CLASS 5 · MATHS MELA · CHAPTER 4

We the Travellers – II

Use addition and subtraction with larger numbers, explore consecutive and palindrome patterns, and solve travel, money and data problems.

129 worked answersAll 8 exercise sets

What you will learn

Add and subtract large whole numbers accurately.
Use inverse operations, estimation and mental strategies.
Reason about consecutive, palindrome, even and odd numbers.

Read the NCERT questions ↗← All chapters

129 worked answers · short steps first, explanations when you need them

Making Sums Equal and Fuel Arithmetic

Textbook pages 42–43

Question Equal sums (a)

Interchange the fewest numbers to make 1+2+7+9 and 3+4+5+9 equal.

Steps only

The sums are 19 and 21, so each must become 20.

Swap 2 from the first group with 3 from the second.

Answer

Both groups then total 20; one interchange is enough.

Question Equal sums (b)

Make the sums 5+7+12+15=39 and 9+11+13+14=47 equal.

Steps only

Each target sum is (39+47)÷2=43.

Swap 5 and 9; the sums become 43 and 43.

Answer

Swap 5 and 9.

Question Equal sums (c)

Make the sums 11+15+19+23=68 and 13+17+21+25=76 equal.

Steps only

Each target is 72.

Swap 15 and 19; each sum changes by 4.

Answer

Swap 15 from the first group with 19 from the second.

Question Equal sums (d)

Make 77+78+79+80 and 81+82+83+84 equal using the fewest interchanges.

Steps only

The sums are 314 and 330; each target is 322.

No single pair differs by 8, so one interchange cannot work.

Swap 77↔81 and 78↔82; the first sum gains 8.

Answer

Both groups total 322 after 2 interchanges.

Question Fuel 1

A lorry has 28 L and receives 75 L. Find the total.

Steps only

28+75=103.

Answer

103 L.

Question Fuel 2

Find 49+89.

Steps only

49+89=49+90−1=138.

Answer

138.

Question Add a

Find 15+79.

Steps only

15+79=94.

Answer

94.

Question Add b

Find 46+99.

Steps only

46+99=145.

Answer

145.

Question Add c

Find 38+35.

Steps only

38+35=73.

Answer

73.

Question Add d

Find 5+89.

Steps only

5+89=94.

Answer

94.

Question Add e

Find 76+28.

Steps only

76+28=104.

Answer

104.

Question Add f

Find 69+20.

Steps only

69+20=89.

Answer

89.

Addition and Subtraction Relationships

Textbook pages 44–45

Question 1(a)

If 46+21=67, complete both related subtractions.

Steps only

67−21=46.

67−46=21.

Answer

The blanks are 46 and 21.

Question 1(b)

If 198−98=100, complete 100+=198 and 198−=98.

Steps only

100+98=198.

198−100=98.

Answer

The blanks are 98 and 100.

Question 1(c)

If 189+98=287, complete the related subtractions.

Steps only

287−98=189.

287−189=98.

Answer

The blanks are 189 and 98.

Question 1(d)

If 872−672=200, complete 200+=872 and 872−=672.

Steps only

200+672=872.

872−200=672.

Answer

The blanks are 672 and 200.

Question 2(a)

Write the related addition and subtraction sentences for 78+164=242.

Steps only

242−78=164 and 242−164=78.

Answer

242−78=164 and 242−164=78.

Question 2(b)

Write the related addition and subtraction sentences for 462+839=1,301.

Steps only

1,301−462=839 and 1,301−839=462.

Answer

1,301−462=839 and 1,301−839=462.

Question 2(c)

Write the related addition and subtraction sentences for 921−137=784.

Steps only

784+137=921 and 921−784=137.

Answer

784+137=921 and 921−784=137.

Question 2(d)

Write the related addition and subtraction sentences for 824−234=590.

Steps only

590+234=824 and 824−590=234.

Answer

590+234=824 and 824−590=234.

Question Minibus

A minibus had 18 L and shows 65 L after refuelling. How much was filled?

Steps only

65−18=47.

Check: 18+47=65.

Answer

47 L.

Question Subtract 1

Find 82−37.

Steps only

82−37=45.

Answer

45.

Question Subtract 2

Find 57−11.

Steps only

57−11=46.

Answer

46.

Question Subtract 3

Find 23−19.

Steps only

23−19=4.

Answer

Question Subtract 4

Find 49−21.

Steps only

49−21=28.

Answer

28.

Question Subtract 5

Find 56−18.

Steps only

56−18=38.

Answer

38.

Question Subtract 6

Find 93−35.

Steps only

93−35=58.

Answer

58.

