We the Travellers—II
CBSE · Class 5 · Mathematics
NCERT Solutions for We the Travellers—II — CBSE Class 5 Mathematics.
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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?Show solution
We need to find the total quantity of fuel.
Step 1: Add the ones digits: . Write 3, carry 1.
Step 2: Add the tens digits: . Write 10.
The total quantity of fuel in the lorry is 103 litres.
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2Find the sum of 49 and 89.Show solution
Step 1: Add the ones digits: . Write 8, carry 1.
Step 2: Add the tens digits: . Write 13.
The sum of 49 and 89 is 138.
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Let Us Solve (Addition)
a15 + 79Show solution
Easier way:
Or by column addition:
- Ones: , write 4, carry 1
- Tens:
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c38 + 35Show solution
Step 1: Ones: , write 3, carry 1.
Step 2: Tens: .
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e76 + 28Show solution
Step 1: Ones: , write 4, carry 1.
Step 2: Tens: .
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f69 + 20Show solution
Easier way: Adding 20 only changes the tens digit.
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Relationship Between Addition and Subtraction
1Find the relationship between the numbers in the given statements and fill in the blanks appropriately.
(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.Show solution
(a) If , then:
-
-
(b) If , then:
-
-
(c) If , then:
-
-
(d) If , then:
-
-
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2In 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 = 1301, then __________.
(c) If 921 − 137 = 784, then __________.
(d) If 824 − 234 = 590, then __________.Show solution
(a) If , then:
(b) If , then:
(c) If , then:
(d) If , then:
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Let Us Solve (Subtraction)
1What is the difference between 82 and 37? Check your answer: Is 37 + ___ = 82?Show solution
Step 1: Ones digit — we cannot subtract 7 from 2, so we borrow 1 ten from the tens place.
Step 2: Tens digit — after borrowing, we have .
Check: ✓
The difference between 82 and 37 is 45.
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257 − 11 = ?Show solution
- Ones:
- Tens:
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323 − 19 = ?Show solution
- Ones: Cannot subtract 9 from 3; borrow 1 ten.
- Tens:
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449 − 21 = ?Show solution
- Ones:
- Tens:
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556 − 18 = ?Show solution
- Ones: Cannot subtract 8 from 6; borrow 1 ten.
- Tens:
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693 − 35 = ?Show solution
- Ones: Cannot subtract 5 from 3; borrow 1 ten.
- Tens:
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784 − 23 = ?Show solution
- Ones:
- Tens:
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870 − 43 = ?Show solution
- Ones: Cannot subtract 3 from 0; borrow 1 ten.
- Tens:
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965 − 47 = ?Show solution
- Ones: Cannot subtract 7 from 5; borrow 1 ten.
- Tens:
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Sums of Consecutive Numbers
1In each of the boxes (sum of 2, 3, and 4 consecutive numbers), state whether the sums are even or odd. Explain why this is happening.Show solution
*Why:* Two consecutive numbers are always one even and one odd. Even + Odd = Odd. So the sum of any 2 consecutive numbers is always odd.
Sum of 3 consecutive numbers: — alternately even and odd.
*Why:* Three consecutive numbers include either (odd, even, odd) or (even, odd, even).
- Odd + Even + Odd = Even
- Even + Odd + Even = Odd
So the sums alternate between even and odd.
Sum of 4 consecutive numbers: — all even.
*Why:* Four consecutive numbers always contain 2 odd and 2 even numbers. Odd + Odd = Even, Even + Even = Even, so the total sum is always even.
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2What is the difference between two successive sums in each box? Is it the same throughout?Show solution
Difference: . The difference is 2 throughout.
Sum of 3 consecutive numbers:
Difference: . The difference is 3 throughout.
Sum of 4 consecutive numbers:
Difference: . The difference is 4 throughout.
Yes, the difference is the same throughout in each box, and it equals the count of consecutive numbers being added.
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3What will be the difference between two successive sums for—
(a) 5 consecutive numbers
(b) 6 consecutive numbersShow solution
(a) 5 consecutive numbers:
Difference
(b) 6 consecutive numbers:
Difference
The difference between two successive sums equals the number of consecutive numbers being added.
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Let Us Solve (Large Number Addition)
1a238 + 367Show solution
- Ones: , write 5, carry 1
- Tens: , write 0, carry 1
- Hundreds:
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1b1,234 + 12,345Show solution
- Ones:
- Tens:
- Hundreds:
- Thousands:
- Ten-thousands:
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1c12 + 123Show solution
- Ones:
- Tens:
- Hundreds:
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1d46,120 + 12,890Show solution
- Ones:
- Tens: , write 1, carry 1
- Hundreds: , write 0, carry 1
- Thousands:
- Ten-thousands:
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1e878 + 8,789Show solution
- Ones: , write 7, carry 1
- Tens: , write 6, carry 1
- Hundreds: , write 6, carry 1
- Thousands:
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1f1,749 + 17,490Show solution
- Ones:
- Tens: , write 3, carry 1
- Hundreds: , write 2, carry 1
- Thousands:
- Ten-thousands:
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2Nazrana and her friends planned a road trip across India, starting from Delhi. They first drove to Mumbai, then Goa, then Hyderabad, and finally Puri. Look at the distances marked on the map and help them find the total distance travelled. (Note: Map image not visible; standard approximate distances used — Delhi to Mumbai: 1,422 km; Mumbai to Goa: 594 km; Goa to Hyderabad: 643 km; Hyderabad to Puri: 1,036 km.)Show solution
Given distances (as typically shown in this NCERT chapter):
- Delhi to Mumbai = 1,422 km
- Mumbai to Goa = 594 km
- Goa to Hyderabad = 643 km
- Hyderabad to Puri = 1,036 km
Total distance =
Step 1:
Step 2:
Step 3:
Total distance travelled = 3,695 km (Students should use the actual distances from their map.)
