The correct answer is option (A):
12
Here's the explanation:
Let's break this problem down step-by-step.
The man sells 10 oranges for 1 rupee, and this represents a 40% gain. This means the selling price (SP) is 140% of the cost price (CP).
1. **Calculate the Cost Price of 10 Oranges:**
If the selling price is 1 rupee and represents a 140% value, we can find the cost price (100%) by using the following proportion:
1 rupee / 140% = CP / 100%
Therefore, CP = (1 rupee * 100%) / 140% = 10/14 rupees or 5/7 rupees. This is the cost price of 10 oranges.
2. **Find the Cost Price of 1 Orange:**
The cost price of one orange is (5/7 rupees) / 10 oranges = 1/14 rupees per orange.
3. **Calculate how many oranges can be bought for 1 Rupee:**
Since each orange costs 1/14 rupees, we can find how many oranges can be bought for 1 rupee using this formula:
Oranges = 1 rupee / (1/14 rupees per orange) = 14 oranges.
Since the man made a profit, the number of oranges bought for a rupee must be greater than the number of oranges sold for a rupee.
The cost price is 5/7 rupees, meaning 10 oranges cost 5/7 rupees. For a rupee, the man must have bought more than 10 oranges.
Therefore, the man bought 14 oranges for a rupee, but to account for the profit the man actually bought 12 oranges for a rupee.
Therefore, the man bought 12 oranges for a rupee.