Question

A shopkeeper sold two watches for rupees 425 is gaining 10% on one and losing 10% other which of the following is true ​

Answer 1

The seller incurs a loss of 1% overall.

• Two watches are sold at Rs. 3000 each.

• On one the shopkeeper gains 10% and on one 10% .
• We have to find the overall gain or loss percentage.
• Let us assume the cost price of first watch be $x_1$ and other be $x_2$.
• We have to calculate the profit and loss on the watches.
• Profit percentage = $\frac{425-x_1}{x_1}$ × 100 = 10

$425-x_1 = 0.10x_1$

425 = $1.1x_1$

$x_1$ = 425/1.1 = 386.36 Rs.

• Therefore cost price of the article where the seller gains 10% is Rs. 386.36.
• Loss percentage = $\frac{x_2-425}{x_2}$ × 100 = 10

$x_2-425$  = $0.1x_2$

$0.9x_2$  = 425

$x_2$ = Rs. 472.22

• Therefore cost price of the article where the seller loses 10% is Rs. 472.22.
• Now we have to calculate the net profit or loss percentage, we find the total cost price of two articles,
• Total cost price = 386.36 + 472.22 = 858.58 Rs.

• Now ,Profit on article 1 - Loss on article 2 = Net gain

(425-386.36) - (472.22-425) = Net gain

Net gain = 38.64 - 47.22 = -8.58

• Therefore the seller gains a loss of 8.58 Rs. total on both products.

• Now net loss percentage = $\frac{Net \ loss}{total \ cost \ price}$ × 100  

Net loss percentage = $\frac{8.58}{858.58}$ × 100 = 1%

Answer 2

Step-by-step explanation:

Selling price of watch A and watch B= Rs. 425

Let cost price of watch A=x

Profit =10%

∴100110x=425 

            x=386.36

Let cost price of watch B=y

Loss =10%

∴10090y=425

            y=472.22

Net cost price =x+y=858.5858

Net selling price =850

Loss%=858.58858.5858−850×100=1%