I once cashed a cheque at the bank. I had spent £1.06 before I realised the bank clerk had made a mistake. He had transposed the pounds with the pence. I now had exactly 8 times the value of the original cheque. What was the original cheque's value?
You have the misfortune to own an unreliable clock. This one loses exactly 8 minutes every hour. It is now showing 4:15pm and you know that is was correct at midnight, when you set it. The clock stopped one hour ago, what is the correct time now?
Answer: 7:45pm: since the clock is losing 8 minutes every hour, for every real hour that has passed, the clock will only show 52 minutes. Since the clock shows 4.15pm, we know that 975 clock minutes have passed. This therefore equals 1125 real minutes and hence 18 hours 45 minutes. The clock stopped 60 minutes ago, therefore the time must now be 19.45pm. QED.
In a football collective, the winnings amounted to £1,475.
There were more than 30 people in the syndicate but fewer than 100.
Each won exactly the same number of pounds and no pence were involved. How much did each win?