Class 5 Mathematics · Chapter 4

4. We the Travellers — II

Solutions to all Let Us Solve, Let Us Think and Let Us Do questions. CBSE / NCERT Class 5 Maths Mela.

Making Sums Equal

1Think what will happen to the sums if we interchange 2 and 5.

In (a), if we interchange 2 and 5, the first sum becomes 22 and the second becomes 18.

The difference becomes bigger. So, this move does not help.

2Interchange pairs of numbers between the two groups to make their sums equal, using the least number of moves.

(a) 19 and 21 (difference = 2)

Interchange 2 and 3.

First group: 1 + 3 + 7 + 9 = 20. Second group: 2 + 4 + 5 + 9 = 20.

(b) 39 and 47 (difference = 8)

Interchange 5 and 9 (they differ by 4).

First group: 9 + 7 + 12 + 15 = 43. Second group: 5 + 11 + 13 + 14 = 43.

No pair differs by 4. So, make two moves. Interchange 11 and 13, and 15 and 17.

First group: 13 + 17 + 19 + 23 = 72. Second group: 11 + 15 + 21 + 25 = 72.

(d) 314 and 330 (difference = 16)

We need pairs whose differences add up to 8. Interchange 77 and 84 (difference 7), and 80 and 81 (difference 1).

First group: 84 + 78 + 79 + 81 = 322. Second group: 77 + 82 + 83 + 80 = 322.

Trick: Interchanging two numbers changes each sum by their difference. So, find numbers whose difference is half of the difference of the sums.

Fuel Arithmetic

1A 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 = 103 l

2Find the sum of 49 and 89.

49 + 89 = 138

Let Us Solve

1Add the following numbers. Wherever possible, find easier ways to add the pairs of numbers.

a. 15 + 79 = 15 + 80 − 1 = 94

b. 46 + 99 = 46 + 100 − 1 = 145

c. 38 + 35 = 38 + 2 + 33 = 40 + 33 = 73

d. 5 + 89 = 89 + 1 + 4 = 90 + 4 = 94

e. 76 + 28 = 76 + 30 − 2 = 104

f. 69 + 20 = 89

Relationship Between Addition and Subtraction

1Find the relationship between the numbers in the given statements and fill in the blanks.

(a) 67 − 21 = 46; 67 − 46 = 21

(b) 100 + 98 = 198; 198 − 100 = 98

(d) 200 + 672 = 872; 872 − 200 = 672

2Write the subtraction and addition sentences that follow from the given sentence.

(a) If 78 + 164 = 242, then 242 − 164 = 78 and 242 − 78 = 164.

(b) If 462 + 839 = 1,301, then 1,301 − 839 = 462 and 1,301 − 462 = 839.

(d) If 824 − 234 = 590, then 590 + 234 = 824 and 824 − 590 = 234.

More Fuel Arithmetic — Let Us Solve

1A minibus has 18 l of fuel left. After refuelling, the fuel meter shows 65 l. How much fuel has been filled?

Fuel filled = 65 l − 18 l = 47 l. Check: 18 + 47 = 65.

2What is the difference between 82 and 37?

82 − 37 = 45. Check: 37 + 45 = 82.

3Subtract.

2. 57 − 11 = 46
3. 23 − 19 = 4
4. 49 − 21 = 28

5. 56 − 18 = 38
6. 93 − 35 = 58
7. 84 − 23 = 61

8. 70 − 43 = 27
9. 65 − 47 = 18

Sums of Consecutive Numbers

1In each of the boxes, state whether the sums are even or odd. Explain why this is happening.

2 consecutive numbers: the sums (3, 5, 7, 9) are always odd. One number is odd and the other is even.

3 consecutive numbers: the sums (6, 9, 12, 15) are even and odd by turns. Sometimes there are two odd numbers, sometimes only one.

4 consecutive numbers: the sums (10, 14, 18, 22) are always even. There are always two odd and two even numbers.

2What is the difference between two successive sums in each box? Is it the same throughout?

2 consecutive numbers: difference is 2. 3 consecutive numbers: difference is 3. 4 consecutive numbers: difference is 4.

Yes, it is the same throughout each box.

3What will be the difference between two successive sums for (a) 5 consecutive numbers (b) 6 consecutive numbers?

(a) 5
(b) 6

4Find the following sums without adding the numbers directly.

(a) 67 + 68 + 69 = 3 × 68 = 204 (3 times the middle number)

(b) 24 + 25 + 26 + 27 = 2 × (24 + 27) = 2 × 51 = 102

(d) 237 + 238 + 239 + 240 + 241 + 242 = 3 × (237 + 242) = 3 × 479 = 1,437

The Longest Land Route — Adding Large Numbers

1A place on the North–South Corridor was 1,855 km from Srinagar and 1,862 km from Kanniyakumari. What was the total length of the corridor in 2019?

Total length = 1,855 km + 1,862 km = 3,717 km

2Mahesh spends ₹21,880 on fuel and toll tax, and ₹38,900 on other expenses. How much did he spend in total?

