Question

An oil dealer had three types of oil. 403 litres of the first kind, 434 litres of the second kind and 465 litres of the third kind. Find the maximum volume of oil, filled in each barrel, if equal number of barrels are filled.

• A. 52 litres
• B. 48 litres
• C. 31 litres
• D. 41 litres

Answer 1

Answer:

C. 31 litres

To fill equal number of barrels with no oil left over, the capacity of each barrel must be the greatest possible volume that divides 403, 434, and 465 exactly.

So we need:
$\gcd(403,;434,;465)$

Find GCD

• $(403 = 13 \times 31)$

• $(434 = 2 \times 7 \times 31)$

• $(465 = 3 \times 5 \times 31)$

Common factor in all three is:
31
So,
$\gcd(403,434,465) = 31$

Interpretation

Each barrel will contain 31 litres, so all quantities can be evenly divided.

Final Answer:

Maximum volume of oil in each barrel = 31 litres