Question Subtract 7

Find 84−23.

Steps only

84−23=61.

Answer

61.

Question Subtract 8

Find 70−43.

Steps only

70−43=27.

Answer

27.

Question Subtract 9

Find 65−47.

Steps only

65−47=18.

Answer

18.

Sums of Consecutive Numbers

Textbook pages 45–46

Question Parity of 2

Are sums of two consecutive whole numbers even or odd?

Steps only

One of two consecutive numbers is even and the other is odd.

Even+odd=odd.

Answer

Every sum of 2 consecutive numbers is odd.

Question Parity of 3

Describe the parity of successive sums of three consecutive numbers.

Steps only

The shown sums are 6,9,12,15.

Answer

They alternate even, odd, even, odd.

Question Parity of 4

Are the shown sums of four consecutive numbers even or odd?

Steps only

The sums are 10,14,18,22.

Answer

They are all even.

Question Successive difference

What is the difference between successive sums of n consecutive numbers?

Steps only

The entering number is n greater than the leaving number.

Answer

The difference is n.

Question Difference 5

Find the difference between successive sums of 5 consecutive numbers.

Steps only

Use the rule: difference=n.

Answer

Question Difference 6

Find the difference between successive sums of 6 consecutive numbers.

Steps only

Use the rule: difference=n.

Answer

Question Quick (a)

Find 67+68+69 without adding one by one.

Steps only

The middle number is 68.

3×68=204.

Answer

204.

Question Quick (b)

Find 24+25+26+27 without adding one by one.

Steps only

Pair the ends: 24+27=51 and 25+26=51.

2×51=102.

Answer

102.

Question Quick (c)

Find 48+49+50+51+52 without adding one by one.

Steps only

The middle number is 50.

5×50=250.

Answer

250.

Question Quick (d)

Find 237+238+239+240+241+242 without adding one by one.

Steps only

Pair ends: each pair totals 479.

3×479=1,437.

Answer

1,437.

Adding Large Numbers

Textbook pages 46–48

Question Corridor

A point is 1,855 km from Srinagar and 1,862 km from Kanniyakumari. Find the route length.

Steps only

1,855+1,862=3,717.

Answer

3,717 km.

Question Journey cost

Mahesh spends ₹21,880 on fuel and tolls and ₹38,900 otherwise. Find the total.

Steps only

21,880+38,900=60,780.

Answer

₹60,780.

Question 1(a)

Find 238+367.

Steps only

238+367=605.

Answer

605.

Question 1(b)

Find 1,234+12,345.

Steps only

1,234+12,345=13,579.

Answer

13,579.

Question 1(c)

Find 12+123.

Steps only

12+123=135.

Answer

135.

Question 1(d)

Find 46,120+12,890.

Steps only

46,120+12,890=59,010.

Answer

59,010.

Question 1(e)

Find 878+8,789.

Steps only

878+8,789=9,667.

Answer

9,667.

Question 1(f)

Find 1,749+17,490.

Steps only

1,749+17,490=19,239.

Answer

19,239.

Question Road trip

Add the four marked road-trip distances: 1,600 km, 590 km, 1,055 km and 670 km.

Steps only

1,600+590=2,190.

1,055+670=1,725.

2,190+1,725=3,915.

Answer

3,915 km.

Question 3(a)

From 5,205, 6,220, 7,095, 8,455 and 4,840, choose two whose sum is closest to 10,000.

Steps only

5,205 and 4,840 give 10,045; difference 45.

Answer

5,205 and 4,840.

Question 3(b)

From 5,205, 6,220, 7,095, 8,455 and 4,840, choose two whose sum is closest to 15,000.

Steps only

6,220 and 8,455 give 14,675; difference 325.

Answer

6,220 and 8,455.

Question 3(c)

From 5,205, 6,220, 7,095, 8,455 and 4,840, choose two whose sum is closest to 13,000.

Steps only

4,840 and 8,455 give 13,295; difference 295.

Answer

4,840 and 8,455.

Question 3(d)

From 5,205, 6,220, 7,095, 8,455 and 4,840, choose two whose sum is closest to 16,000.

Steps only

7,095 and 8,455 give 15,550; difference 450.

Answer

7,095 and 8,455.

Subtracting Large Numbers

Textbook pages 49–51

Question Sea route

A 2,700 km sea route has 1,083 km completed. How much remains?

Steps only

2,700−1,083=1,617.

Check: 1,083+1,617=2,700.

Answer

1,617 km.

Question Land routes

How much longer is 15,150 km than 10,228 km?

Steps only

15,150−10,228=4,922.

Answer

4,922 km.

Question 1(a)

Find 4,578−2,222.

