Class 5 Mathematics

Chapter 4 Solutions — We the Travellers — II

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Solutions

Overview

Step-by-step NCERT solutions for We the Travellers — II (Chapter 4, NCERT Class 5 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the We the Travellers — II textbook chapter.

Solved

What these solutions cover

All 39 questions in We the Travellers — II are solved in the PDF. Here's what's inside, exercise by exercise:

Making Sums Equal (p. 41–42)

1.
In each of the following, there are two groups of numbers with their sums. Interchange pairs of numbers between the two groups to make their sums equal. Use the least number of moves.
- (a) Group 1: 1, 2, 7, 9 (sum = 19) Group 2: 3, 4, 5, 9 (sum = 21)
- (b) Group 1: 5, 7, 12, 15 (sum = 39) Group 2: 9, 11, 13, 14 (sum = 47)
- (c) Group 1: 11, 15, 19, 23 (sum = 68) Group 2: 13, 17, 21, 25 (sum = 76) (d)…

Fuel Arithmetic — Addition with Regrouping (p. 42–43)

A lorry has 28 litres of fuel in its tank. An additional 75 litres is filled. What is the total quantity of fuel in the lorry?
Find the sum of 49 and 89.

Let Us Solve — Adding Two-Digit Numbers (p. 43)

1.
Add the following numbers. Wherever possible, find easier ways to add the pairs of numbers.
- (a) 15 + 79
- (b) 46 + 99
- (c) 38 + 35
- (d) 5 + 89
- (e) 76 + 28
- (f) 69 + 20

Relationship Between Addition and Subtraction (p. 44)

1.
Find the relationship between the numbers in the given statements and fill in the blanks.
- (a) If 46 + 21 = 67, then 67 - 21 = ___ and 67 - 46 = ___.
- (b) If 198 - 98 = 100, then 100 + ___ = 198 and 198 - ___ = 98.
- (c) If 189 + 98 = 287, then 287 - 98 = ___ and 287 - 189 = ___.
- (d) If 872 - 672 = 200, then 200 + ___ = 872 and 872 - ___ = 672.
2.
In each of the following, write the subtraction and addition sentences that follow from the given sentence.
- (a) If 78 + 164 = 242, then ...
- (b) If 462 + 839 = 1,301, then ...
- (c) If 921 - 137 = 784, then ...
- (d) If 824 - 234 = 590, then ...

Let Us Solve — Subtracting Two-Digit Numbers (p. 44–45)

What is the difference between 82 and 37? Check your answer: Is 37 + ___ = 82?
Find the following differences. 2. 57 - 11 3. 23 - 19 4. 49 - 21 5. 56 - 18 6. 93 - 35 7. 84 - 23 8. 70 - 43 9. 65 - 47

Sums of Consecutive Numbers (p. 45–46)

In each of the boxes (sum of 2, sum of 3, sum of 4 consecutive numbers), state whether the sums are even or odd. Explain why this is happening.
What is the difference between two successive sums in each box? Is it the same throughout?
3.
What will be the difference between two successive sums for:
- (a) 5 consecutive numbers
- (b) 6 consecutive numbers
4.
Use the pattern (sums of 3, 4, and 5 consecutive numbers are related to the middle number or average) to find the following sums WITHOUT adding directly.
- (a) 67 + 68 + 69
- (b) 24 + 25 + 26 + 27
- (c) 48 + 49 + 50 + 51 + 52
- (d) 237 + 238 + 239 + 240 + 241 + 242

The Longest Land Route — Adding Large Numbers (p. 46–48)

One of the places on the North-South Corridor was 1,855 km from Srinagar and 1,862 km from Kanniyakumari. What was the total length of the North-South Corridor in 2019?
Mahesh spends Rs 21,880 on fuel and toll tax, and Rs 38,900 on other expenses during his drive from Srinagar to Kanniyakumari. How much did he spend in total?

