19. 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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Accepted Answer

The correct answer is option B. To bottle petrol and diesel separately in bottles of equal size, the capacity of the bottle must be a common divisor of the quantities of petrol (399 litres) and diesel (532 litres). We need to find all common factors of 399 and 532. First, let's find the prime factorization of each number:
399 = 3 × 7 × 19
532 = 2 × 2 × 7 × 19 = 2^2 × 7 × 19
The common prime factors are 7 and 19. The Highest Common Factor (HCF) of 399 and 532 is 7 × 19 = 133. The common divisors are the factors of the HCF (133). The factors of 133 are: 1, 7, 19, and 133. These are the possible integer bottle capacities. Therefore, there are 4 different possible bottle sizes. This question tests the application of HCF in a practical scenario.

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