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Ques:- A merchant has 140 litres, 260 litres, 320 litres of three kinds of oil. He wants to sell the oil by filling the three kinds separately in tins of equal volume. The volume of such a tin will be
A. 13 litres
B. 16 litres
C. 20 litres
D. 70 litres
Right Answer:
-
Quantities of three kinds of oil:
✓ 140 litres
✓ 260 litres
✓ 320 litres
We need to find the largest possible volume of a tin (in litres) such that all three oils can be exactly filled in separate tins of equal capacity.
🧠 This is a Highest Common Factor (HCF) problem.
✅ Step 1: Find the HCF of 140, 260, and 320
Let’s do the prime factorization:
-
140 = 2 × 2 × 5 × 7 = 2² × 5 × 7
-
260 = 2 × 2 × 5 × 13 = 2² × 5 × 13
-
320 = 2 × 2 × 2 × 2 × 2 × 5 = 2⁵ × 5
Now take the common factors:
-
2² = 4
-
5 = 5
HCF = 2² × 5 = 4 × 5 = 20
—
✅ Final Answer: The volume of each tin will be 20 litres.
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