Let Us Solve — Adding Large Numbers (p. 47–48)

1.
Find the following sums. Align the digits properly.
- (a) 238 + 367
- (b) 1,234 + 12,345
- (c) 12 + 123
- (d) 46,120 + 12,890
- (e) 878 + 8,789
- (f) 1,749 + 17,490
The great Indian road trip! Nazrana and her friends drove from Delhi to Mumbai (1,600 km), then Mumbai to Goa (590 km), then Goa to Hyderabad (670 km), and finally Hyderabad to Puri (1,055 km). What was the total distance travelled?
3.
Find 2 numbers from the list — 5,205; 6,220; 7,095; 8,455; 4,840 — whose sum is closest to:
- (a) 10,000
- (b) 15,000
- (c) 13,000
- (d) 16,000

Subtracting Large Numbers (p. 49–50)

The total distance of the sea route from Mumbai to Chennai is 2,700 km. A ship from Mumbai first reaches Cochin port, travelling 1,083 km. How much more distance does it have to travel to reach Chennai?
The longest land route (Talon to Sagres) is 15,150 km. The longest highway in Africa (Cairo to Cape Town) is 10,228 km. How much longer is the Talon–Sagres route?

Let Us Solve — Subtracting Large Numbers (p. 50–51)

1.
Subtract the following. Align the digits carefully.
- (a) 4,578 - 2,222
- (b) 15,324 - 11,780
- (c) 5,423 - 423
- (d) 123 - 12
- (e) 77,777 - 777
- (f) 826 - 752
Mary's train journey to Delhi. Mary starts from Kolkata with Rs 12,540. She spends Rs 3,275 on food during her trip to Varanasi. Her uncle gives her a gift worth Rs 4,900 in Varanasi. She then spends Rs 2,645 on a train ticket to Delhi and Rs 1,275 on souvenirs in Delhi. How much money is Mary left with at the end?
3.
Members of a school council have raised Rs 70,500. They plan to set up a Maths Lab (Rs 39,785), buy library books (Rs 9,545), and purchase sports equipment (Rs 19,548).
- (a) Estimate whether the council has raised enough money.
- (b) Check your estimate with calculations.
4.
A truck can carry 8,250 kg of goods. A factory loads 3,675 kg of cement and 2,850 kg of steel on it.
- (a) What is the total weight loaded onto the truck?
- (b) How much more weight can the truck carry before reaching its maximum capacity?

Quick Sums and Differences (p. 51–52)

1.
Help Sukanta fill in the blanks so that the sum is 100: 32 + ___ = 100 59 + ___ = 100 Also solve using Piku's method (add to get 99 first, then add 1 more), then apply to: 877 + ___ = 1,000 666 + ___ = 1,000 4,103 + ___ = 10,000 5,555 + ___ = 10,000 Also find:
- (a) 180 + ___ = 1,000
- (b) 760 + ___ = 1,000
- (c) 400 + ___ = 1,000
2.
Namita wants to quickly subtract 9 or 99 from any number. Find a quick way, then solve:
- (a) 67 - 9
- (b) 83 - 9
- (c) 144 - 9
- (d) 187 - 99
- (e) 247 - 99
- (f) 763 - 99 Then use the above results (without recalculating) to find:
- (a) 32 - ___ = 9
- (b) 56 - ___ = 9
- (c) 877 - ___ = 99
- (d) 666 - ___ = 99

Let Us Think and Solve — Palindromes and Number Grids (p. 53)

Nitin likes palindrome numbers (numbers that read the same forwards and backwards, e.g. 22, 363, 404, 8,558). List all palindrome numbers between 100 and 200. List all palindrome numbers between 900 and 1,200. List all palindrome numbers between 25,000 and 27,000.
In a 3x3 grid, arrange the numbers 1 to 9 so that: (Part 1) Each row and each column has numbers in increasing (inc) order. (Part 2) Each row and each column has numbers in decreasing (dec) order. (Part 3) Fill three more grids using the mixed inc/dec patterns shown: Grid A: rows inc, columns inc. Grid B: rows dec, first 2 columns dec, last column inc. Grid C: rows mixed (row 1 inc, row 2 inc…

