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
This questions was previously asked in
UPSC CSAT, Previous year (2024)
Explanation:
- We need to find the greatest common divisor (GCD) of 399 and 532 to determine the largest bottle size.
- Finding the GCD helps us understand the maximum size that allows exact division of petrol and diesel separately.
- The GCD of 399 and 532 is 133.
- Possible sizes must divide both 399 and 532 entirely, meaning the divisors of 133.
- Divisors of 133 are 1, 7, 19, and 133.
- Option:1, 3 proposes 3 bottle sizes, which is fewer than the actual.
- Option:2, 4 is correct as it matches the 4 possible sizes.
- Option:3, 5 suggests 5 bottle sizes, which is too many.
- Option:4, 6 is incorrect as it exceeds the actual number.
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By: Parvesh Mehta