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NCERT Solutions

The Cleanest Village

CBSE · Class 4 · Mathematics

NCERT Solutions for The Cleanest Village — CBSE Class 4 Mathematics.

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71 Questions Solved · 15 Sections

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Balance Problems (Finding Missing Numbers)

1Cost: ₹185, Paid: ₹200, Balance: ?Show solution
Given: Cost = ₹185, Paid = ₹200

Formula: Balance = Paid − Cost

200−185=15200 - 185 = 15

Balance = ₹15

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2Cost: ?, Paid: ₹200, Balance: ₹0Show solution
Given: Paid = ₹200, Balance = ₹0

Formula: Cost = Paid − Balance

200−0=200200 - 0 = 200

Cost = ₹200

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3Cost: ₹435, Paid: ₹500, Balance: ?Show solution
Given: Cost = ₹435, Paid = ₹500

Formula: Balance = Paid − Cost

500−435=65500 - 435 = 65

Balance = ₹65

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4Cost: ₹149, Paid: ₹500, Balance: ?Show solution
Given: Cost = ₹149, Paid = ₹500

Formula: Balance = Paid − Cost

500−149=351500 - 149 = 351

Balance = ₹351

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5Cost: ₹46, Paid: ?, Balance: ?Show solution
Given: Cost = ₹46

This problem has multiple valid answers depending on the note paid. One common possibility:

If Paid = ₹50, then Balance = ₹50 − ₹46 = ₹4

If Paid = ₹100, then Balance = ₹100 − ₹46 = ₹54

One valid answer: Paid = ₹50, Balance = ₹4

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6Cost: ?, Paid: ₹200, Balance: ₹75Show solution
Given: Paid = ₹200, Balance = ₹75

Formula: Cost = Paid − Balance

200−75=125200 - 75 = 125

Cost = ₹125

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7Cost: ₹580, Paid: ?, Balance: ₹120Show solution
Given: Cost = ₹580, Balance = ₹120

Formula: Paid = Cost + Balance

580+120=700580 + 120 = 700

Paid = ₹700

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8Cost: ?, Paid: ?, Balance: ? (open-ended)Show solution
This is an open-ended question. Students may fill in any valid combination where:

Balance=Paid−Cost\text{Balance} = \text{Paid} - \text{Cost}

For example: Cost = ₹250, Paid = ₹500, Balance = ₹250

Any correct combination satisfying Balance = Paid − Cost is acceptable.

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Their mother buys things for ₹163

1Their mother buys things for ₹163. What might she have bought? There is more than one possibility.Show solution
Given: Total amount spent = ₹163

We need to find combinations of items that add up to ₹163. (Prices are based on the price list shown in the chapter.)

Possibility 1: 2 kg of beans (assume ₹80) + 1 kg of onion and 1 kg of potato (assume ₹83) = ₹163

Possibility 2: Any other combination of items from the price list that totals ₹163.

Note: Students should refer to the price list in their textbook and find at least two different combinations of items whose total cost equals ₹163.

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A Strange Puzzle — Balance for each child buying 2 oranges at ₹21 each

1Each orange costs ₹21. Each child buys 2 oranges. Krishna paid ₹50, Sudama paid ₹100, Mala paid ₹200, Neela paid ₹500. Find the balance each child received.Show solution
Step 1: Find the cost of 2 oranges.

Cost of 1 orange = ₹21

Cost of 2 oranges = 21×2=₹4221 \times 2 = ₹42

Step 2: Find each child's balance.

Krishna:
Paid = ₹50
Balance=50−42=₹8\text{Balance} = 50 - 42 = ₹8

Sudama:
Paid = ₹100
Balance=100−42=₹58\text{Balance} = 100 - 42 = ₹58

Mala:
Paid = ₹200
Balance=200−42=₹158\text{Balance} = 200 - 42 = ₹158

Neela:
Paid = ₹500
Balance=500−42=₹458\text{Balance} = 500 - 42 = ₹458

Summary:
| Child | Paid | Balance |
|-------|------|---------|
| Krishna | ₹50 | ₹8 |
| Sudama | ₹100 | ₹58 |
| Mala | ₹200 | ₹158 |
| Neela | ₹500 | ₹458 |

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Let Us Play — Triangle Number Puzzle

1Place the numbers 1–6 in the blanks such that the sum on each side of the triangle is 9. No numbers should be repeated.Show solution
Concept: In a triangle with 3 corners and 3 sides, each number at a corner is counted twice (once for each side it belongs to).

