The largest measuring cylinder that can accurately fill 3 tanks of capacity 98…

2024

The largest measuring cylinder that can accurately fill 3 tanks of capacity 98 , 182 & 266 liters each , is of capacity

  1. A.

    2 L

  2. B.

    7 L

  3. C.

    14 L

  4. D.

    98 L

Attempted by 79 students.

Show answer & explanation

Correct answer: C

Answer: 14 liters

Key idea: The largest measuring cylinder that can exactly fill all three tanks must be the highest common factor (HCF) of 98, 182 and 266 liters.

  1. Find HCF of 98 and 182 using the Euclidean algorithm:

    182 = 98 × 1 + 84

    98 = 84 × 1 + 14

    84 = 14 × 6 + 0 ⇒ HCF(98, 182) = 14

  2. Now find HCF of the result 14 and 266:

    266 = 14 × 19 + 0 ⇒ HCF(14, 266) = 14

Conclusion: HCF(98, 182, 266) = 14, so the largest measuring cylinder that can accurately fill all three tanks has capacity 14 liters.

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