A shopkeeper sells bed sheets for Rs. 320 each at a profit of 24%. He gives one bed sheet free on a purchase of four bed sheets. Sunil needs 7 bed sheets whereas Piyush needs 8. How much will they save, if they purchase the bed sheets together rather than separately?

Options

A. 480
B. 320
C. 960
D. 640

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the Cost Price of One Bed Sheet
Given that the selling price of one bed sheet is Rs. 320 and the profit is 24%, we can find the cost price (CP) using the formula:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]

Since Profit = 24% of CP, we can express SP as:

\[ SP = CP + 0.24 \times CP = 1.24 \times CP \]

Rearranging gives us:

\[ CP = \frac{SP}{1.24} = \frac{320}{1.24} \approx 258.06 \]

### Step 2: Determine How Many Bed Sheets Each Person Needs
- Sunil needs 7 bed sheets.
- Piyush needs 8 bed sheets.

### Step 3: Calculate the Total Cost for Sunil
Sunil can buy 4 bed sheets and get 1 free. Therefore, to get 7 bed sheets, he needs to buy:

- 4 bed sheets (gets 1 free) = 5 bed sheets
- He still needs 2 more, so he buys 2 more bed sheets.

Total bed sheets he pays for = 4 + 2 = 6 bed sheets.

Total cost for Sunil:

\[ \text{Total Cost for Sunil} = 6 \times 320 = 1920 \]

### Step 4: Calculate the Total Cost for Piyush
Piyush can also buy 4 bed sheets and get 1 free. Therefore, to get 8 bed sheets, he needs to buy:

- 4 bed sheets (gets 1 free) = 5 bed sheets
- He still needs 3 more, so he buys 3 more bed sheets.

Total bed sheets he pays for = 4 + 3 = 7 bed sheets.

Total cost for Piyush:

\[ \text{Total Cost for Piyush} = 7 \times 320 = 2240 \]

### Step 5: Calculate the Total Cost if They Buy Separately
Total cost if they buy separately:

\[ \text{Total Cost (Separate)} = \text{Total Cost for Sunil} + \text{Total Cost for Piyush} = 1920 + 2240 = 4160 \]

### Step 6: Calculate the Total Cost if They Buy Together
If they buy together, they need a total of:

\[ 7 + 8 = 15 \text{ bed sheets} \]

They can buy 4 bed sheets and get 1 free, so they can buy:

- 12 bed sheets (3 sets of 4 bed sheets) and get 3 free = 15 bed sheets.

Total bed sheets they pay for = 12.

Total cost if they buy together:

\[ \text{Total Cost (Together)} = 12 \times 320 = 3840 \]

### Step 7: Calculate the Savings
Now, we can find the savings by subtracting the total cost if they buy together from the total cost if they buy separately:

\[ \text{Savings} = \text{Total Cost (Separate)} - \text{Total Cost (Together)} = 4160 - 3840 = 320 \]

### Final Answer
Sunil and Piyush will save Rs. 320 if they purchase the bed sheets together rather than separately.

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