A shopkeeper offers 30% discount on tables which have been marked 80% above the cost price. Shalini bought the table for Rs . 567. What was the cost price (in Rs.) of the table ?

Options

A. 450
B. 468
C. 500
D. 510

Answer

To find the cost price of the table, we can follow these steps:

### Step 1: Understand the given information
- Shalini bought the table for Rs. 567, which is the selling price (SP) after a discount.
- The shopkeeper offers a 30% discount on the marked price (MP).
- The marked price is 80% above the cost price (CP).

### Step 2: Calculate the marked price (MP)
Since the selling price (SP) is after a 30% discount, we can express the relationship between SP and MP as follows:

\[ SP = MP \times (1 - \text{Discount Rate}) \]

Here, the discount rate is 30%, or 0.30. Therefore:

\[ SP = MP \times (1 - 0.30) = MP \times 0.70 \]

Now, substituting the value of SP:

\[ 567 = MP \times 0.70 \]

To find the marked price (MP), we rearrange the equation:

\[ MP = \frac{567}{0.70} \]

Calculating this gives:

\[ MP = \frac{567 \times 100}{70} = 810 \]

### Step 3: Calculate the cost price (CP)
We know that the marked price is 80% above the cost price. This can be expressed as:

\[ MP = CP \times (1 + 0.80) = CP \times 1.80 \]

Now, substituting the value of MP:

\[ 810 = CP \times 1.80 \]

To find the cost price (CP), we rearrange the equation:

\[ CP = \frac{810}{1.80} \]

Calculating this gives:

\[ CP = \frac{810 \times 100}{180} = 450 \]

### Conclusion
The cost price of the table is Rs. 450.

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