The Cleanest Village

Given: Cost = ₹185, Paid = ₹200

Formula: Balance = Paid − Cost

$$200 - 185 = 15$$

Balance = ₹15

Given: Paid = ₹200, Balance = ₹0

Formula: Cost = Paid − Balance

$$200 - 0 = 200$$

Cost = ₹200

Given: Cost = ₹435, Paid = ₹500

Formula: Balance = Paid − Cost

$$500 - 435 = 65$$

Balance = ₹65

Given: Cost = ₹149, Paid = ₹500

Formula: Balance = Paid − Cost

$$500 - 149 = 351$$

Balance = ₹351

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

Given: Paid = ₹200, Balance = ₹75

Formula: Cost = Paid − Balance

$$200 - 75 = 125$$

Cost = ₹125

Given: Cost = ₹580, Balance = ₹120

Formula: Paid = Cost + Balance

$$580 + 120 = 700$$

Paid = ₹700

This is an open-ended question. Students may fill in any valid combination where:

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

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

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

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.

Step 1: Find the cost of 2 oranges.

Cost of 1 orange = ₹21

Cost of 2 oranges = $$21 \times 2 = ₹42$$

Step 2: Find each child's balance.

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

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

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

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

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

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 = $$1+2+3+4+5+6 = 21$$

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

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

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

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

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

Concept: Each side sums to 10, 3 sides: Total counted = $$10 \times 3 = 30$$

Sum of corner numbers = $$30 - 21 = 9$$

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

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

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

Try corners 1, 3, 5 ($1+3+5=9$):
- Side with 1 and 3: middle = $10-1-3=6$ ✓
- Side with 3 and 5: middle = $10-3-5=2$ ✓
- Side with 1 and 5: middle = $10-1-5=4$ ✓

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).

Finding possible sums:

For a sum $S$ on each side:
- Sum of corner numbers = $3S - 21$
- Corner numbers must be 3 distinct numbers from 1–6 with sum = $3S - 21$
- Minimum sum of 3 numbers from 1–6 = $1+2+3=6$, so $3S-21 \geq 6 \Rightarrow S \geq 9$
- Maximum sum of 3 numbers from 1–6 = $4+5+6=15$, so $3S-21 \leq 15 \Rightarrow S \leq 12$

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

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

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

Given: Teachers from School 1 = 24, Teachers from School 2 = 28

Total teachers = $$24 + 28 = 52$$

There are 52 teachers accompanying the children.

Given: Children from School 1 = 438, Children from School 2 = 476

Total children:
$$438 + 476$$

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

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

914 children are going on the trip.

Rounding to nearest hundred:

$438 \approx 400$ and $476 \approx 500$

$$400 + 500 = 900$$

Estimated number of children ≈ 900

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

Given: Cost of large piece = ₹38, Cost of small piece = ₹16

Total spent:
$$38 + 16$$

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

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

They spent ₹54 on pusaw.

Given: Money in piggy bank = ₹185, Money from mother = ₹125

Total money for trip:
$$185 + 125$$

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

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

Daisy and Lou took ₹310 for the trip.

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

Total boys = $78 + 532$
$$\begin{array}{r} 532 \\ +78 \\ \hline 610 \end{array}$$
Ones: $2+8=10$, write 0 carry 1; Tens: $3+7+1=11$, write 1 carry 1; Hundreds: $5+0+1=6$
Total boys = 610

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

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

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

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

$$\begin{array}{r} 654 \\ +95 \\ \hline 749 \end{array}$$
Ones: $4+5=9$; Tens: $5+9=14$, write 4 carry 1; Hundreds: $6+0+1=7$
Answer: 749

$$\begin{array}{r} 286 \\ +123 \\ \hline 409 \end{array}$$
Ones: $6+3=9$; Tens: $8+2=10$, write 0 carry 1; Hundreds: $2+1+1=4$
Answer: 409

$$\begin{array}{r} 476 \\ +324 \\ \hline 800 \end{array}$$
Ones: $6+4=10$, write 0 carry 1; Tens: $7+2+1=10$, write 0 carry 1; Hundreds: $4+3+1=8$
Answer: 800

$$\begin{array}{r} 534 \\ +483 \\ \hline 1017 \end{array}$$
Ones: $4+3=7$; Tens: $3+8=11$, write 1 carry 1; Hundreds: $5+4+1=10$
Answer: 1017

Given: Preeti's school = 423 children; Cousin's school has 178 more children.

