Pepsi and Coke, there are two companies selling the packs of cold-drinks. For the same selling price Pepsi gives two successive discounts of `10%` and `25%`. While Coke sells it by giving two successive discounts of `15%` and `20%`. What is the ratio of their marked price?

Options

A. 143:144
B. 112:114
C. 136:135
D. 73:77

Answer

To solve the problem of finding the ratio of the marked prices of Pepsi and Coke after applying their respective discounts, we can follow these steps:

### Step 1: Calculate the effective discount for Pepsi
Pepsi offers two successive discounts of 10% and 25%. We can calculate the effective discount using the formula:
\[ \text{Effective Discount} = d_1 + d_2 - \left(\frac{d_1 \times d_2}{100}\right) \]
Where \(d_1 = 10\%\) and \(d_2 = 25\%\).

Calculating:
\[ \text{Effective Discount} = 10 + 25 - \left(\frac{10 \times 25}{100}\right) = 10 + 25 - 2.5 = 32.5\% \]

### Step 2: Calculate the selling price for Pepsi
Assuming the marked price (MP) of Pepsi is 100, the selling price (SP) after the discount can be calculated as:
\[ \text{SP} = \text{MP} - \text{Effective Discount} = 100 - 32.5 = 67.5 \]

### Step 3: Calculate the effective discount for Coke
Coke offers two successive discounts of 15% and 20%. We can use the same formula:
\[ \text{Effective Discount} = d_1 + d_2 - \left(\frac{d_1 \times d_2}{100}\right) \]
Where \(d_1 = 15\%\) and \(d_2 = 20\%\).

Calculating:
\[ \text{Effective Discount} = 15 + 20 - \left(\frac{15 \times 20}{100}\right) = 15 + 20 - 3 = 32\% \]

### Step 4: Calculate the selling price for Coke
Assuming the marked price (MP) of Coke is also 100, the selling price (SP) after the discount can be calculated as:
\[ \text{SP} = \text{MP} - \text{Effective Discount} = 100 - 32 = 68 \]

### Step 5: Set the selling prices equal
Since both companies sell their products at the same selling price, we set the selling prices equal:
\[ 67.5x = 68y \]
Where \(x\) is the marked price of Pepsi and \(y\) is the marked price of Coke.

### Step 6: Find the ratio of marked prices
From the equation \(67.5x = 68y\), we can express the ratio of the marked prices:
\[ \frac{x}{y} = \frac{68}{67.5} \]

To simplify:
\[ \frac{x}{y} = \frac{68 \times 10}{67.5 \times 10} = \frac{680}{675} = \frac{136}{135} \]

### Final Answer
Thus, the ratio of the marked prices of Pepsi to Coke is:
\[ \text{Ratio of marked prices} = 136 : 135 \]

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