Steps only

4,578−2,222=2,356.

Answer

2,356.

Question 1(b)

Find 15,324−11,780.

Steps only

15,324−11,780=3,544.

Answer

3,544.

Question 1(c)

Find 5,423−423.

Steps only

5,423−423=5,000.

Answer

5,000.

Question 1(d)

Find 123−12.

Steps only

123−12=111.

Answer

111.

Question 1(e)

Find 77,777−777.

Steps only

77,777−777=77,000.

Answer

77,000.

Question 1(f)

Find 826−752.

Steps only

826−752=74.

Answer

74.

Question Mary

Mary starts with ₹12,540, spends ₹3,275, receives ₹4,900, then spends ₹2,645 and ₹1,275. What remains?

Steps only

12,540−3,275=9,265.

9,265+4,900=14,165.

14,165−2,645−1,275=10,245.

Answer

₹10,245.

Question Council estimate

Estimate whether ₹70,500 is enough for items costing ₹39,785, ₹9,545 and ₹19,548.

Steps only

Round to thousands: 40,000+10,000+20,000≈70,000.

Answer

The estimate suggests ₹70,500 may be enough, but only by a small amount.

Question Council exact

Check the school council purchases exactly.

Steps only

39,785+9,545+19,548=68,878.

70,500−68,878=1,622.

Answer

Yes; ₹1,622 remains.

Question Truck (a)

A truck receives 3,675 kg cement and 2,850 kg steel. Find the load.

Steps only

3,675+2,850=6,525.

Answer

6,525 kg.

Question Truck (b)

The truck capacity is 8,250 kg. How much more can it carry?

Steps only

8,250−6,525=1,725.

Answer

1,725 kg.

Quick Sums and Differences

Textbook pages 51–52

Question 32 to 100

Complete 32+__=100.

Steps only

Subtract the given number from the target: the blank is 68.

Answer

68.

Question 59 to 100

Complete 59+__=100.

Steps only

Subtract the given number from the target: the blank is 41.

Answer

41.

Question 877 to 1,000

Complete 877+__=1,000.

Steps only

Subtract the given number from the target: the blank is 123.

Answer

123.

Question 666 to 1,000

Complete 666+__=1,000.

Steps only

Subtract the given number from the target: the blank is 334.

Answer

334.

Question 4,103 to 10,000

Complete 4,103+__=10,000.

Steps only

Subtract the given number from the target: the blank is 5,897.

Answer

5,897.

Question 5,555 to 10,000

Complete 5,555+__=10,000.

Steps only

Subtract the given number from the target: the blank is 4,445.

Answer

4,445.

Question 180 to 1,000

Complete 180+__=1,000.

Steps only

Subtract the given number from the target: the blank is 820.

Answer

820.

Question 760 to 1,000

Complete 760+__=1,000.

Steps only

Subtract the given number from the target: the blank is 240.

Answer

240.

Question 400 to 1,000

Complete 400+__=1,000.

Steps only

Subtract the given number from the target: the blank is 600.

Answer

600.

Question Method

Does “add to 99, then add 1” always find the complement to 100?

Steps only

Yes: (99−n)+1=100−n for whole numbers n from 0 to 99.

Answer

Yes, including when the units digit is 0; direct subtraction is another method.

Question 9(a)

Find 67−9.

Steps only

Subtract 10 or 100, then add 1: 67−9=58.

Answer

58.

Question 9(b)

Find 83−9.

Steps only

Subtract 10 or 100, then add 1: 83−9=74.

Answer

74.

Question 9(c)

Find 144−9.

Steps only

Subtract 10 or 100, then add 1: 144−9=135.

Answer

135.

Question 99(d)

Find 187−99.

Steps only

Subtract 10 or 100, then add 1: 187−99=88.

Answer

88.

Question 99(e)

Find 247−99.

Steps only

Subtract 10 or 100, then add 1: 247−99=148.

Answer

148.

Question 99(f)

Find 763−99.

Steps only

Subtract 10 or 100, then add 1: 763−99=664.

Answer

664.

Question Missing (a)

Complete 32−__=9.

Steps only

The blank is the starting number minus the required difference: 23.

Answer

23.

Question Missing (b)

Complete 56−__=9.

Steps only

The blank is the starting number minus the required difference: 47.

Answer

47.

Question Missing (c)

Complete 877−__=99.

Steps only

The blank is the starting number minus the required difference: 778.

Answer

778.

Question Missing (d)

Complete 666−__=99.

Steps only

The blank is the starting number minus the required difference: 567.

Answer

567.

Let Us Think and Solve

Textbook pages 53–54

Question Palindrome 100–200

List all palindrome numbers between 100 and 200.

