A man sold two cows for Rs. 210 at a total profit of 5%. He sold one cow at a…
2024
A man sold two cows for Rs. 210 at a total profit of 5%. He sold one cow at a loss of 10% and another at a profit of 10%. What is the price of each row ?
- A.
29,58
- B.
50,100
- C.
50,150
- D.
12,150
Attempted by 22 students.
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Correct answer: C
Key idea: use the overall profit to find total cost, then set up two equations and solve.
Total selling price is 210 with an overall profit of 5%, so the total cost of the two cows is 210 ÷ 1.05 = 200.
Let the cost prices be x and y. Then x + y = 200.
One cow is sold at 10% loss and the other at 10% profit, so the selling prices sum to 0.9x + 1.1y = 210.
Multiply x + y = 200 by 0.9 to get 0.9x + 0.9y = 180. Subtract this from 0.9x + 1.1y = 210 to get 0.2y = 30, so y = 150.
Then x = 200 − 150 = 50.
Check: 0.9×50 + 1.1×150 = 45 + 165 = 210, which matches the given selling total.
Answer: The cost prices are 50 and 150.