Answers to last issue's Brain Teasers

1. Palani makes and sells wooden tables from his yard for Rs. 100 each. His only costs are for materials. It takes him an hour and half to make a table. He sold 200 last year, for a profit of Rs. 3,000. This year he raises the price by 15%, but sells 30% fewer tables. Assuming his cost for making each table hasn't changed, by what percentage does his profit increase?
Ans: His profit increases by 40%. His profit on 200 tables was Rs. 3,000, or Rs. 15 per table. So we can deduce that his cost is Rs. 85 per table. At the new price of Rs. 115 (15% more) he makes Rs. 30 per table. Thus, even though he sells only 140 tables (30% fewer), he makes Rs. 4,200 - 40% more than the previous year.
Interestingly, a 15% price increase makes his profit per-hour-of-labour go up 100%, from Rs. 10 per hour to Rs. 20 per hour - showing the importance of selecting the right price.
2. The Jail Cell Clock Riddle
You are locked in a jail cell with no windows and you need to tap out a message on the wall for the man in the other cell next to you. The problem is that you have to do it at exactly 9:15 PM, when the guard outside is switched, so your noise won't be noticed. You can't hear the switching of the guards through your walls, and you have no clock.
There is a faucet with water dripping very consistently from it in the corner, but you don't know how many drops fall per minute, and that wouldn't give you the time in any case. You can just make out the chiming of a church bell, but it chimes just once at the start of each hour, so you can't tell the time from that. Your dinner is not given to you at any exact time, but only passed into your cell between 6:15 and 6:45 PM. How do you determine when it is exactly 9:15 PM?
Ans: After dinner arrives, you listen for the church bell. Since dinner comes between 6:15 and 6:45 PM, the next chiming has to be at 7:00 PM.
When you hear it, you start to count the drips from the faucet until you hear the chime again at 8:00 PM. This is a long time to count, but your freedom depends on it, so you do it carefully and correctly.
Divide the number of drips by four, and you'll have the number of drips that fall in fifteen minutes (Or you can divide by sixty to get the drops per minute, and then multiply this by fifteen). Remember this number.
When the bell chimes again at 9:00, you start counting drips until you reach the specified number. It is now 9:15 PM, and time to tap out your message!