Steps only

Keep the first and last digits equal.

Answer

101, 111, 121, 131, 141, 151, 161, 171, 181, 191.

Question Palindrome 900–1,200

List all palindrome numbers between 900 and 1,200.

Steps only

Use three-digit ABA and four-digit ABBA forms.

Answer

909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1,001, 1,111.

Question Palindrome 25,000–27,000

List all palindrome numbers between 25,000 and 27,000.

Steps only

For 25 thousand use 25C52; for 26 thousand use 26C62, where C is 0–9.

Answer

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.

Question Grid increasing

Arrange 1–9 so every row and column increases.

Steps only

Place the smallest numbers toward the top-left.

Answer

One answer is 1 2 3 / 4 5 6 / 7 8 9.

Question Grid decreasing

Arrange 1–9 so every row and column decreases.

Steps only

Reverse the fully increasing grid.

Answer

One answer is 9 8 7 / 6 5 4 / 3 2 1.

Question Mixed grids

How should the mixed increasing/decreasing grids be completed?

Steps only

Start with the corner forced to be smallest or largest by its arrows.

Fill neighbouring cells in the required direction, using each of 1–9 once.

Check every row and column after filling.

Answer

More than one grid can be correct; any arrangement using 1–9 once and satisfying every printed inc/dec direction is valid.

Question Even list

Circle the even numbers in the list.

Steps only

An even number ends in 0,2,4,6 or 8.

Answer

498, 724, 100, 846 and 222.

Question Add 2 to 18

What changes when 2 is added to the paired arrangement for 18?

Steps only

18 has 9 pairs; 20 has 10 pairs.

Answer

One pair is added; the number remains even.

Question Add 2 to 23

What changes when 2 is added to the paired arrangement for 23?

Steps only

23 has pairs plus one unpaired object; 25 does too.

Answer

One pair is added; the number remains odd.

Question Even + even

What happens when two even numbers are added?

Steps only

Examples: 12+6=18, 4+8=12, 10+20=30.

Answer

The sum is always even.

Question Odd + odd

What happens when two odd numbers are added?

Steps only

Examples: 13+9=22, 5+7=12, 11+3=14.

Answer

The sum is always even.

Question Odd + even

What happens when one odd and one even number are added?

Steps only

Examples: 7+12=19, 5+8=13, 11+6=17.

Answer

The sum is always odd.

Question Coins

Use available ₹1, ₹2 and ₹5 coins to pay exactly ₹38.

Steps only

Use five ₹5 coins: ₹25.

Use six ₹2 coins: ₹12.

Use one ₹1 coin: ₹1. Total=25+12+1=38.

Answer

One valid choice is 5 five-rupee coins, 6 two-rupee coins and 1 one-rupee coin.

Question Torch 23

The torch alternates ON and OFF, starting ON at press 1. What happens at press 23?

Steps only

23 is odd.

Answer

The torch is ON.

Question Torch rule

For which press numbers is the torch ON or OFF?

Steps only

The state alternates after every press.

Answer

ON after odd press numbers; OFF after even press numbers.

Mountain Data, Certificates and Let Us Do

Textbook pages 55–56

Question Mountain (a)

Which listed peak is highest?

Steps only

Compare the heights; 8,848 m is greatest.

Answer

Mount Everest, 8,848 m.

Question Mountain (b)

Find the difference between the highest and lowest listed peaks.

Steps only

8,848−5,642=3,206.

Answer

3,206 m.

Question Mountain (c)

Find the height difference between Mount Elbrus and Mount Kanchenjunga.

Steps only

8,586−5,642=2,944.

Answer

2,944 m.

Question Mountain (d)

Priyanka was 20 in 2013. Find her birth year.

Steps only

2013−20=1993.

Answer

1993.

Question Certificates Chittoor

Chittoor printed 18,225 certificates for 18,104 students.

Steps only

18,225−18,104=121.

Answer

Sufficient; 121 extra.

Question Certificates Jaunpur

Jaunpur printed 19,043 certificates for 19,265 students.

Steps only

19,265−19,043=222.

Answer

Insufficient; 222 short.

Question Certificates Raigad

Raigad printed 20,863 certificates for 19,974 students.

Steps only

20,863−19,974=889.

Answer

Sufficient; 889 extra.

Question 1(a)

Find 2,009+7,388.

Steps only

2,009+7,388=9,397.

Answer

9,397.

Question 1(b)

Find 26,444+71,111.

Steps only

26,444+71,111=97,555.

Answer

97,555.

Question 1(c)

Find 777+888.

Steps only

777+888=1,665.