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

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

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

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

Given: Dolls made = 639, Dolls sold = 531

Dolls left = $639 - 531$

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

Ones: $9-1=8$; Tens: $3-3=0$; Hundreds: $6-5=1$

Estimate: $639 \approx 600$, $531 \approx 500$; $600-500=100$ ≈ 108 ✓

Number of dolls left = 108

$$\begin{array}{r} 83 \\ -29 \\ \hline 54 \end{array}$$
Ones: $3-9$ not possible, regroup: $13-9=4$; Tens: $7-2=5$
Answer: 54

$$\begin{array}{r} 345 \\ -123 \\ \hline 222 \end{array}$$
Ones: $5-3=2$; Tens: $4-2=2$; Hundreds: $3-1=2$
Answer: 222

$$\begin{array}{r} 763 \\ -437 \\ \hline 326 \end{array}$$
Ones: $3-7$ not possible, regroup: $13-7=6$; Tens: $5-3=2$; Hundreds: $7-4=3$
Answer: 326

$$\begin{array}{r} 803 \\ -350 \\ \hline 453 \end{array}$$
Ones: $3-0=3$; Tens: $0-5$ not possible, regroup from hundreds: $10-5=5$; Hundreds: $7-3=4$
Answer: 453

$$\begin{array}{r} 900 \\ -328 \\ \hline 572 \end{array}$$
Ones: $0-8$ not possible, regroup (borrow from tens, but tens is 0 too, so borrow from hundreds): $10-8=2$; Tens: $9-2-1=6$...

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

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

Rami's pages: 236

Kesu's pages: $96 + 30 + 90$
$$96 + 30 = 126$$
$$126 + 90 = 216$$

Kesu read 216 pages.

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

$$236 - 216 = 20$$

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

Given: Total pages = 128, Pages read = 23

Pages left = $128 - 23$

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

Ones: $8-3=5$; Tens: $2-2=0$; Hundreds: $1-0=1$

105 more pages are left to complete the book.

Step 1: Total pages of all books.
$$179 + 236 + 30 + 96 + 90 + 128$$
$$= 179 + 236 = 415$$
$$415 + 30 = 445$$
$$445 + 96 = 541$$
$$541 + 90 = 631$$
$$631 + 128 = 759$$
Total pages = 759

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

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

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

Jaggu has to read 434 more pages.

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.

Note: Exact numbers depend on the figure (img_28) not visible here.

General method: People who got off at Aligarh = Passengers on train arriving at Aligarh − Passengers remaining after Aligarh stop

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

Note: Exact numbers depend on the figure (img_28) not visible here.

General method: Compare the number of passengers at New Delhi and at Aligarh, then subtract the smaller from the larger to find the difference.

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

Note: Exact numbers depend on the figure (img_28) not visible here.

General method: Total people who travelled = sum of all passengers who boarded the train at each station.

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

$$\begin{array}{r} 452 \\ +89 \\ \hline 541 \end{array}$$

Ones: $2+9=11$, write 1 carry 1
Tens: $5+8+1=14$, write 4 carry 1
Hundreds: $4+0+1=5$

Answer: 541

$$\begin{array}{r} 641 \\ -273 \\ \hline 368 \end{array}$$

Ones: $1-3$ not possible, regroup: $11-3=8$; Tens: $3-7$ not possible (after giving 1), regroup: $13-7=6$; Hundreds: $5-2=3$

Answer: 368

$$\begin{array}{r} 943 \\ +38 \\ \hline 981 \end{array}$$
Ones: $3+8=11$, write 1 carry 1; Tens: $4+3+1=8$; Hundreds: $9+0=9$
Answer: 981

$$\begin{array}{r} 465 \\ +305 \\ \hline 770 \end{array}$$
Ones: $5+5=10$, write 0 carry 1; Tens: $6+0+1=7$; Hundreds: $4+3=7$
Answer: 770

$$\begin{array}{r} 435 \\ +462 \\ \hline 897 \end{array}$$
Ones: $5+2=7$; Tens: $3+6=9$; Hundreds: $4+4=8$
Answer: 897

$$\begin{array}{r} 764 \\ -657 \\ \hline 107 \end{array}$$
Ones: $4-7$ not possible, regroup: $14-7=7$; Tens: $5-5-1=$ wait — $5-1=4$ (after giving 1 to ones), $4-5$ not possible, regroup: $14-5=9$...