Sum of all numbers 1 to 6 = 1+2+3+4+5+6=211+2+3+4+5+6 = 21

If each side sums to 9 and there are 3 sides: Total counted = 9×3=279 \times 3 = 27

Since corner numbers are counted twice: Sum of corner numbers = 27−21=627 - 21 = 6

So the three corner numbers must add up to 6. One possibility: corners = 1, 2, 3 (since 1+2+3=61+2+3=6).

Place 1, 2, 3 at the corners. Then fill the sides:
- Side with corners 1 and 2: middle number = 9−1−2=69 - 1 - 2 = 6
- Side with corners 2 and 3: middle number = 9−2−3=49 - 2 - 3 = 4
- Side with corners 1 and 3: middle number = 9−1−3=59 - 1 - 3 = 5

Answer: Corners: 1, 2, 3; Middle of sides: 6, 4, 5 (each side sums to 9).

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2Use the same numbers 1–6 and make the sum 10 on each side of the triangle.Show solution
Concept: Each side sums to 10, 3 sides: Total counted = 10×3=3010 \times 3 = 30

Sum of corner numbers = 30−21=930 - 21 = 9

Three numbers from 1–6 that add to 9: e.g., 2, 3, 4 (since 2+3+4=92+3+4=9).

Place 2, 3, 4 at the corners. Fill the sides:
- Side with corners 2 and 3: middle = 10−2−3=510 - 2 - 3 = 5
- Side with corners 3 and 4: middle = 10−3−4=310 - 3 - 4 = 3... (3 is already used)

Try corners 1, 2, 6 (1+2+6=91+2+6=9):
- Side with 1 and 2: middle = 10−1−2=710-1-2=7... 7 is not in 1–6.

Try corners 1, 3, 5 (1+3+5=91+3+5=9):
- Side with 1 and 3: middle = 10−1−3=610-1-3=6 ✓
- Side with 3 and 5: middle = 10−3−5=210-3-5=2 ✓
- Side with 1 and 5: middle = 10−1−5=410-1-5=4 ✓

All numbers used: corners 1, 3, 5 and middles 6, 2, 4 — all six numbers 1–6 used once.

Answer: Corners: 1, 3, 5; Middle of sides: 6, 2, 4 (each side sums to 10).

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3What other sums can you make with these 6 numbers? Can you make 12 on each side? Can you make 13?Show solution
Finding possible sums:

For a sum SS on each side:
- Sum of corner numbers = 3S−213S - 21
- Corner numbers must be 3 distinct numbers from 1–6 with sum = 3S−213S - 21
- Minimum sum of 3 numbers from 1–6 = 1+2+3=61+2+3=6, so 3S−21≥6⇒S≥93S-21 \geq 6 \Rightarrow S \geq 9
- Maximum sum of 3 numbers from 1–6 = 4+5+6=154+5+6=15, so 3S−21≤15⇒S≤123S-21 \leq 15 \Rightarrow S \leq 12

So possible sums are 9, 10, 11, and 12.

Sum = 12: Corner sum = 3(12)−21=153(12)-21=15, so corners = 4, 5, 6.
- Side with 4 and 5: middle = 12−4−5=312-4-5=3 ✓
- Side with 5 and 6: middle = 12−5−6=112-5-6=1 ✓
- Side with 4 and 6: middle = 12−4−6=212-4-6=2 ✓
Yes, sum of 12 is possible.

Sum = 13: Corner sum = 3(13)−21=183(13)-21=18, but maximum sum of 3 numbers from 1–6 is 15. So sum of 13 is NOT possible.

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Add Up — Teachers and Children on the Trip

124 teachers and 438 children are going from one school. 476 children and 28 teachers are going from a neighbourhood school. How many teachers are accompanying the children?Show solution
Given: Teachers from School 1 = 24, Teachers from School 2 = 28

Total teachers = 24+28=5224 + 28 = 52

There are 52 teachers accompanying the children.

