A person sold a cycle at Rs. 935 with a gain of 10% then at how much amount did he purchase the cycle ?

Question

Accepted Answer

To determine the purchase price of the cycle, we need to understand the relationship between the selling price, the gain percentage, and the cost price. The problem states that the cycle was sold for Rs. 935 with a gain of 10%. This means that the selling price is 110% of the cost price (since a 10% gain implies the selling price is 100% + 10% of the cost price).

Let's denote the cost price as $ C $.

According to the problem:
$$ \text{Selling Price} = C + \text{Gain} $$
$$ 935 = C + 0.10C $$
$$ 935 = 1.10C $$

To find the cost price $ C $, we solve the equation:
$$ C = \frac{935}{1.10} $$
$$ C = 850 $$

Therefore, the purchase price of the cycle is Rs. 850, which corresponds to Option 2.

Now, let's explain why the other options are incorrect:

1. **Option 1: Rs. 945** - If the cycle were purchased for Rs. 945, then selling it for Rs. 935 would result in a loss, not a gain. Therefore, this option is incorrect.

2. **Option 3: Rs. 925** - If the cycle were purchased for Rs. 925, the gain would be calculated as follows:
   $$ \text{Gain} = 935 - 925 = 10 $$
   $$ \text{Gain Percentage} = \left(\frac{10}{925}\right) \times 100 \approx 1.08\% $$
   This is far less than the 10% gain stated in the problem, making this option incorrect.

3. **Option 4: Rs. 1,085** - If the cycle were purchased for Rs. 1,085, selling it for Rs. 935 would result in a significant loss, not a gain. Thus, this option is incorrect.

In conclusion, the only option that satisfies the condition of a 10% gain when selling the cycle for Rs. 935 is Option 2, Rs. 850.