# Solution

My friend was selling two mangoes for one rupee. Since my friend was selling mangoes in twos and had 30 mangoes to sell, he needed 15 customers to sell off his stock. Now, this is not strictly true because one single customer could buy 2, 4, 6, 8, ........ or the entire lot of 30 mangoes. But, just for ease of understanding let's consider that when two mangoes are bought it makes for one purchase; if one single customer buys all the 30 mangoes, let's assume that the customer has come 15 times to buy two mangoes at every visit.

I sold three mangoes for one rupee. Since I sold mangoes in threes and had 30 mangoes to sell every day, I needed ten customers to sell off my day's stock.

On the day when my friend requested me to sell his mangoes along with mine, I had 60 mangoes to sell and I sold them in fives. I sold five mangoes for two rupees. So, I needed 12 customers to sell off the 60 mangoes. Because I had 12 customers and each paid me two rupees, I had 24 rupees at the end of the day. So, what went wrong? Why did I end up getting 24 rupees instead of 25 rupees?

As mentioned above, I need ten customers to sell off my mangoes. So, after the tenth customer had bought mangoes from me all my mangoes were sold, and all the remaining mangoes belonged to my friend. After the tenth customer had made his purchase, I had sold 50 mangoes of which 30 were mine and 20 belonged to my friend (as I have mentioned earlier, it isn't necessary that ten customers should have bought from me; a single customer could have bought the 50 mangoes. But, what is important is the fact that once I had sold 50 mangoes, they included 30 mangoes belonging to me and 20 mangoes belonging to my friend). There were ten mangoes remaining, and all of them belonged to my friend. At that stage, I had collected 20 rupees. Since the remaining ten mangoes belonged to my friend, I should, thereafter, have sold two mangoes for one rupee (or, four mangoes for two rupees). But I continued to sell five mangoes for two rupees, thereby incurring a loss. If I had sold two mangoes for one rupee, then the ten mangoes would have fetched five rupees and I would have collected 20+5 = 25 rupees at the end of the day. No, I will never make a good seller!

• Union Public Service Commission - www.upsc.gov.in
• IIT-Kharagpur - www.iitkgp.ac.in
• Indian Statistical Institute - www.isical.ac.in
• Indian Institute of Technology Madras - www.iitm.ac.in
• Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
• Indian Institute of Mass Commission - www.iimc.nic.in
• IIT Bombay - www.iitb.ac.in