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2How many children are going on the trip? (438 children from one school and 476 from another)Show solution
Given: Children from School 1 = 438, Children from School 2 = 476

Total children:
438+476438 + 476

Column addition:
438+476914\begin{array}{r} 438 \\ +476 \\ \hline 914 \end{array}

Ones: 8+6=148+6=14, write 4 carry 1
Tens: 3+7+1=113+7+1=11, write 1 carry 1
Hundreds: 4+4+1=94+4+1=9

914 children are going on the trip.

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3Estimate the number of children going on the trip (438 + 476).Show solution
Rounding to nearest hundred:

438≈400438 \approx 400 and 476≈500476 \approx 500

400+500=900400 + 500 = 900

Estimated number of children ≈ 900

(Actual answer is 914, which is close to the estimate.)

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Pusaw Problem

1Daisy and Lou ate one large piece of pusaw for ₹38. They bought another small piece for ₹16. How much did they spend on pusaw?Show solution
Given: Cost of large piece = ₹38, Cost of small piece = ₹16

Total spent:
38+1638 + 16

38+1654\begin{array}{r} 38 \\ +16 \\ \hline 54 \end{array}

Ones: 8+6=148+6=14, write 4 carry 1
Tens: 3+1+1=53+1+1=5

They spent ₹54 on pusaw.

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Piggy Bank Problem

1Daisy and Lou had ₹185 in their piggy bank. Their mother gave them ₹125 more. How much money did they take for the trip?Show solution
Given: Money in piggy bank = ₹185, Money from mother = ₹125

Total money for trip:
185+125185 + 125

185+125310\begin{array}{r} 185 \\ +125 \\ \hline 310 \end{array}

Ones: 5+5=105+5=10, write 0 carry 1
Tens: 8+2+1=118+2+1=11, write 1 carry 1
Hundreds: 1+1+1=31+1+1=3

Daisy and Lou took ₹310 for the trip.

Estimate: 185≈200185 \approx 200, 125≈100125 \approx 100; 200+100=300200+100=300 ≈ ₹300 (close to actual ₹310).

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Let Us Do — Exercise Questions

1In Kalakshitij, Boys: 78 tabla players and 532 singers. Girls: 95 tabla players and 346 singers. Find total boys, total girls, total tabla players, total singers. Also, 15 more girls join to play tabla — how many girls play tabla now?Show solution
Total boys = 78+53278 + 532
532+78610\begin{array}{r} 532 \\ +78 \\ \hline 610 \end{array}
Ones: 2+8=102+8=10, write 0 carry 1; Tens: 3+7+1=113+7+1=11, write 1 carry 1; Hundreds: 5+0+1=65+0+1=6
Total boys = 610

Total girls = 95+34695 + 346
346+95441\begin{array}{r} 346 \\ +95 \\ \hline 441 \end{array}
Ones: 6+5=116+5=11, write 1 carry 1; Tens: 4+9+1=144+9+1=14, write 4 carry 1; Hundreds: 3+0+1=43+0+1=4
Total girls = 441

Total tabla players = 78+9578 + 95
78+95173\begin{array}{r} 78 \\ +95 \\ \hline 173 \end{array}
Ones: 8+5=138+5=13, write 3 carry 1; Tens: 7+9+1=177+9+1=17
Total tabla players = 173

Total singers = 532+346532 + 346
532+346878\begin{array}{r} 532 \\ +346 \\ \hline 878 \end{array}
Total singers = 878

Girls playing tabla after 15 more join = 95+15=11095 + 15 = 110
110 girls play tabla now.

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2aAdd: 32 + 47Show solution
32+4779\begin{array}{r} 32 \\ +47 \\ \hline 79 \end{array}
Answer: 79

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2bAdd: 654 + 95Show solution
654+95749\begin{array}{r} 654 \\ +95 \\ \hline 749 \end{array}
Ones: 4+5=94+5=9; Tens: 5+9=145+9=14, write 4 carry 1; Hundreds: 6+0+1=76+0+1=7
Answer: 749

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2cAdd: 286 + 123Show solution
286+123409\begin{array}{r} 286 \\ +123 \\ \hline 409 \end{array}
Ones: 6+3=96+3=9; Tens: 8+2=108+2=10, write 0 carry 1; Hundreds: 2+1+1=42+1+1=4
Answer: 409

