A shopkeeper mixed 7kg of salt worth Rs.6 per kg, 5kg of salt worth Rs.4 per…
2024
A shopkeeper mixed 7kg of salt worth Rs.6 per kg, 5kg of salt worth Rs.4 per kg and 6 kg of salt worth Rs.5 per kg. For what amount of money should he sell 4 kg of the mixed variety of salt in order to make a profit of 12 1/2%?
- A.
23
- B.
25
- C.
27
- D.
30
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept: when quantities bought at different rates are mixed together, the cost price per kg of the blend is a quantity-weighted average — multiply each rate by its own quantity, add these products, and divide by the total quantity. Once the blended cost per kg is known, the selling price for a profit of p% is simply CP × (1 + p/100).
Applying this to the mixture:
Total salt mixed = 7 kg + 5 kg + 6 kg = 18 kg.
Total cost of the mixture = (7 × 6) + (5 × 4) + (6 × 5) = 42 + 20 + 30 = ₹92.
Cost price per kg of the blended salt = 92 / 18 = 46/9 rupees per kg.
Cost price of 4 kg of this blended salt = 4 × 46/9 = 184/9 rupees.
A profit of 12½% (= 12.5/100 = 1/8) means the selling price is 9/8 times the cost price, so SP = 184/9 × 9/8 = 184/8 = ₹23.
Cross-check: work out the selling price per kg first — 46/9 × 9/8 = 46/8 = 23/4 rupees per kg — then scale to 4 kg: 4 × 23/4 = ₹23. Both routes agree, confirming ₹23.
