Two mobile phones are sold at Rs.6000 each. The first mobile is sold at 20 %…
2024
Two mobile phones are sold at Rs.6000 each. The first mobile is sold at 20 % profit and the other one at 25 % loss. What is the percentage of loss or profit incurred during the deal?
- A.
Profit 7.69 %
- B.
Loss 7.69 %
- C.
Profit 6.98 %
- D.
Loss 6.98 %
Attempted by 2 students.
Show answer & explanation
Correct answer: B
CONCEPT: When an item is sold at a profit of p%, its cost price equals the selling price divided by (1 + p/100). When sold at a loss of l%, its cost price equals the selling price divided by (1 - l/100). To judge the overall result of two or more such transactions, the individual cost prices must first be found and totalled, then compared with the total selling price — the two percentages cannot simply be averaged when the selling prices or bases differ.
Applying this step by step:
Cost price of the first phone (sold at 20% profit) = 6000 / (1 + 20/100) = 6000 / 1.2 = Rs. 5000.
Cost price of the second phone (sold at 25% loss) = 6000 / (1 - 25/100) = 6000 / 0.75 = Rs. 8000.
Total cost price = 5000 + 8000 = Rs. 13000.
Total selling price = 6000 + 6000 = Rs. 12000.
Since the total selling price is less than the total cost price, the deal results in a net loss = 13000 - 12000 = Rs. 1000.
Loss percentage = (Net loss / Total cost price) x 100 = (1000 / 13000) x 100 ≈ 7.69%.
CROSS-CHECK: 5000 x 1.2 = 6000 (matches the first selling price) and 8000 x 0.75 = 6000 (matches the second selling price), confirming both cost prices; and 13000 - 1000 = 12000, which matches the total selling price, confirming the loss figure.