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2dAdd: 476 + 324Show solution
476+324800\begin{array}{r} 476 \\ +324 \\ \hline 800 \end{array}
Ones: 6+4=106+4=10, write 0 carry 1; Tens: 7+2+1=107+2+1=10, write 0 carry 1; Hundreds: 4+3+1=84+3+1=8
Answer: 800

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2eAdd: 700 + 289Show solution
700+289989\begin{array}{r} 700 \\ +289 \\ \hline 989 \end{array}
Answer: 989

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2fAdd: 534 + 483Show solution
534+4831017\begin{array}{r} 534 \\ +483 \\ \hline 1017 \end{array}
Ones: 4+3=74+3=7; Tens: 3+8=113+8=11, write 1 carry 1; Hundreds: 5+4+1=105+4+1=10
Answer: 1017

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3Preeti's school has 423 children. Her school has 178 children less than her cousin's school. How many children study in Preeti's cousin's school?Show solution
Given: Preeti's school = 423 children; Cousin's school has 178 more children.

Children in cousin's school = 423+178423 + 178

423+178601\begin{array}{r} 423 \\ +178 \\ \hline 601 \end{array}

Ones: 3+8=113+8=11, write 1 carry 1; Tens: 2+7+1=102+7+1=10, write 0 carry 1; Hundreds: 4+1+1=64+1+1=6

601 children study in Preeti's cousin's school.

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Subtract It — Worked Examples and Problems

4During Gombe Habba, Ranganna made 639 dolls and sold 531. How many dolls are left?Show solution
Given: Dolls made = 639, Dolls sold = 531

Dolls left = 639−531639 - 531

639−531108\begin{array}{r} 639 \\ -531 \\ \hline 108 \end{array}

Ones: 9−1=89-1=8; Tens: 3−3=03-3=0; Hundreds: 6−5=16-5=1

Estimate: 639≈600639 \approx 600, 531≈500531 \approx 500; 600−500=100600-500=100 ≈ 108 ✓

Number of dolls left = 108

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5aSubtract: 83 – 29Show solution
83−2954\begin{array}{r} 83 \\ -29 \\ \hline 54 \end{array}
Ones: 3−93-9 not possible, regroup: 13−9=413-9=4; Tens: 7−2=57-2=5
Answer: 54

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5bSubtract: 345 – 123Show solution
345−123222\begin{array}{r} 345 \\ -123 \\ \hline 222 \end{array}
Ones: 5−3=25-3=2; Tens: 4−2=24-2=2; Hundreds: 3−1=23-1=2
Answer: 222

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5cSubtract: 763 – 437Show solution
763−437326\begin{array}{r} 763 \\ -437 \\ \hline 326 \end{array}
Ones: 3−73-7 not possible, regroup: 13−7=613-7=6; Tens: 5−3=25-3=2; Hundreds: 7−4=37-4=3
Answer: 326

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5dSubtract: 803 – 350Show solution
803−350453\begin{array}{r} 803 \\ -350 \\ \hline 453 \end{array}
Ones: 3−0=33-0=3; Tens: 0−50-5 not possible, regroup from hundreds: 10−5=510-5=5; Hundreds: 7−3=47-3=4
Answer: 453

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5eSubtract: 900 – 328Show solution
900−328572\begin{array}{r} 900 \\ -328 \\ \hline 572 \end{array}
Ones: 0−80-8 not possible, regroup (borrow from tens, but tens is 0 too, so borrow from hundreds): 10−8=210-8=2; Tens: 9−2−1=69-2-1=6...

Step by step: Regroup 900 as 8 hundreds, 9 tens, 10 ones.
Ones: 10−8=210-8=2; Tens: 9−2=79-2=7...

Actually: 900 → regroup to 8H 10T 0O → regroup to 8H 9T 10O
Ones: 10−8=210-8=2; Tens: 9−2=79-2=7; Hundreds: 8−3=58-3=5
Answer: 572

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Let Us Solve — Library Books

1aRami read Panchatantra Tales (236 pages). Kesu read Akbar Birbal (96), Karadi Tales (30) and Blue Umbrella (90). Who read more? How many more pages?Show solution
Rami's pages: 236

Kesu's pages: 96+30+9096 + 30 + 90
96+30=12696 + 30 = 126
126+90=216126 + 90 = 216

Kesu read 216 pages.

Comparison: Rami read 236 pages, Kesu read 216 pages.

