Let's break this down step-by-step.
### Step 1: Determining the Cost Price
The shopkeeper loses 5% by selling the watch for Rs 1,140.
Loss percentage is given as 5%.
We know the formula for loss:
[tex]\[ \text{Selling Price} = \text{Cost Price} \times \left(1 - \frac{\text{Loss Percentage}}{100}\right) \][/tex]
Given:
[tex]\[ \text{Selling Price} = Rs \, 1,140 \][/tex]
[tex]\[ \text{Loss Percentage} = 5\% \][/tex]
Using the formula:
[tex]\[ 1140 = \text{Cost Price} \times (1 - \frac{5}{100}) \][/tex]
[tex]\[ 1140 = \text{Cost Price} \times 0.95 \][/tex]
To find the Cost Price:
[tex]\[ \text{Cost Price} = \frac{1140}{0.95} \][/tex]
[tex]\[ \text{Cost Price} = 1200 \][/tex]
So, the Cost Price of the watch is Rs 1,200.
### Step 2: Selling Price to Gain 5%
We need to find the selling price to gain a profit of 5%.
Profit percentage is given as 5%.
We know the formula for profit:
[tex]\[ \text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \][/tex]
Given:
[tex]\[ \text{Profit Percentage} = 5\% \][/tex]
[tex]\[ \text{Cost Price} = Rs \, 1200 \][/tex]
Using the formula:
[tex]\[ \text{Selling Price} = 1200 \times \left(1 + \frac{5}{100}\right) \][/tex]
[tex]\[ \text{Selling Price} = 1200 \times 1.05 \][/tex]
[tex]\[ \text{Selling Price} = 1260 \][/tex]
So, to gain a profit of 5%, the shopkeeper must sell the watch for Rs 1,260.
### Summary:
1. The cost price of the watch is Rs 1,200.
2. The shopkeeper must sell the watch for Rs 1,260 to gain a 5% profit.
