Surendra has 102 litres of Oil A and 224 litres of Oil B. He fills a number of identical containers with the two types of oil in a manner that each container has only one type of oil, and all containers are completely filled. What can be the maximum volume (in litres) of each container that Surendra uses, so that all the oil that Surendra has, of both the types, can be poured into these containers?

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 2)

Answer 1

Given:

Volume of Oil A = 102 litres

Volume of Oil B = 224 litres

Each container has only one type of oil, and all containers are completely filled.

Formula used:

To find the maximum volume of each container, we need to find the Highest Common Factor (HCF) of the given volumes of oil.

Calculations:

Find the prime factors of 102:

102 = 2 × 51

⇒ 102 = 2 × 3 × 17

Find the prime factors of 224:

224 = 2 × 112

⇒ 224 = 2 × 2 × 56

⇒ 224 = 2 × 2 × 2 × 28

⇒ 224 = 2 × 2 × 2 × 2 × 14

⇒ 224 = 2 × 2 × 2 × 2 × 2 × 7

⇒ 224 = 2⁵ × 7

Now, find the HCF of 102 and 224 by taking the common prime factors with the lowest power:

HCF(102, 224) = 2¹

⇒ HCF = 2

∴ The maximum volume of each container that Surendra uses is 2 litres.