Total = ₹21,880 + ₹38,900 = ₹60,780

Let Us Solve

1Find the following sums.

(a) 238 + 367 = 605
(b) 1,234 + 12,345 = 13,579

(e) 878 + 8,789 = 9,667
(f) 1,749 + 17,490 = 19,239

2The great Indian road trip! Find the total distance travelled from Delhi to Mumbai, Goa, Hyderabad and Puri.

Delhi to Mumbai = 1,600 km, Mumbai to Goa = 590 km, Goa to Hyderabad = 670 km, Hyderabad to Puri = 1,055 km

Total distance = 1,600 + 590 + 670 + 1,055 = 3,915 km

3Find 2 numbers among 5,205, 6,220, 7,095, 8,455 and 4,840 whose sum is closest to the following.

(a) 10,000 → 5,205 + 4,840 = 10,045

(b) 15,000 → 6,220 + 8,455 = 14,675

(d) 16,000 → 7,095 + 8,455 = 15,550

Subtracting Large Numbers

1A ship from Mumbai travels 1,083 km to reach Cochin. The total sea route to Chennai is 2,700 km. How much more distance does it have to travel?

Remaining distance = 2,700 km − 1,083 km = 1,617 km

2How much longer is the land route between Talon and Sagres (15,150 km) compared to the highway between Cairo and Cape Town (10,228 km)?

Difference = 15,150 km − 10,228 km = 4,922 km

Let Us Solve

1Subtract the following.

(a) 4,578 − 2,222 = 2,356
(b) 15,324 − 11,780 = 3,544

(e) 77,777 − 777 = 77,000
(f) 826 − 752 = 74

2Mary’s train journey to Delhi. How much money is Mary left with at the end of the Delhi trip?

Starts with ₹12,540

Spends ₹3,275 → ₹12,540 − ₹3,275 = ₹9,265

Gets a gift of ₹4,900 → ₹9,265 + ₹4,900 = ₹14,165

Train ticket ₹2,645 → ₹14,165 − ₹2,645 = ₹11,520

Souvenirs ₹1,275 → ₹11,520 − ₹1,275 = ₹10,245

Mary is left with ₹10,245.

3A school council raised ₹70,500. It plans to spend ₹39,785 on a Maths Lab, ₹9,545 on library books and ₹19,548 on sports equipment.

(a) Estimate whether they have raised enough money.

About ₹40,000 + ₹10,000 + ₹20,000 = ₹70,000. This is less than ₹70,500. So, the money seems to be enough.

(b) Check your estimate with calculations.

₹39,785 + ₹9,545 + ₹19,548 = ₹68,878

₹70,500 − ₹68,878 = ₹1,622

Yes, the money is enough. ₹1,622 will be left.

4A truck can carry 8,250 kg. A factory loads 3,675 kg of cement and 2,850 kg of steel.

(a) Total weight loaded = 3,675 kg + 2,850 kg = 6,525 kg

(b) More weight it can carry = 8,250 kg − 6,525 kg = 1,725 kg

Quick Sums and Differences

1Fill in the blank: 32 + ___ = 100. Do you think Piku’s method will always work? Try it for 59.

32 + 67 = 99. Add 1 more: 32 + 68 = 100.

59 + 40 = 99. Add 1 more: 59 + 41 = 100.

Yes. First make 99 (or 999) by making each digit 9. Then add 1.

2Use this method to solve the following.

877 + 123 = 1,000
666 + 334 = 1,000

4,103 + 5,897 = 10,000
5,555 + 4,445 = 10,000

3Will this method work if the units digit is 0? What other methods can you use?

Yes, it works. For example, 180 + 819 = 999, and 819 + 1 = 820.

An easier way is to count in tens: 18 tens + 82 tens = 100 tens = 1,000.

(a) 180 + 820 = 1,000
(b) 760 + 240 = 1,000
(c) 400 + 600 = 1,000

4Find a way to quickly subtract 9 or 99 from any number.

To subtract 9, subtract 10 and add 1. To subtract 99, subtract 100 and add 1.

(a) 67 − 9 = 58
(b) 83 − 9 = 74
(c) 144 − 9 = 135

(d) 187 − 99 = 88
(e) 247 − 99 = 148
(f) 763 − 99 = 664

5Find a way to get 9 or 99 as the answer.

Subtract a number that is 9 (or 99) less than the given number.

(a) 32 − 23 = 9
(b) 56 − 47 = 9

Let Us Think and Solve

1List palindrome numbers in the given ranges.

Between 100 and 200: 101, 111, 121, 131, 141, 151, 161, 171, 181, 191

Between 900 and 1,200: 909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1,001, 1,111

Between 25,000 and 27,000: 25,052, 25,152, 25,252, 25,352, 25,452, 25,552, 25,652, 25,752, 25,852, 25,952, 26,062, 26,162, 26,262, 26,362, 26,462, 26,562, 26,662, 26,762, 26,862, 26,962

2In a 3×3 grid, arrange the numbers 1 to 9 according to the inc (increasing) and dec (decreasing) conditions.

