A sold a tape-recorder to B for 74,860 at a loss of 19%. Again B sold it to Cat a price that would give A a profit of 17%. The gain% of B is

Options

A. 22 `2/9` %
B. 33 `1/3` %
C. 44 `4/9` %
D. 66 `2/3` %

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Cost Price of A
A sold the tape recorder to B for Rs 74,860 at a loss of 19%. This means that the selling price (SP) is 81% of the cost price (CP) of A.

Let the cost price of A be \( CP_A \).

Using the formula for selling price:
\[ SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
We can write:
\[ 74,860 = CP_A \times \left(1 - \frac{19}{100}\right) \]
\[ 74,860 = CP_A \times 0.81 \]

Now, we can solve for \( CP_A \):
\[ CP_A = \frac{74,860}{0.81} = 92,000 \]

### Step 2: Determine the Selling Price of B
B sold the tape recorder to C at a price that would give A a profit of 17%. This means that the selling price (SP) for B is 117% of the cost price (CP) of A.

Let the selling price of B be \( SP_B \).

Using the formula for selling price:
\[ SP_B = CP_A \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]
Substituting the values:
\[ SP_B = 92,000 \times \left(1 + \frac{17}{100}\right) \]
\[ SP_B = 92,000 \times 1.17 = 107,640 \]

### Step 3: Determine the Gain of B
Now, we can find the gain of B. The cost price of B is the price at which A sold it to B, which is Rs 74,860.

The gain for B is:
\[ \text{Gain} = SP_B - CP_B \]
\[ \text{Gain} = 107,640 - 74,860 = 32,780 \]

### Step 4: Calculate the Gain Percentage of B
Now we can find the gain percentage of B using the formula:
\[ \text{Gain \%} = \left(\frac{\text{Gain}}{\text{Cost Price}} \times 100\right) \]
Substituting the values:
\[ \text{Gain \%} = \left(\frac{32,780}{74,860} \times 100\right) \approx 43.7\% \]

### Final Answer
The gain percentage of B is approximately **43.7%**.

---