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3Find 2 numbers among 5,205; 6,220; 7,095; 8,455; and 4,840 whose sum is closest to:
(a) 10,000
(b) 15,000
(c) 13,000
(d) 16,000Show solution
(a) Closest to 10,000:
Try (difference = 45)
Try (too far)
Try — closest.
(b) Closest to 15,000:
Try (difference = 325)
Try (difference = 550)
is closer.
(c) Closest to 13,000:
Try (difference = 295)
Try (difference = 700)
Try (difference = 315)
is closest.
(d) Closest to 16,000:
Try (difference = 450)
Try (difference = 1,325)
is closest.
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Let Us Solve (Large Number Subtraction)
1a4,578 – 2,222Show solution
- Ones:
- Tens:
- Hundreds:
- Thousands:
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1b15,324 – 11,780Show solution
- Ones: Cannot subtract 0 from 4...
- Tens: Cannot subtract 8 from 2; borrow. , carry reduces hundreds.
- Hundreds: : borrow. ... Let us redo carefully:
Ones:
Tens: : borrow from hundreds.
Hundreds: : borrow from thousands.
Thousands:
Ten-thousands:
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1c5,423 – 423Show solution
- Ones:
- Tens:
- Hundreds:
- Thousands:
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1d123 – 12Show solution
- Ones:
- Tens:
- Hundreds:
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1e77,777 – 777Show solution
- Ones:
- Tens:
- Hundreds:
- Thousands:
- Ten-thousands:
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1f826 – 752Show solution
- Ones:
- Tens: : borrow.
- Hundreds:
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2Mary's train journey to Delhi.
Mary starts from Kolkata with ₹12,540. She spends ₹3,275 on food during her trip to Varanasi. In Varanasi, her uncle gives her ₹4,900. She then spends ₹2,645 on the train ticket to Delhi. She spends ₹1,275 on souvenirs in Delhi. How much money is Mary left with at the end of the Delhi trip?Show solution
- Starting amount = ₹12,540
- Spent on food (Kolkata to Varanasi) = ₹3,275
- Gift received in Varanasi = ₹4,900
- Train ticket (Varanasi to Delhi) = ₹2,645
- Souvenirs in Delhi = ₹1,275
Step 1: Money after spending on food:
Step 2: Money after receiving gift:
Step 3: Money after buying train ticket:
Step 4: Money after buying souvenirs:
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3Members of a school council have raised ₹70,500. They plan to set up a Maths Lab worth ₹39,785, buy library books worth ₹9,545, and purchase sports equipment worth ₹19,548.
(a) Estimate whether the school council has raised enough money.
(b) Check your estimate with calculations.Show solution
- Maths Lab ≈ ₹40,000
- Library books ≈ ₹9,500
- Sports equipment ≈ ₹20,000
- Total estimated expenditure ≈ ₹69,500
Money raised = ₹70,500 ≈ ₹70,000
Since ₹70,000 ≈ ₹69,500, the school council seems to have just enough money, but it is very close.
(b) Exact Calculation:
Total expenditure:
Step 1:
Step 2:
Money raised = ₹70,500
Money needed = ₹68,878
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(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
(b) 760 + ___ = 1,000
(c) 400 + ___ = 1,000
(a) 67 − 9
(b) 83 − 9
(c) 144 − 9
(d) 187 − 99
(e) 247 − 99
(f) 763 − 99
(a) 32 − ___ = 9
(b) 56 − ___ = 9
(c) 877 − ___ = 99
(d) 666 − ___ = 99
Let Us Think and Solve
List all palindrome numbers between 900 and 1,200.
List all palindrome numbers between 25,000 and 27,000.
Even and Odd Numbers
(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
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?
(a) 12 and 6 are a pair of even numbers. Choose 5 such pairs of even numbers. Add the numbers in each of the pairs.
(b) 13 and 9 are a pair of odd numbers. Choose 5 such pairs of odd numbers. Add the numbers in each of the pairs.
(c) 7 and 12 are a pair of odd and even numbers. Choose 5 such pairs of odd and even numbers. Add the numbers in each of the pairs.
Let Us Think
(a) Which is the highest peak she climbed?
(b) What is the difference in height between the highest and lowest peaks she has climbed?
(c) What is the difference between heights of Mount Elbrus and Mount Kanchenjunga?
(d) If Priyanka was 20 years old when she summited Mount Everest in 2013, in which year was she born?
Math Metric Mela
- Chittoor, A.P.: Printed 18,225; Attended 18,104
- Jaunpur, U.P.: Printed 19,043; Attended 19,265
- Raigad, Maharashtra: Printed 20,863; Attended 19,974
Let Us Do
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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