Let me redo:
Ones: $4-7$, regroup from tens: $14-7=7$, tens becomes $6-1=5$
Tens: $5-5=0$... wait tens digit of 764 is 6, after giving 1 it is 5; tens digit of 657 is 5; $5-5=0$
Hundreds: $7-6=1$

Answer: 107

$$\begin{array}{r} 518 \\ -209 \\ \hline 309 \end{array}$$
Ones: $8-9$ not possible, regroup: $18-9=9$; Tens: $0-0=0$ (after giving 1, tens of 518 becomes 0); Hundreds: $5-2=3$

Wait: tens of 518 is 1, after giving 1 to ones it becomes 0; tens of 209 is 0; $0-0=0$; Hundreds: $5-2=3$

Answer: 309

$$\begin{array}{r} 879 \\ -53 \\ \hline 826 \end{array}$$
Ones: $9-3=6$; Tens: $7-5=2$; Hundreds: $8-0=8$
Answer: 826

Sum = 856:
Many possibilities. One example:
$$400 + 456 = 856$$
Another: $500 + 356 = 856$

Difference = 563:
Many possibilities. One example:
$$800 - 237 = 563$$
Another: $700 - 137 = 563$

Sample word problem for sum:
A library has 400 English books and 456 Hindi books. How many books are there in all?
Answer: $400 + 456 = 856$ books.

Sample word problem for difference:
A farmer harvested 800 kg of wheat. He sold 237 kg. How much wheat is left?
Answer: $800 - 237 = 563$ kg.

Note: The grid values are shown in figure (img_36) which is not fully visible.

General method: Look at all adjacent pairs (horizontal and vertical) in the grid, add each pair, and identify the pair with the largest sum.

Students should identify the two largest numbers that are adjacent in the grid and add them to find the greatest sum.

Note: The grid values are shown in figure (img_36) which is not fully visible.

General method: Look at all adjacent pairs in the grid, add each pair, and identify the pair with the smallest sum.

Students should identify the two smallest numbers that are adjacent in the grid and add them to find the smallest sum.

Note: The grid values are shown in figure (img_36) which is not fully visible.

General method: Look at all adjacent pairs in the grid, subtract the smaller from the larger, and identify the pair with the greatest difference.

Students should find the adjacent pair where one number is as large as possible and the other as small as possible.

Note: The grid values are shown in figure (img_36) which is not fully visible.

General method: Look at all adjacent pairs in the grid, subtract the smaller from the larger, and identify the pair with the smallest difference (closest in value).

Students should find the adjacent pair whose values are closest to each other.

Puzzle 1 (Addition):
$$\begin{array}{r} \square 16 \\ +\square 2\square \\ \hline 503 \end{array}$$

Ones: $6 + \square = 3$ → not possible without carry; try $6+7=13$, write 3 carry 1 → middle number's ones digit = 7
Tens: $1+2+1=4$... but we need 0 in tens of answer. Try: $1+\square+1=10$ → $\square=8$, write 0 carry 1
Hundreds: $\square+\square+1=5$

If first number is $\mathbf{416}$ and second is $\mathbf{87}$: $416+87=503$ ✓

Answer for Puzzle 1: $416 + 87 = 503$

Puzzle 2 (Addition):
$$\begin{array}{r} 132 \\ +88\square \\ \hline 890 \end{array}$$

Ones: $2+\square=0$ → $\square=8$ (with carry: $2+8=10$, write 0 carry 1)
Tens: $3+8+1=12$, write 2... but answer tens = 9. Try $132+758=890$: $2+8=10$✓, $3+5+1=9$✓, $1+7=8$✓

Answer for Puzzle 2: $132 + 758 = 890$

Note: Students should verify by substituting back into the original puzzle format from their textbook, as the exact layout of missing digits depends on the printed table.

$$\begin{array}{r} 489 \\ +23 \\ \hline 512 \end{array}$$
Ones: $9+3=12$, write 2 carry 1; Tens: $8+2+1=11$, write 1 carry 1; Hundreds: $4+0+1=5$
Answer: 512

$$\begin{array}{r} 105 \\ +295 \\ \hline 400 \end{array}$$
Ones: $5+5=10$, write 0 carry 1; Tens: $0+9+1=10$, write 0 carry 1; Hundreds: $1+2+1=4$
Answer: 400

$$\begin{array}{r} 630 \\ +56 \\ \hline 686 \end{array}$$
Ones: $0+6=6$; Tens: $3+5=8$; Hundreds: $6+0=6$
Answer: 686

$$\begin{array}{r} 35 \\ +99 \\ \hline 134 \end{array}$$
Ones: $5+9=14$, write 4 carry 1; Tens: $3+9+1=13$, write 3 carry 1; Hundreds: $0+0+1=1$
Answer: 134

$$\begin{array}{r} 409 \\ +387 \\ \hline 796 \end{array}$$
Ones: $9+7=16$, write 6 carry 1; Tens: $0+8+1=9$; Hundreds: $4+3=7$
Answer: 796

