back: 17 × 20 = 340 ✓ 17 × 40 = 680 ✓ 34 × 20 = 680 ✓ 17 × 10 = 170 ✓ 68 × 10 = 680 ✓

Q6.

B. (a) 192 ÷ 4 = 48 (b) 192 ÷ 8 = ___ (c) 384 ÷ 8 = ___ (d) 384 ÷ 4 = ___ (e) 384 ÷ 8 = ___ (f) 86 ÷ 2 = ___

Answer

Part	Division	Answer	The relation used
(a)	192 ÷ 4	48	given in the book
(b)	192 ÷ 8	24	the divisor doubled (4 → 8), so the answer halves: 48 ÷ 2
(c)	384 ÷ 8	48	both doubled from (a), so the answer is unchanged
(d)	384 ÷ 4	96	only the dividend doubled, so the answer doubles: 48 × 2
(e)	384 ÷ 8	48	the same question as (c), so the same answer
(f)	86 ÷ 2	43	split 86 = 80 + 6, so 40 + 3 = 43

Why (c) gives the same answer as (a): In 384 ÷ 8, both numbers are exactly double those in 192 ÷ 4. Twice the sweets shared among twice the children means each child still gets the same.

A note about the book: Parts (c) and (e) are the same question, 384 ÷ 8, printed twice in the English edition. Both have the answer 48.
Check: 8 × 24 = 192 ✓ 8 × 48 = 384 ✓ 4 × 96 = 384 ✓ 2 × 43 = 86 ✓

Q7.

C. (a) 352 ÷ 11 = 32 (b) 704 ÷ 22 = ___ (c) 704 ÷ 11 = ___ (d) 352 ÷ 22 = ___ (e) 1,408 ÷ 44 = ___

Answer

Part	Division	Answer	The relation used
(a)	352 ÷ 11	32	given in the book
(b)	704 ÷ 22	32	both doubled from (a), so the answer is unchanged
(c)	704 ÷ 11	64	only the dividend doubled, so the answer doubles: 32 × 2
(d)	352 ÷ 22	16	only the divisor doubled, so the answer halves: 32 ÷ 2
(e)	1,408 ÷ 44	32	both are four times those in (a), so the answer is unchanged

Look at (e) closely. 1,408 is 352 × 4 and 44 is 11 × 4. Both grew by the same amount, so the quotient did not change at all.

352 ÷ 11 = 32
704 ÷ 22 = 32 (both × 2)
1408 ÷ 44 = 32 (both × 4)

The big idea in all of part 5: Division cares about the ratio of the two numbers, not their size. Grow both by the same amount and nothing changes. Grow only one and the answer moves.
Check: 22 × 32 = 704 ✓ 11 × 64 = 704 ✓ 22 × 16 = 352 ✓ 44 × 32 = 1,408 ✓

Q8.

6. A company in Mumbai organises cycle rallies from Mumbai to Panjim, Goa every year. They aim to cover 576 km in 12 days. (a) How much distance should they cycle every day, to cover the distance evenly? (b) After reaching Ratnagiri, they rest for 1 day. How much distance should they cycle each day to reach Goa in 4 days? Assume that they cover the distance evenly.

Answer

(a) 48 km each day. (b) 58 km each day.

(a) The whole rally, 576 km in 12 days.

Step 1: Distance for one day = 576 ÷ 12
Step 2: Split 576 into 480 + 96
Step 3: 480 ÷ 12 = 40 and 96 ÷ 12 = 8
Step 4: 40 + 8 = 48 km per day

(b) The last stretch, Ratnagiri to Goa. Read the map printed in the book. It marks three distances:

Stretch	Distance on the map
Mumbai to Ratnagiri	344 km
Ratnagiri to Goa	232 km
Mumbai to Goa (whole rally)	576 km

Step 1 — check the map adds up:
344 + 232 = 576 ✓

Step 2 — the stretch still to ride is 232 km, in 4 days:
232 ÷ 4
Split 232 into 200 + 32
200 ÷ 4 = 50 and 32 ÷ 4 = 8
50 + 8 = 58 km per day

Why the daily distance goes up: They lose a whole day resting at Ratnagiri, so the days left are fewer. The same distance in fewer days means more cycling each day — 58 km instead of 48 km.

