By selling 45 lemons for Rs. 40, a man loses 20%. How many should he sell for Rs. 24 to gain 20% in the transaction?Options1518None of these19

To solve this problem, we first need to find the cost price of one lemon.

1. We know that by selling 45 lemons for Rs. 40, the man incurs a loss of 20%. This means that Rs. 40 is only 80% of the cost price (because 100% - 20% = 80%).

2. To find the cost price (100%), we can set up the equation: 80/100 = 40/Cost Price. Solving for Cost Price gives us Rs. 50.

3. So, the cost price of 45 lemons is Rs. 50. Therefore, the cost price of one lemon is 50/45 = Rs. 1.11 (approximately).

4. Now, if the man wants to gain 20% in the transaction, he needs to sell each lemon for 120% of the cost price.

5. 120% of Rs. 1.11 is 1.33 (approximately).

6. Finally, to find out how many lemons he should sell for Rs. 24 to gain 20%, we divide 24 by the selling price of one lemon (Rs. 1.33).

7. This gives us approximately 18 lemons.

So, the man should sell around 18 lemons for Rs. 24 to gain 20% in the transaction. The closest option is 18.