QUESTION

CSAT

Medium

Maths

Prelims 2024

A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?

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Explanation

To solve this, we need to find the common divisors of $399$ (the amount of petrol) and $532$ (the amount of diesel). The common divisors will give us the possible bottle sizes.

Step 1: Find the prime factors of $399$ and $532$

$399 = 1 \times 3 \times 7 \times 19$ $532 = 1 \times 2 \times 2 \times 7 \times 19$

Step 2: Determine common divisors

The common factors between $399$ and $532$ are $1$ , $7$ and $19$ , and their multiple, $133$ .

The possible bottle sizes are the common divisors of $399$ and $532$ , which are $1$ , $7$ , $19$ , and $133$ . Therefore, there are 4 possible bottle sizes.