Even and Odd Numbers (p. 53–54)

1.
Circle the numbers that are even.
- (a) 297
- (b) 498
- (c) 724
- (d) 100
- (e) 199
- (f) 789
- (g) 49
- (h) 6,893
- (i) 846
- (j) 111
- (k) 222
- (l) 1,023
Observe the paired arrangement for 18 and for 23. Add 2 to 18. What changes or does not change in the arrangement? Add 2 to 23. What changes or does not change in the arrangement?
3.
What do you notice about the sums in each case? Will it be true for all such pairs? Explain using the paired arrangement.
- (a) Add pairs of even numbers (e.g. 12 and 6). Choose 5 such pairs.
- (b) Add pairs of odd numbers (e.g. 13 and 9). Choose 5 such pairs.
- (c) Add one odd and one even number (e.g. 7 and 12). Choose 5 such pairs.

Let Us Think — Logic Puzzles (p. 54–55)

Jincy opened her piggy bank. She found 8 coins of Rs 1, 9 coins of Rs 2, and 5 coins of Rs 5. She wants to buy stickers worth Rs 38. What possible combination of coins can she use to pay the exact amount?
2.
Raghu presses a torch switch: 1st press = ON, 2nd press = OFF, 3rd press = ON, and so on.
- (a) Will the torch be ON or OFF after the 23rd press?
- (b) For what number of presses will the torch be ON? For what number will it be OFF?
3.
Mountain climbing — Priyanka Mohite's peaks (read the table): Mount Kanchenjunga: 8,586 m (2022) Mount Everest: 8,848 m (2013) Mount Makalu: 8,485 m (2019) Mount Lhotse: 8,516 m (2018) Mount Kilimanjaro: 5,895 m (2016) Mount Elbrus: 5,642 m (2017) Mount Annapurna I: 8,091 m (2021)
- (a) Which is the highest peak she climbed?
- (b) What is the difference in height between the highest and lowest…

Math Metric Mela (p. 55–56)

A grand Math Metric Mela was held. For each district, find if the certificates were sufficient. If insufficient, find how many fell short; if extra, find how many were in excess. Chittoor (A.P.): Certificates printed = 18,225; Students attended = 18,104. Jaunpur (U.P.): Certificates printed = 19,043; Students attended = 19,265. Raigad (Maharashtra): Certificates printed = 20,863; Students…

Let Us Do — Addition and Subtraction Practice (p. 56)

1.
Add.
- (a) 2,009 + 7,388
- (b) 26,444 + 71,111
- (c) 777 + 888
- (d) 1,234 + 1,234
- (e) 56 + 56,789
- (f) 777 + 77,777
- (g) 5,922 + 9,221
- (h) 4,321 + 8,765
- (i) 50,050 + 55,000
2.
Subtract.
- (a) 458 - 226
- (b) 7,777 - 4,449
- (c) 65,447 - 47,299
- (d) 1,234 - 123
- (e) 12,345 - 1,234
- (f) 56,789 - 56
- (g) 87,326 - 11,111
- (h) 878 - 52
- (i) 749 - 222
Ambrish saved Rs 92,375 over a year to buy cows and goats. He buys a cow for Rs 26,000 and a goat for Rs 17,000. He also buys a milking machine for Rs 19,873. Does he have enough money? How much more or less does he have than he needs?
A factory produces 54,000 nuts and bolts in a day. An order is placed for 85,300 nuts and bolts. How many more nuts and bolts does the factory need to produce to complete the order?
Virat Kohli has scored 27,599 runs. He has 6,758 runs less than Sachin Tendulkar. How many runs has Sachin Tendulkar scored?

