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NCERT Solutions Ganita Prakash Chapter 5 & 109Playing with other number pairs — In-text Questions

Book page 108 Updated on2026-09-05

Q1.
Let us now play the ‘idli-vada’ game with different pairs of numbers: a. 2 and 5, b. 3 and 7, c. 4 and 6. We will say ‘idli’ for multiples of the smaller number, ‘vada’ for multiples of the larger number and ‘idli-vada’ for common multiples. Draw a figure similar to Fig. 5.1 if the game is played up to 60.
Answer

For each pair, first find the first common multiple. Then every next common multiple is obtained by adding that number again.

Pair‘idli’ (smaller number)‘vada’ (larger number)‘idli-vada’ up to 60
a. 2 and 5multiples of 2multiples of 510, 20, 30, 40, 50, 60
b. 3 and 7multiples of 3multiples of 721, 42
c. 4 and 6multiples of 4multiples of 612, 24, 36, 48, 60

Now the three figures. In each one, write the ‘idli’-only numbers in the left circle, the ‘vada’-only numbers in the right circle and the common multiples in the overlap.

a. 2 and 5 — first common multiple 10
‘idli’ only: 2, 4, 6, 8, 12, 14, 16, 18, 22, 24, 26, 28, 32, 34, 36, 38, 42, 44, 46, 48, 52, 54, 56, 58 (24 numbers)
‘vada’ only: 5, 15, 25, 35, 45, 55 (6 numbers)
‘idli-vada’: 10, 20, 30, 40, 50, 60 (6 numbers)
b. 3 and 7 — first common multiple 21
‘idli’ only: 3, 6, 9, 12, 15, 18, 24, 27, 30, 33, 36, 39, 45, 48, 51, 54, 57, 60 (18 numbers)
‘vada’ only: 7, 14, 28, 35, 49, 56 (6 numbers)
‘idli-vada’: 21, 42 (2 numbers)
c. 4 and 6 — first common multiple 12
‘idli’ only: 4, 8, 16, 20, 28, 32, 40, 44, 52, 56 (10 numbers)
‘vada’ only: 6, 18, 30, 42, 54 (5 numbers)
‘idli-vada’: 12, 24, 36, 48, 60 (5 numbers)
Something worth noticing: for 2 and 5 the first ‘idli-vada’ is 10 = 2 × 5, and for 3 and 7 it is 21 = 3 × 7 — the product itself. But for 4 and 6 it is only 12, which is less than 4 × 6 = 24. The reason is that 4 and 6 share the common factor 2. You will meet this idea again on page 116.
Q2.
Yesterday, we played this game with two numbers. We ended up saying just ‘idli’ or ‘idli-vada’ and nobody said just ‘vada’! One of the numbers was 4. Which of the following could be the other number: 2, 3, 5, 8, 10?
Answer

Answer: 8.

Nobody said just ‘vada’. That means every multiple of the other number was also a multiple of 4 — so it always turned into an ‘idli-vada’. This happens only when the other number is itself a multiple of 4.

Other numberA ‘vada’ number that is not a multiple of 4Works?
22, 6, 10, … are multiples of 2 but not of 4No
33, 6, 9, … are not multiples of 4No
55, 10, 15, … are not multiples of 4No
88, 16, 24, 32, … every one is a multiple of 4Yes ✔
1010, 30, 50, … are not multiples of 4No
With 4 and 8: 4 → idli, 8 → idli-vada, 12 → idli, 16 → idli-vada, 20 → idli, 24 → idli-vada, …
Why: ‘vada’ is said at multiples of 8, and every multiple of 8 (8, 16, 24, …) is also a multiple of 4. So a plain ‘vada’ never gets a chance — it is always upgraded to ‘idli-vada’.
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