After giving two successive discounts of 20% and 25% a cycle is sold for Rs. 4200. What is the amrked price (in Rs.) of the cycle ?

Options

A. 7200
B. 7000
C. 6500
D. 6200

Answer

To find the marked price of the cycle after giving two successive discounts of 20% and 25%, we can follow these steps:

### Step 1: Understand the discounts
The cycle is sold for Rs. 4200 after applying two successive discounts of 20% and 25%. We need to find the marked price (MP) before the discounts were applied.

### Step 2: Calculate the effective discount
To find the effective discount from two successive discounts, we can use the formula:
\[ \text{Effective Discount} = x + y - \left(\frac{x \cdot y}{100}\right) \]
where \(x\) is the first discount (20%) and \(y\) is the second discount (25%).

Substituting the values:
\[ \text{Effective Discount} = 20 + 25 - \left(\frac{20 \cdot 25}{100}\right) \]
\[ = 20 + 25 - \left(\frac{500}{100}\right) \]
\[ = 20 + 25 - 5 = 40\% \]

### Step 3: Relate selling price to marked price
If the effective discount is 40%, then the selling price (SP) is 60% of the marked price (MP). This is because:
\[ \text{SP} = \text{MP} \times \left(1 - \frac{\text{Effective Discount}}{100}\right) \]
Thus:
\[ 4200 = \text{MP} \times 0.60 \]

### Step 4: Solve for the marked price
To find the marked price, we rearrange the equation:
\[ \text{MP} = \frac{4200}{0.60} \]
Calculating this gives:
\[ \text{MP} = 4200 \div 0.60 = 7000 \]

### Final Answer
The marked price of the cycle is Rs. 7000.

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