Sample

Worked examples

3 questions from We the Travellers — II, solved step by step.

Fuel Arithmetic — Addition with Regrouping (p. 42–43)

A lorry has 28 litres of fuel in its tank. An additional 75 litres is filled. What is the total quantity of fuel in the lorry?

Total fuel = 28 l + 75 l.

Ones: 8 + 5 = 13. Write 3, carry 1 Ten.

Tens: 2 + 7 + 1 (carry) = 10. Write 0, carry 1 Hundred.

Hundreds: 0 + 0 + 1 (carry) = 1.

Total = 103 litres.

Answer: 103 litres

Sums of Consecutive Numbers (p. 45–46)

In each of the boxes (sum of 2, sum of 3, sum of 4 consecutive numbers), state whether the sums are even or odd. Explain why this is happening.

Sum of 2 consecutive numbers (3, 5, 7, 9, ...): always ODD.

Two consecutive numbers are one even and one odd. Even + Odd = Odd. So the sum is always odd.

Sum of 3 consecutive numbers (6, 9, 12, 15, ...): they alternate even and odd, but all are multiples of 3.

6 = even, 9 = odd, 12 = even, 15 = odd — the sums alternate even and odd.

This is because 3 consecutive numbers have 2 of one parity and 1 of the other; the total switches with each step.

Sum of 4 consecutive numbers (10, 14, 18, 22, ...): always EVEN.

4 consecutive numbers contain 2 even and 2 odd numbers. Even + Even + Odd + Odd = Even.

Answer: Sum of 2 consecutive: always odd (one even + one odd). Sum of 3 consecutive: alternates even/odd. Sum of 4 consecutive: always even (2 even + 2 odd).

The Longest Land Route — Adding Large Numbers (p. 46–48)

One of the places on the North-South Corridor was 1,855 km from Srinagar and 1,862 km from Kanniyakumari. What was the total length of the North-South Corridor in 2019?

Total length = 1,855 + 1,862.

Ones: 5 + 2 = 7.

Tens: 5 + 6 = 11. Write 1, carry 1.

Hundreds: 8 + 8 + 1 = 17. Write 7, carry 1.

Thousands: 1 + 1 + 1 = 3.

Total = 3,717 km.

Answer: 3,717 km

All 39 questions in We the Travellers — II are solved step by step in the Solutions PDF above.

Keep solving

Chapter 4 Solutions — We the Travellers — II

Overview

What these solutions cover

Making Sums Equal (p. 41–42)

Fuel Arithmetic — Addition with Regrouping (p. 42–43)

Let Us Solve — Adding Two-Digit Numbers (p. 43)

Relationship Between Addition and Subtraction (p. 44)

Let Us Solve — Subtracting Two-Digit Numbers (p. 44–45)

Sums of Consecutive Numbers (p. 45–46)

The Longest Land Route — Adding Large Numbers (p. 46–48)

Let Us Solve — Adding Large Numbers (p. 47–48)

Subtracting Large Numbers (p. 49–50)

Let Us Solve — Subtracting Large Numbers (p. 50–51)

Quick Sums and Differences (p. 51–52)

Let Us Think and Solve — Palindromes and Number Grids (p. 53)

Even and Odd Numbers (p. 53–54)

Let Us Think — Logic Puzzles (p. 54–55)

Math Metric Mela (p. 55–56)

Let Us Do — Addition and Subtraction Practice (p. 56)

Worked examples

A lorry has 28 litres of fuel in its tank. An additional 75 litres is filled. What is the total quantity of fuel in the lorry?

In each of the boxes (sum of 2, sum of 3, sum of 4 consecutive numbers), state whether the sums are even or odd. Explain why this is happening.

One of the places on the North-South Corridor was 1,855 km from Srinagar and 1,862 km from Kanniyakumari. What was the total length of the North-South Corridor in 2019?

More solutions in Maths Mela

More NCERT Solutions for Class 5