A trader allows two successive discount of `20%` and `10%`. If he gets Rs. 108 for an article, then its marked price is

Options

A. Rs. `142 cdot 56`
B. Rs. `140 cdot 40`
C. Rs. 160
D. Rs. 150

Answer

To find the marked price of the article after allowing two successive discounts of 20% and 10%, we can follow these steps:

### Step 1: Calculate the net discount percentage
The formula for calculating the net discount when two successive discounts are applied is:
\[ \text{Net Discount} = x + y - \frac{xy}{100} \]
where \(x\) is the first discount percentage and \(y\) is the second discount percentage.

Here, \(x = 20\%\) and \(y = 10\%\).

Substituting the values:
\[ \text{Net Discount} = 20 + 10 - \frac{20 \times 10}{100} \]
\[ = 30 - \frac{200}{100} \]
\[ = 30 - 2 = 28\% \]

### Step 2: Determine the selling price after the discount
Let the marked price be \(M\). After applying a 28% discount, the selling price (SP) can be expressed as:
\[ \text{SP} = M - \text{Discount} \]
\[ \text{SP} = M - 0.28M = 0.72M \]

### Step 3: Set up the equation with the given selling price
We know from the problem that the selling price (SP) is Rs. 108. Therefore, we can set up the equation:
\[ 0.72M = 108 \]

### Step 4: Solve for the marked price \(M\)
To find \(M\), we can rearrange the equation:
\[ M = \frac{108}{0.72} \]

Calculating the right side:
\[ M = \frac{108 \times 100}{72} = \frac{10800}{72} = 150 \]

### Conclusion
The marked price of the article is Rs. 150.

---