236−216=20236 - 216 = 20

Rami read more. Rami read 20 more pages than Kesu.

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1bSumi has read 23 pages of Adventures of Feluda (128 pages). How many more pages are left?Show solution
Given: Total pages = 128, Pages read = 23

Pages left = 128−23128 - 23

128−23105\begin{array}{r} 128 \\ -23 \\ \hline 105 \end{array}

Ones: 8−3=58-3=5; Tens: 2−2=02-2=0; Hundreds: 1−0=11-0=1

105 more pages are left to complete the book.

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1cJaggu decides to read all books. Total pages of all books = 179+236+30+96+90+128. He has finished Swami and Friends (179), Akbar Birbal (96) and 50 pages of Feluda. How many more pages does he have to read?Show solution
Step 1: Total pages of all books.
179+236+30+96+90+128179 + 236 + 30 + 96 + 90 + 128
=179+236=415= 179 + 236 = 415
415+30=445415 + 30 = 445
445+96=541445 + 96 = 541
541+90=631541 + 90 = 631
631+128=759631 + 128 = 759
Total pages = 759

Step 2: Pages already read.
Swami and Friends = 179
Akbar Birbal = 96
50 pages of Feluda = 50
179+96+50=325179 + 96 + 50 = 325

Step 3: Pages left to read.
759−325=434759 - 325 = 434

759−325434\begin{array}{r} 759 \\ -325 \\ \hline 434 \end{array}

Jaggu has to read 434 more pages.

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Let Us Solve — Train Problem

2aHow many passengers are there on the train when it leaves Dadri? (Based on the train picture — assuming the picture shows passengers boarding/alighting at each station. Note: exact numbers depend on the figure which cannot be seen. Solution uses typical textbook values.)Show solution
Note: The exact numbers at each station are shown in the figure (img_28) which is not visible here. Students should refer to their textbook figure.

General method: Passengers when leaving Dadri = (Passengers when arriving at Dadri) + (Passengers who boarded at Dadri) − (Passengers who got off at Dadri)

Students should substitute the values from the figure and compute accordingly.

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2bFind the number of people who got off the train at Aligarh.
2cWere there more people on the train in New Delhi or in Aligarh? How much more/less?
2dHow many people travelled altogether by the train?

Let Us Solve — Column Addition and Subtraction

aAdd: 452 + 89 (H T O format)
bSubtract: 641 – 273 (H T O format)
d1Add: 38 + 943
d2Add: 465 + 305
d3Add: 435 + 462
d4Subtract: 764 – 657
d5Subtract: 518 – 209
d6Subtract: 879 – 53
eFind two numbers such that their sum is 856. Find another two numbers such that their difference is 563. Make your own word problems with these numbers.

Number Pair Hunt

1Find the number pair whose sum is the greatest.
2Find the number pair whose sum is the smallest.
3Find the number pair whose difference is the greatest.
4Find the number pair whose difference is the smallest.

The Missing Digits

1Fill the missing digits to make each sum correct. (Two addition puzzles and subtraction puzzles as shown in the table.)

Let Us Do — Final Practice

1aAdd: 23 + 489
1bAdd: 105 + 295
1cAdd: 630 + 56
1dAdd: 35 + 99
1eAdd: 409 + 387
1fAdd: 67 + 76
1gAdd: 580 + 207
1hAdd: 333 + 666
1iAdd: 826 + 268
2aSubtract: 300 – 45
2bSubtract: 962 – 268
2cSubtract: 706 – 209
2dSubtract: 842 – 387
2eSubtract: 674 – 76
2fSubtract: 754 – 409
2gSubtract: 403 – 245
2hSubtract: 600 – 384
2iSubtract: 546 – 538

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Frequently Asked Questions

What are the important topics in The Cleanest Village for CBSE Class 4 Mathematics?
The Cleanest Village covers several key topics that are frequently asked in CBSE Class 4 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in The Cleanest Village — CBSE Class 4 Mathematics?
Understand the core concepts first, then work through the 40 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
Where can I get free NCERT Solutions for The Cleanest Village Class 4 Mathematics?
This page has free step-by-step NCERT Solutions for every exercise question in The Cleanest Village (CBSE Class 4 Mathematics) — written the way examiners award marks: given, formula, working, answer.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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