“We the Travellers I Ncert Solutions Chapter 1 Class 5” is our little help to teachers, parents, and students regarding ready-to-check answers to all the questions of Chapter 1 on Math Mela for class 5
Here we have enlisted solutions to all the questions:
- Questions within the chapter.
- Questions at the end of the chapter.
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🚂 Chapter 1: We the Travellers — I
Complete Solutions · Class 4 Mathematics · NCERT
(a) 456 → 567 → 678 → __ → __ → __ → __
(b) 1,050 → __ → 3,150 → 4,200 → __ → __ → __
(c) 5,501 → 6,401 → 7,301 → __ → __ → __ → __
(d) 10,100 → 10,200 → 10,300 → … → 10,900 (snake pattern)
(e) 10,105 → 10,125 → __ → … (snake)
(f) 10,992 → 10,993 → __ → … (snake)
(g) 10,794 → 10,796 → 10,798 → __ → … (snake)
(h) 73,005 → 72,004 → __ → … (snake)
(i) 82,350 → 83,350 → __ → … (snake)
| Number | Number Name |
|---|---|
| 8,045 | Eight thousand forty-five (given) |
| 7,209 | Seven thousand two hundred nine |
| 10,599 | Ten thousand five hundred ninety-nine |
| 10,743 | Ten thousand seven hundred forty-three |
| 20,869 | Twenty thousand eight hundred sixty-nine (given) |
| 13,579 | Thirteen thousand five hundred seventy-nine |
| 10,010 | Ten thousand ten |
| 56,491 | Fifty-six thousand four hundred ninety-one |
| 45,045 | Forty-five thousand forty-five |
| 39,593 | Thirty-nine thousand five hundred ninety-three |
| 50,005 | Fifty thousand five |
| 26,050 | Twenty-six thousand fifty |
| 81,200 | Eighty-one thousand two hundred |
| 90,009 | Ninety thousand nine |
| 23,230 | Twenty-three thousand two hundred thirty |
| 36,001 | Thirty-six thousand one |
Green cells = answers to fill in. Blue cells = numbers/names that were given in the question.
Tip: Compare the TTh (ten-thousands) digit first. If equal, compare Th (thousands) digit, and so on.
Increasing (Ascending) Order:
The student compared only the first digits, which is wrong!
The student is WRONG.
- 9,990 has 4 digits
- 49,014 has 5 digits (has a digit in the Ten-Thousands place)
- A number with more digits is always greater
- Therefore 49,014 > 9,990
You always compare the number of digits first, then digit by digit from left.
(a) Interchange digits of 1,478 to make a number larger than 5,500
- Swap 1 (Th) and 7 (T) → 7,418 ✅ (greater than 5,500)
- Swap 1 (Th) and 8 (O) → 8,471 ✅ (also valid)
(b) Interchange two digits of 10,593
Digits: TTh=1, Th=0, H=5, T=9, O=3
- (i) Between 11,000 and 15,000: Swap 0 (Th) and 3 (O) → 13,590 ✅
- (ii) More than 35,000: Swap 1 (TTh) and 5 (H) → 50,193 ✅
(c) Interchange two digits of 48,247
Digits: TTh=4, Th=8, H=2, T=4, O=7
- (i) As small as possible: Swap 4 (TTh) and 2 (H) → 28,447 ✅ (smallest)
- (ii) As big as possible: Swap 4 (TTh) and 8 (Th) → 84,247 ✅ (largest)
Rule: If the digit to be rounded is 5 or more, round up. If less than 5, round down.
Nearest Ten of 2,346:
2,346 lies between 2,340 and 2,350. The ones digit is 6 (≥5), so round UP.
Nearest Ten = 2,350 (needs 4 jumps)
Nearest Hundred of 2,346:
2,346 lies between 2,300 and 2,400. Distance to 2,300 = 46; distance to 2,400 = 54. Closer to 2,300.
Nearest Hundred = 2,300 (needs 46 jumps)
Nearest Thousand of 2,346:
2,346 lies between 2,000 and 3,000. Distance to 2,000 = 346; distance to 3,000 = 654. Closer to 2,000.
Nearest Thousand = 2,000 (needs 346 jumps)
Fill in the Table — Nearest Tens, Hundreds, Thousands:
| Number | Nearest Tens | Nearest Hundreds | Nearest Thousands |
|---|---|---|---|
| 3,176 | 3,180 | 3,200 | 3,000 |
| 4,017 | 4,020 | 4,000 | 4,000 |
| 5,789 | 5,790 | 5,800 | 6,000 |
| 8,203 | 8,200 | 8,200 | 8,000 |
| Number | Nearest Hundred | Nearest Thousand | Same? |
|---|---|---|---|
| 7,126 | 7,100 | 7,000 | ❌ No |
| 7,835 | 7,800 | 8,000 | ❌ No |
| 7,030 | 7,000 | 7,000 | ✅ YES — Circle this! |
| 6,999 | 7,000 | 7,000 | ✅ YES — Circle this! |
Circle 7,030 and 6,999 — both round to 7,000 when rounded to hundreds AND to thousands.
