How many kgs of wheat costing Rs.24/- per kg must be mixed with 30 kgs of…
2025
How many kgs of wheat costing Rs.24/- per kg must be mixed with 30 kgs of wheat costing Rs.18.40/- per kg so that 15% profit can be obtained by selling the mixture at Rs.23/- per kg?
- A.
18
- B.
12
- C.
11
- D.
9
Show answer & explanation
Correct answer: B
Concept: The cost price of a mixture of two items is the weighted average of their individual cost prices, weighted by quantity — CP(mixture) = (q1p1 + q2p2)/(q1+q2). Also, if an item is sold at a profit of P% over its cost price, then CP = SP ÷ (1 + P/100).
Application:
The mixture is sold at Rs. 23/kg with a 15% profit, so its cost price = 23 ÷ 1.15 = Rs. 20/kg.
Let x kg of wheat costing Rs. 24/kg be mixed with the given 30 kg of wheat costing Rs. 18.40/kg.
Setting the weighted-average cost price of the mixture to Rs. 20/kg: (24x + 18.40 × 30) ÷ (x + 30) = 20
24x + 552 = 20x + 600
4x = 48, so x = 12
Cross-check: With x = 12 kg, the mixture's cost price = (24×12 + 552) ÷ (12+30) = 840 ÷ 42 = Rs. 20/kg. Selling this mixture at Rs. 23/kg gives a profit of (23−20)/20 = 15%, confirming the result.
