A vendor has 120 kg rice of one kind, 160 kg of another kind and 210 kg of a third kind. He wants to sell the rice by filling the three kinds of rice in bags of equal capacity. What should be the greatest capacity of such a bag?

Given:

A vendor has 120 kg rice of one kind, 160 kg of another kind, and 210 kg of a third kind.

He wants to sell the rice by filling the three kinds of rice in bags of equal capacity.

Formula used:

To find the greatest capacity of each bag, we need to find the Greatest Common Divisor (GCD) of the quantities of rice.

Calculation:

Finding GCD of 120, 160, and 210:

Prime factorization of 120: 2³ × 3 × 5

Prime factorization of 160: 2⁵ × 5

Prime factorization of 210: 2 × 3 × 5 × 7

Common factors: 2 and 5

Minimum power of common factors: 2¹ × 5¹

⇒ GCD = 2 × 5 = 10

∴ The greatest capacity of such a bag should be 10 kg. The correct answer is option (3).