Rows are read from left to right. Columns are read from top to bottom.

All rows inc, all columns inc

1	2	3
4	5	6
7	8	9

All rows dec, all columns dec

9	8	7
6	5	4
3	2	1

Rows dec, columns inc

3	2	1
6	5	4
9	8	7

Rows dec, dec, inc; columns dec, dec, inc

9	7	1
8	6	2
3	4	5

Rows inc, inc, dec; columns inc, dec, dec

1	7	8
2	5	6
9	4	3

Other arrangements are also possible. Check each row and column with the given condition.

Even and Odd Numbers

1Circle the numbers that are even.

Circle: 498, 724, 100, 846, 222

These numbers end with 0, 2, 4, 6 or 8.

2Add 2 to 18. What changes or does not change in the arrangement? Add 2 to 23.

18 has 9 pairs and no dot is left alone. 18 + 2 = 20 has 10 pairs. One more pair is added. Still no dot is left alone, so it stays even.

23 has 11 pairs and 1 dot left alone. 23 + 2 = 25 has 12 pairs and still 1 dot left alone. It stays odd.

3What do you notice about the sums in each case? Will it be true for all such pairs?

(a) Even + Even

12 + 6 = 18, 4 + 8 = 12, 10 + 20 = 30, 14 + 2 = 16, 22 + 16 = 38

The sum is always even. Both numbers are made of full pairs.

(b) Odd + Odd

13 + 9 = 22, 3 + 5 = 8, 7 + 11 = 18, 15 + 1 = 16, 21 + 9 = 30

The sum is always even. The two left-over dots join to make a new pair.

7 + 12 = 19, 3 + 4 = 7, 5 + 10 = 15, 9 + 2 = 11, 11 + 6 = 17

The sum is always odd. One dot is still left alone.

Yes, this is true for all such pairs.

Let Us Think

1Jincy has 8 coins of ₹1, 9 coins of ₹2 and 5 coins of ₹5. What combination of coins can she use to pay exactly ₹38?

5 coins of ₹5 + 6 coins of ₹2 + 1 coin of ₹1 = ₹25 + ₹12 + ₹1 = ₹38

Another way: 4 coins of ₹5 + 9 coins of ₹2 = ₹20 + ₹18 = ₹38

2Will the torch be ON or OFF after the 23rd press? For what number of presses will the torch be ON or OFF?

The torch is ON after an odd number of presses (1, 3, 5, …). It is OFF after an even number of presses (2, 4, 6, …).

23 is an odd number. So, the torch will be ON after the 23rd press.

3Mountain climbing — answer the questions.

(a) The highest peak she climbed is Mount Everest (8,848 m).

(b) Highest − lowest = 8,848 m − 5,642 m (Mount Elbrus) = 3,206 m

(d) Year of birth = 2013 − 20 = 1993

Math Metric Mela

1For each district, find out if the number of certificates was sufficient.

District	Printed	Attended	Result
Chittoor, A.P.	18,225	18,104	Sufficient — 18,225 − 18,104 = 121 extra
Jaunpur, U.P.	19,043	19,265	Insufficient — 19,265 − 19,043 = 222 short
Raigad, Maharashtra	20,863	19,974	Sufficient — 20,863 − 19,974 = 889 extra

Let Us Do

1Add.

(a) 2,009 + 7,388 = 9,397
(b) 26,444 + 71,111 = 97,555

(e) 56 + 56,789 = 56,845
(f) 777 + 77,777 = 78,554

(f) 5,922 + 9,221 = 15,143
(g) 4,321 + 8,765 = 13,086

(h) 50,050 + 55,000 = 1,05,050 (one lakh five thousand fifty)

2Subtract.

(a) 458 − 226 = 232
(b) 7,777 − 4,449 = 3,328

(e) 12,345 − 1,234 = 11,111
(f) 56,789 − 56 = 56,733

(f) 87,326 − 11,111 = 76,215
(g) 878 − 52 = 826

(h) 749 − 222 = 527

3Ambrish saved ₹92,375. He buys a cow for ₹26,000, a goat for ₹17,000 and a milking machine for ₹19,873. Does he have enough money? How much more or less does he have than he needs?

Total cost = ₹26,000 + ₹17,000 + ₹19,873 = ₹62,873

Money left = ₹92,375 − ₹62,873 = ₹29,502

Yes, he has enough money. He has ₹29,502 more than he needs.

4A factory produces 54,000 nuts and bolts in a day. An order is placed for 85,300. How many more does it need to produce?

85,300 − 54,000 = 31,300 nuts and bolts

5Virat Kohli has scored 27,599 runs. He has 6,758 runs less than Sachin Tendulkar. How many runs has Sachin Tendulkar scored?

Sachin’s runs = 27,599 + 6,758 = 34,357 runs

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