- (a) Same nearest ten: 24 and 26 — both round to 20. Or 31 and 33 (both → 30).
- (b) Same nearest hundred: 251 and 349 — both round to 300.
- (c) Same nearest thousand: 1,200 and 1,400 — both round to 1,000.
- (a) Same nearest ten AND hundred: 198 and 202 — nearest ten of both = 200; nearest hundred of both = 200 ✅
- (b) Same nearest hundred AND thousand: 4,950 and 5,049 — nearest hundred of both = 5,000; nearest thousand of both = 5,000 ✅
- (c) Same nearest ten, hundred AND thousand: 4,998 and 5,001 — nearest ten = 5,000; nearest hundred = 5,000; nearest thousand = 5,000 ✅
The cyclist will cover 60 km in 4 hours.
Key Insight: Take the sheep first (the most dangerous relationship). The trick is bringing the sheep BACK on trip 4!
Minimum 7 trips needed. The key is bringing the sheep BACK on Trip 4!
Try playing with 1 pebble each, then 2 each, then 3 each to find the pattern.
Winning Strategy (for Player 2 — the one who goes second):
- When both piles are equal, the second player always wins by mirroring.
- Whatever your opponent takes from one pile, you take the same amount from the other pile.
- This keeps both piles equal after every one of your turns.
- Eventually your opponent is forced to break the balance, then you pick last!
−37
−36
−27
−45
Answers to exploration questions:
- (1) All differences (36, 27, 45, 9) are multiples of 9.
- (2) No matter which 2 digits you choose, you always reach 9 in the end.
- (3) To get a 1-digit number in the first step, choose digits that differ by 1: e.g., (2,3) → 32−23=9 ✅. These are consecutive digits.
- (4) For a difference of 27: digits must differ by 3. Example: 4 & 7 → 74−47=27 ✅
(5) Mira’s Table — Extended:
| Digits | Diff. in Digits | Diff. in Numbers |
|---|---|---|
| 3, 7 | 7−3=4 | 73−37=36 |
| 1, 9 | 9−1=8 | 91−19=72 |
| 2, 8 | 8−2=6 | 82−28=54 |
| 4, 5 | 5−4=1 | 54−45=9 |
| 1, 3 | 3−1=2 | 31−13=18 |
| 1, 4 | 4−1=3 | 41−14=27 |
| 1, 6 | 6−1=5 | 61−16=45 |
| 1, 8 | 8−1=7 | 81−18=63 |
Note: Any 5 numbers greater than 23,568 and less than 24,234 are correct!
67,543 > 56,987 → Sheetal’s car has been driven more (67,543 km).
Ones = Tens = Hundreds = 0 means the number ends in ,000 — it must be a multiple of 1,000.
Think of it as regrouping: 90 Tens = 900, 20 Hundreds = 2,000, etc.
For ₹7,934:
For ₹65,342:
Think: The square has 4 sides and 4 corners. Each corner is shared by 2 sides — so corners get counted TWICE when you multiply 5 × 4!
How many horses were actually there?
Actual total = 5×4 − 4×1 = 20 − 4 = 16 horses
The caretaker’s mistake: He said 5 × 4 = 20, but this counts the 4 corner horses twice (once for each side they belong to). The actual number was 16 horses, not 20!
General Formula for hollow square arrangement:
(because 4 corners are each counted in 2 sides)
After thief steals — possible arrangements (5 per side):
| Horses Left | Arrangement (5 per side) | How? |
|---|---|---|
| 16 (original) | 5 per side × 4 sides − 4 corners = 16 | 1 horse at each of 4 corners, 3 on each side |
| 14 | 5 per side × 4 sides − 4 corners = still works | Put 0 horses at 2 corners; 2 horses at the other 2 corners; 3 non-corner per side. Total = 0+0+2+2 + 4×3 = 16 — adjust non-corner count |
| 12 | Still 5 per side possible! | Use 0 horses at all 4 corners; place 5 horses on only 4 specific non-corner positions. (The thief can steal 4 more = 4 total stolen) |
Key insight: Using Total = 4×(n−1) formula: n=5 gives 16. The caretaker can fool the king as long as he can redistribute horses so each side still shows 5. The thief can steal up to 4 horses (from 16 down to 12) and the caretaker can still arrange 5 per side by changing the corner counts!
Chapter 1: We the Travellers — I · Solutions Complete
Class 4 Mathematics · NCERT · Reprint 2026–27