$$\begin{array}{r} 67 \\ +76 \\ \hline 143 \end{array}$$
Ones: $7+6=13$, write 3 carry 1; Tens: $6+7+1=14$, write 4 carry 1; Hundreds: $0+0+1=1$
Answer: 143

$$\begin{array}{r} 580 \\ +207 \\ \hline 787 \end{array}$$
Ones: $0+7=7$; Tens: $8+0=8$; Hundreds: $5+2=7$
Answer: 787

$$\begin{array}{r} 333 \\ +666 \\ \hline 999 \end{array}$$
Ones: $3+6=9$; Tens: $3+6=9$; Hundreds: $3+6=9$
Answer: 999

$$\begin{array}{r} 826 \\ +268 \\ \hline 1094 \end{array}$$
Ones: $6+8=14$, write 4 carry 1; Tens: $2+6+1=9$; Hundreds: $8+2=10$, write 0 carry 1; Thousands: $0+0+1=1$
Answer: 1094

$$\begin{array}{r} 300 \\ -45 \\ \hline 255 \end{array}$$
Ones: $0-5$, regroup (borrow from tens, but tens=0, so borrow from hundreds): $10-5=5$; Tens: $9-4=5$ (after regrouping, hundreds becomes 2, tens becomes 9); Hundreds: $2$
Answer: 255

$$\begin{array}{r} 962 \\ -268 \\ \hline 694 \end{array}$$
Ones: $2-8$, regroup: $12-8=4$; Tens: $5-6$, regroup: $15-6=9$; Hundreds: $8-2=6$
Answer: 694

$$\begin{array}{r} 706 \\ -209 \\ \hline 497 \end{array}$$
Ones: $6-9$, regroup: $16-9=7$; Tens: $0-1-0$... after giving 1 to ones, tens of 706 = 0; $0-0=0$... but we need to borrow from hundreds: tens becomes 9 (after borrowing from hundreds which becomes 6); $9-0=9$...

Redo carefully: 706 → ones=6, tens=0, hundreds=7
Ones: $6-9$ impossible, borrow from tens. Tens=0, so borrow from hundreds: hundreds becomes 6, tens becomes 10. Now borrow from tens for ones: tens becomes 9, ones becomes 16.
Ones: $16-9=7$; Tens: $9-0=9$; Hundreds: $6-2=4$
Answer: 497

$$\begin{array}{r} 842 \\ -387 \\ \hline 455 \end{array}$$
Ones: $2-7$, regroup: $12-7=5$; Tens: $3-8$, regroup: $13-8=5$; Hundreds: $7-3=4$
Answer: 455

$$\begin{array}{r} 674 \\ -76 \\ \hline 598 \end{array}$$
Ones: $4-6$, regroup: $14-6=8$; Tens: $6-7-1=$ regroup: $16-7=9$... wait: tens of 674 is 7, after giving 1 to ones it is 6; $6-7$ impossible, regroup: $16-7=9$; Hundreds: $5-0=5$
Answer: 598

$$\begin{array}{r} 754 \\ -409 \\ \hline 345 \end{array}$$
Ones: $4-9$, regroup: $14-9=5$; Tens: $4-0-1=3$ (after giving 1 to ones, tens of 754 = 4; $4-0=4$... wait tens of 754 is 5, after giving 1 it is 4; $4-0=4$);

Redo: 754: H=7, T=5, O=4
Ones: $4-9$ impossible, regroup: O=14, T=4; $14-9=5$
Tens: $4-0=4$
Hundreds: $7-4=3$
Answer: 345

$$\begin{array}{r} 403 \\ -245 \\ \hline 158 \end{array}$$
Ones: $3-5$, regroup (tens=0, borrow from hundreds): H=3, T=10, then borrow for ones: T=9, O=13; $13-5=8$
Tens: $9-4=5$
Hundreds: $3-2=1$
Answer: 158

$$\begin{array}{r} 600 \\ -384 \\ \hline 216 \end{array}$$
Ones: $0-4$, regroup (tens=0, borrow from hundreds): H=5, T=10, borrow for ones: T=9, O=10; $10-4=6$
Tens: $9-8=1$
Hundreds: $5-3=2$
Answer: 216

$$\begin{array}{r} 546 \\ -538 \\ \hline 8 \end{array}$$
Ones: $6-8$, regroup: $16-8=8$; Tens: $3-3-1=$ (after giving 1 to ones, tens of 546 = 3; $3-3=0$); Hundreds: $5-5=0$
Answer: 8