Check by a second route: 12 days × 48 km = 576 km ✓ and 4 days × 58 km = 232 km ✓

Q9.

7. Given below are a few problems. You may need some additional information to solve these. Identify the missing information. Write the missing information and find the answer. (a) A fruit vendor sells 6 baskets of mangoes. Each basket contains 12 mangoes. How much did the vendor earn in total? (b) A school has 8 classrooms, and each classroom has an equal number of desks. How many desks are there in each classroom? (c) Rahul buys 5 cricket bats for his team. The total bill is ₹3500. How much does one bat cost? (d) A restaurant serves 125 plates of idlis in a day. The total earnings from selling all the idli plates is ₹6250. How many idlis are there in each plate?

Answer

For each part, first ask: what number do I need that the question has not given me?

Part	What is missing	A sensible value to add	Answer with that value
(a)	the price of one mango	₹15 per mango	₹1,080
(b)	the total number of desks in the school	96 desks in all	12 desks per classroom
(c)	nothing is missing	—	₹700 per bat
(d)	the price of one idli	₹10 per idli	5 idlis per plate

(a) The mangoes. We can find how many mangoes there are, but not how much money they bring, because no price is given.

Mangoes = 6 baskets × 12 = 72 mangoes
Missing information: the price of one mango
Suppose one mango costs ₹15
Earnings = 72 × 15 = ₹1,080

(b) The desks. We know the number of classrooms but not the number of desks to share out.

Missing information: the total number of desks
Suppose the school has 96 desks
Desks in each classroom = 96 ÷ 8 = 12 desks

(c) The cricket bats. This one is already complete — a trap to keep you reading carefully.

Cost of one bat = 3500 ÷ 5
= ₹700
Check: 5 × ₹700 = ₹3,500 ✓

(d) The idlis. We can find the price of one plate, but not how many idlis sit on it.

Cost of one plate = 6250 ÷ 125 = ₹50
Missing information: the price of one idli
Suppose one idli costs ₹10
Idlis on a plate = 50 ÷ 10 = 5 idlis

Tip: Before you start calculating, list what you are given and what you are asked for. If a number in the answer cannot be built from the numbers given, that number is the missing information.

Q10.

8. To make one bookshelf, a carpenter needs 4 long wooden panels, 8 short wooden panels, 16 small clips, 4 large clips and 32 screws. The carpenter has a stock of 264 long wooden panels, 306 short wooden panels, 2400 small clips, 120 large clips, and 2800 screws. How many bookshelves can the carpenter make? Discuss your thoughts.

Answer

He can make 30 bookshelves.

Work out, for each part separately, how many bookshelves that part alone would allow. Then take the smallest of those numbers, because the first part to run out stops the work.

Part	Needed for 1 shelf	In stock	Division	Shelves possible
Long panels	4	264	264 ÷ 4 = 66	66
Short panels	8	306	306 ÷ 8 = 38 R 2	38
Small clips	16	2,400	2400 ÷ 16 = 150	150
Large clips	4	120	120 ÷ 4 = 30	30 ← smallest
Screws	32	2,800	2800 ÷ 32 = 87 R 16	87

Answer: 30 bookshelves, because the large clips run out first.

Discuss your thoughts — sample answer: Even though the carpenter has plenty of small clips and screws, he only has 120 large clips, and every shelf swallows 4 of them. 120 ÷ 4 = 30, so after 30 shelves there is not a single large clip left. It does not matter that he still has wood and screws — a bookshelf is not finished without its large clips.

What is left over after 30 shelves:

Long panels: 264 − 30 × 4 = 264 − 120 = 144 left
Short panels: 306 − 30 × 8 = 306 − 240 = 66 left
Small clips: 2400 − 30 × 16 = 2400 − 480 = 1,920 left
Large clips: 120 − 30 × 4 = 0 left
Screws: 2800 − 30 × 32 = 2800 − 960 = 1,840 left

The idea to remember: When several things are needed together, the smallest answer decides. This is the same as making tea for guests — plenty of tea leaves is no help if you have only 3 cups.

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