Q) Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time.

(Q 24- 30/3/3 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s convert the lengths of given planks in single unit:

∵ Length of 1st plank is 4 m 20 cm = 420 cm

and length of 2nd plank is 5 m 4 cm = 504 cm

∴ Lengths of planks are 420 cm and 504 cm

Step 2: ∵ we need to measure both these lengths by a common plank,

∴ its length will be a common factor to 420 and 504

∵ this plank has to measure in least time,

∴ its length has to be longest

∴ we need to calculate Highest common factor of both numbers

Step 3: By prime factorisation, we get:

420 = 2 x 2 x 3 x 5 x 7

504 = 2 x 2 x 2 x 3 x 3 x 7

Here, collecting all common factors, we get HCF = 2 x 2 x 3 x 7 = 84

∴ length of the plank = 84 cm

Therefore, length of the common plank should be 84 cm to measure both planks in the least time.

Check: if common plank is 84 cm, it will measure 420 cm plank in 5 times and 504 cm plank in 6 times.
Since this 84 cm plank is measuring both the planks (common to both), and measuring in the least time (no other planks can measure in lower times), hence both the given conditions are matched ∴ Our answer is correct.

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