Vinod sold a watch to Arun at a gain of 12% and Arun had to sell it to Manoj at a loss of 5%. If Manoj paid Rs. 3990 for it, how much did Vinod pay for the watch?

Answer

To find out how much Vinod paid for the watch, we will work backwards from the information given about Manoj's purchase.

### Step-by-step Solution:

1. **Understand the Selling Price (SP) of Manoj**:
Manoj bought the watch for Rs. 3990.

2. **Calculate the Cost Price (CP) for Arun**:
Arun sold the watch to Manoj at a loss of 5%.
We can use the formula for selling price at a loss:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
Rearranging this formula to find the cost price (CP) of Arun:
\[ CP = \frac{SP}{1 - \frac{Loss\%}{100}} = \frac{3990}{1 - 0.05} = \frac{3990}{0.95} \]
Now, calculate:
\[ CP = \frac{3990}{0.95} = 4200 \]
So, Arun's cost price for the watch is Rs. 4200.

3. **Calculate the Cost Price (CP) for Vinod**:
Vinod sold the watch to Arun at a gain of 12%.
We can use the formula for selling price at a gain:
\[ SP = CP \times \left(1 + \frac{Gain\%}{100}\right) \]
Rearranging this formula to find the cost price (CP) of Vinod:
\[ CP = \frac{SP}{1 + \frac{Gain\%}{100}} = \frac{4200}{1 + 0.12} = \frac{4200}{1.12} \]
Now, calculate:
\[ CP = \frac{4200}{1.12} \approx 3750 \]
So, Vinod paid approximately Rs. 3750 for the watch.

### Final Answer:
Vinod paid Rs. 3750 for the watch.