A man sells a radio-set for Rs 605 and gains 10%. At what price should he sell another radio of the same kind, in order to gain 16% ?

Answer

To solve the problem step by step, we need to find the cost price (CP) of the radio first and then calculate the selling price (SP) for a 16% gain.

### Step 1: Understand the given information
- Selling Price (SP) for the first radio = Rs 605
- Gain percentage for the first radio = 10%

### Step 2: Calculate the Cost Price (CP) of the first radio
We know the relationship between Selling Price, Cost Price, and Gain:
\[ \text{SP} = \text{CP} + \text{Gain} \]

Where Gain can be expressed as:
\[ \text{Gain} = \text{Gain Percentage} \times \text{CP} \]

So, we can rewrite the equation as:
\[ \text{SP} = \text{CP} + (\text{Gain Percentage} \times \text{CP}) \]
\[ \text{SP} = \text{CP} \times (1 + \text{Gain Percentage}) \]

Substituting the known values:
\[ 605 = \text{CP} \times (1 + 0.10) \]
\[ 605 = \text{CP} \times 1.10 \]

Now, we can solve for CP:
\[ \text{CP} = \frac{605}{1.10} \]
\[ \text{CP} = 550 \]

### Step 3: Calculate the Gain for the second radio with a 16% gain
Now we need to find the selling price for a 16% gain. First, we calculate the gain:
\[ \text{Gain} = \text{Gain Percentage} \times \text{CP} \]
\[ \text{Gain} = 0.16 \times 550 \]
\[ \text{Gain} = 88 \]

### Step 4: Calculate the Selling Price (SP) for the second radio
Now we can find the selling price for the second radio:
\[ \text{SP} = \text{CP} + \text{Gain} \]
\[ \text{SP} = 550 + 88 \]
\[ \text{SP} = 638 \]

### Final Answer
The selling price at which he should sell another radio of the same kind to gain 16% is **Rs 638**.

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