A shopkeeper sell a watch for Rs. 575 and makes a profit of 15%, he sells a different watch at a loss of 10%. Over all, he neither gains nor loses. What is cost price of the second watch?a)550b)625c)650d)675Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Answer ( D ) 675

Answer

Given:
- The shopkeeper sells a watch for Rs. 575 and makes a profit of 15%.
- He sells a different watch at a loss of 10%.
- Overall, he neither gains nor loses.

To Find:
The cost price of the second watch.

Assumption:
Let's assume the cost price of the second watch as 'x'.

Calculations:

Profit Calculation:
- The shopkeeper sells the first watch for Rs. 575 and makes a profit of 15%.
- Profit = Selling Price - Cost Price
- Profit = 15% of Cost Price
- Cost Price = Selling Price - Profit
- Cost Price = Rs. 575 - 15% of Cost Price
- Cost Price = Rs. 575 - (15/100) * Cost Price
- Cost Price + (15/100) * Cost Price = Rs. 575
- (115/100) * Cost Price = Rs. 575
- Cost Price = Rs. 575 * (100/115)
- Cost Price = Rs. 500

Loss Calculation:
- The shopkeeper sells the second watch at a loss of 10%.
- Loss = Selling Price - Cost Price
- Loss = 10% of Cost Price
- Selling Price = Cost Price - Loss
- Selling Price = x - 10% of x
- Selling Price = x - (10/100) * x
- Selling Price = x - (1/10) * x
- Selling Price = x - x/10
- Selling Price = (10x - x)/10
- Selling Price = 9x/10

Overall Calculation:
- Overall, the shopkeeper neither gains nor loses.
- The total profit should be equal to the total loss.
- Total Profit = Profit from the first watch + Loss from the second watch
- Total Profit = 15% of Cost Price - 10% of Cost Price
- Total Profit = 5% of Cost Price
- Total Loss = Loss from the second watch = 10% of Cost Price

Equating the total profit and total loss:
5% of Cost Price = 10% of Cost Price
(5/100) * Cost Price = (10/100) * Cost Price
5 * Cost Price = 10 * Cost Price
5 * x = 10 * x
5x = 10x
5x - 10x = 0
-5x = 0
x = 0/-5
x = 0

Conclusion:
The cost price of the second watch is Rs. 0.

However, it seems that there might be an error in the given options for the answer, as none of them match the calculated cost price.

Answer

Let X be the cost price of watch which was sold with 15% profit

so, X+ X*0.15=575

X=500

profit is 575-500=75

since here profit amount of first watch is same as loss amount of second watch

10% 0f loss amount is 75

cost price of second watch is Rs. 750

so, none of the options are valid

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