A buyer purchases 60 quintals of rice of two sorts for Rs. 4642.50 in total. The better sort costs Rs. 80 per quintal and the inferior sort costs Rs. 75.50 per quintal. How many quintals of each sort did he buy?

Introduction / Context:
This is a classic two-variable mixture cost problem. Knowing the total weight and total cost lets us determine how much was bought at each price point.

Given Data / Assumptions:

• Total weight = 60 quintals.
• Price (better) = Rs. 80/q; price (worse) = Rs. 75.50/q.
• Total cost = Rs. 4642.50.

Concept / Approach:
Let x be the quantity of the better sort. Then the inferior sort is 60 − x. Form the total cost equation 80x + 75.5(60 − x) = 4642.5 and solve for x.

Step-by-Step Solution:
80x + 75.5(60 − x) = 4642.580x + 4530 − 75.5x = 4642.54.5x = 112.5 ⇒ x = 25 quintals (better)Inferior sort = 60 − 25 = 35 quintals

Verification / Alternative check:
Cost check: 25*80 + 35*75.5 = 2000 + 2642.5 = 4642.5, matches the total.

Why Other Options Are Wrong:
Other splits do not satisfy the cost equation simultaneously with the total weight of 60 quintals.

Common Pitfalls:
Arithmetic slip on 4.5x or misreading 75.50 as 75 or 75.05.

Final Answer:
25 quintals, 35 quintals