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NCERT Solutions for Class 5th Maths Chapter 4 Let Us Think — Let Us Think

Book page 54–55 Updated on2026-09-19

Q1.
Jincy opened her piggy bank. She found 8 coins of ₹1, 9 coins of ₹2 and 5 coins of ₹5. She wants to buy stickers worth ₹38. What possible combination of coins can she use to pay the exact amount?
Answer

There are eleven different ways. Here are three easy ones to start with.

  • 5 coins of ₹5 + 6 coins of ₹2 + 1 coin of ₹1 = 25 + 12 + 1 = ₹38
  • 4 coins of ₹5 + 9 coins of ₹2 = 20 + 18 = ₹38
  • 3 coins of ₹5 + 9 coins of ₹2 + 5 coins of ₹1 = 15 + 18 + 5 = ₹38

How to search in an orderly way

  1. First see how much money she has in all: 8 × 1 = ₹8, 9 × 2 = ₹18, 5 × 5 = ₹25. Total ₹51. That is more than ₹38, so it can be done.
  2. Start with the biggest coins. Decide how many ₹5 coins to use — she has at most 5.
  3. Whatever is left must be made from ₹2 and ₹1 coins, using at most 9 twos and at most 8 ones.
  4. Write down every case that fits.
₹5 coins₹2 coins₹1 coinsTotal
537₹38
545₹38
553₹38
561₹38
458₹38
466₹38
474₹38
482₹38
490₹38
387₹38
395₹38
Why she cannot use 2 or fewer ₹5 coins: With only 2 five-rupee coins she has ₹10 from them. The most she can add is 9 × 2 + 8 × 1 = 18 + 8 = ₹26. Together that is only ₹36, which is short of ₹38.
Check one row: 4 fives + 7 twos + 4 ones = 20 + 14 + 4 = ₹38 ✓ And she owns enough of each coin: 4 ≤ 5, 7 ≤ 9, 4 ≤ 8.
Q2.
Raghu is fond of his grandfather's torch. He starts playing with it. He presses the switch once and the light turns ON. He presses it a second time and the light turns OFF. He presses the switch a third time and the light turns ON. He keeps doing this several times. Will the torch be ON or OFF after the 23rd press? How do you know? For what number of presses will the torch be ON? For what number of presses of the switch will the torch be OFF?
Answer

After the 23rd press the torch is ON, because 23 is an odd number.

The torch is ON after an odd number of presses and OFF after an even number of presses.

Press number123456
TorchONOFFONOFFONOFF
Odd or evenoddevenoddevenoddeven

How to know without counting all 23 presses

  1. The torch starts OFF. One press turns it ON.
  2. Presses come in twos — one to switch it on, the next to switch it off. Each such pair leaves the torch back where it began, OFF.
  3. 23 presses make 11 such pairs, and 11 × 2 = 22 presses. After those 22 the torch is OFF.
  4. One press is left over — the 23rd. It turns the torch ON.
Why odd and even is the whole answer: This is exactly the paired arrangement from page 54. An even number of presses pairs off completely and cancels out. An odd number always has one press left alone, and that lonely press is the one that leaves the light shining.
Check it yourself: Press 7 times in the air, counting aloud — ON, OFF, ON, OFF, ON, OFF, ON. The 7th press, an odd one, leaves it ON ✓
Q3.
Mountain climbing. Priyanka Mohite is the first Indian woman to climb five Himalayan peaks above 8,000 metres. Read the table and answer:
Mountain RangeHeight (in metres)Climbed in the Year
Mount Kanchenjunga (India and Nepal border)8,5862022
Mount Everest (Nepal–China border)8,8482013
Mount Makalu (China–Nepal border)8,4852019
Mount Lhotse (Tibet–Nepal border)8,5162018
Mount Kilimanjaro (Africa)5,8952016
Mount Elbrus (Russia)5,6422017
Mount Annapurna I (Nepal)8,0912021
(a) Which is the highest peak she climbed? (b) What is the difference in height between the highest and lowest peaks she has climbed, as per the table. (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?
Answer

First, put the seven peaks in order of height so the table is easy to read.

PeakHeight (m)Year climbed
Mount Everest (Nepal–China border)8,8482013
Mount Kanchenjunga (India and Nepal border)8,5862022
Mount Lhotse (Tibet–Nepal border)8,5162018
Mount Makalu (China–Nepal border)8,4852019
Mount Annapurna I (Nepal)8,0912021
Mount Kilimanjaro (Africa)5,8952016
Mount Elbrus (Russia)5,6422017

(a) Mount Everest, 8,848 m. Compare the thousands digits first — all seven begin with 8 or 5, so the 5s are out. Among the 8-thousands, look at the hundreds: 8, 5, 5, 4, 0. The biggest is 8, so 8,848 is the tallest.

(b) The difference is 3,206 m.

  1. Highest peak: Mount Everest, 8,848 m. Lowest peak in the table: Mount Elbrus, 5,642 m.
  2. Ones: 8 − 2 = 6.
  3. Tens: 4 − 4 = 0.
  4. Hundreds: 8 − 6 = 2.
  5. Thousands: 8 − 5 = 3.
8,848 m − 5,642 m = 3,206 m

(c) The difference is 2,944 m.

  1. Mount Kanchenjunga is 8,586 m and Mount Elbrus is 5,642 m.
  2. Ones: 6 − 2 = 4. No regrouping needed here.
  3. Tens: 8 − 4 = 4.
  4. Hundreds: 5 is smaller than 6. Take 1 thousand from the 8 thousands. Hundreds become 15, thousands become 7. 15 − 6 = 9.
  5. Thousands: 7 − 5 = 2.
8,586 m − 5,642 m = 2,944 m

(d) She was born in 1993.

  1. She climbed Everest in 2013, aged 20.
  2. Go back 20 years from 2013: 2013 − 20 = 1993.
Year of birth = 1993
Check them: 5,642 + 3,206 = 8,848 ✓   5,642 + 2,944 = 8,586 ✓   1993 + 20 = 2013 ✓
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