Answer

1,665.

Question 1(d)

Find 1,234+1,234.

Steps only

1,234+1,234=2,468.

Answer

2,468.

Question 1(e)

Find 56+56,789.

Steps only

56+56,789=56,845.

Answer

56,845.

Question 1(f)

Find 777+77,777.

Steps only

777+77,777=78,554.

Answer

78,554.

Question 1(g)

Find 5,922+9,221.

Steps only

5,922+9,221=15,143.

Answer

15,143.

Question 1(h)

Find 4,321+8,765.

Steps only

4,321+8,765=13,086.

Answer

13,086.

Question 1(i)

Find 50,050+55,000.

Steps only

50,050+55,000=105,050.

Answer

105,050.

Question 2(a)

Find 458−226.

Steps only

458−226=232.

Answer

232.

Question 2(b)

Find 7,777−4,449.

Steps only

7,777−4,449=3,328.

Answer

3,328.

Question 2(c)

Find 65,447−47,299.

Steps only

65,447−47,299=18,148.

Answer

18,148.

Question 2(d)

Find 1,234−123.

Steps only

1,234−123=1,111.

Answer

1,111.

Question 2(e)

Find 12,345−1,234.

Steps only

12,345−1,234=11,111.

Answer

11,111.

Question 2(f)

Find 56,789−56.

Steps only

56,789−56=56,733.

Answer

56,733.

Question 2(g)

Find 87,326−11,111.

Steps only

87,326−11,111=76,215.

Answer

76,215.

Question 2(h)

Find 878−52.

Steps only

878−52=826.

Answer

826.

Question 2(i)

Find 749−222.

Steps only

749−222=527.

Answer

527.

Question 3

Ambrish has ₹92,375 and buys items costing ₹26,000, ₹17,000 and ₹19,873. Is it enough?

Steps only

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

92,375−62,873=29,502.

Answer

Yes; he has ₹29,502 left.

Question 4

A factory makes 54,000 items toward an order of 85,300. How many remain?

Steps only

85,300−54,000=31,300.

Answer

31,300 more nuts and bolts.

Question 5

Virat has 27,599 runs, which is 6,758 fewer than Sachin. Find Sachin’s runs.

Steps only

27,599+6,758=34,357.

Answer

34,357 runs.

Making Sums Equal and Fuel Arithmetic

Interchange the fewest numbers to make 1+2+7+9 and 3+4+5+9 equal.

Answer

Make the sums 5+7+12+15=39 and 9+11+13+14=47 equal.

Answer

Make the sums 11+15+19+23=68 and 13+17+21+25=76 equal.

Answer

Make 77+78+79+80 and 81+82+83+84 equal using the fewest interchanges.

Answer

A lorry has 28 L and receives 75 L. Find the total.

Answer

Find 49+89.

Answer

Find 15+79.

Answer

Find 46+99.

Answer

Find 38+35.

Answer

Find 5+89.

Answer

Find 76+28.

Answer

Find 69+20.

Answer

Addition and Subtraction Relationships

If 46+21=67, complete both related subtractions.

Answer

If 198−98=100, complete 100+__=198 and 198−__=98.

Answer

If 189+98=287, complete the related subtractions.

Answer

If 872−672=200, complete 200+__=872 and 872−__=672.

Answer

Write the related addition and subtraction sentences for 78+164=242.

Answer

Write the related addition and subtraction sentences for 462+839=1,301.

Answer

Write the related addition and subtraction sentences for 921−137=784.

Answer

Write the related addition and subtraction sentences for 824−234=590.

Answer

A minibus had 18 L and shows 65 L after refuelling. How much was filled?

Answer

Find 82−37.

Answer

Find 57−11.

Answer

Find 23−19.

Answer

Find 49−21.

Answer

Find 56−18.

Answer

Find 93−35.

Answer

Find 84−23.

Answer

Find 70−43.

Answer

Find 65−47.

Answer

Sums of Consecutive Numbers

Are sums of two consecutive whole numbers even or odd?

Answer

Describe the parity of successive sums of three consecutive numbers.

Answer

Are the shown sums of four consecutive numbers even or odd?

Answer

What is the difference between successive sums of n consecutive numbers?

Answer

Find the difference between successive sums of 5 consecutive numbers.

Answer

Find the difference between successive sums of 6 consecutive numbers.

Answer

Find 67+68+69 without adding one by one.

Answer

Find 24+25+26+27 without adding one by one.

Answer

Find 48+49+50+51+52 without adding one by one.

If 198−98=100, complete 100+=198 and 198−=98.

If 872−672=200, complete 200+=872 and 872−=672.