A vendor bought lemons at 6 for ₹1. How many lemons must he sell for ₹1 to gain 100%?

Given:

Cost Price (CP) of 6 lemons = ₹1

Required Gain = 100%

Formula used:

Selling Price (SP) = CP + Gain

Gain = Percentage Gain of CP

If gain is 100%, then SP = CP × \((1 + \frac{100}{100})\) = CP × 2

Calculations:

CP of 6 lemons = ₹1

To gain 100%, the Selling Price (SP) of 6 lemons must be:

SP of 6 lemons = CP of 6 lemons + 100% of CP of 6 lemons

⇒ SP of 6 lemons = ₹1 + 100% of ₹1

⇒ SP of 6 lemons = ₹1 + ₹1

⇒ SP of 6 lemons = ₹2

This means the vendor must sell 6 lemons for ₹2 to gain 100%.

We need to find how many lemons he must sell for ₹1.

If 6 lemons are sold for ₹2,

Then, for ₹1, the number of lemons sold = \(\frac{6}{2}\)

⇒ Number of lemons = 3

∴ He must sell 3 lemons for ₹1 to gain 100%.