Pyramids

What are the missing numbers in the pyramids?

Burning Down

One night two candles, one of which was 3 cm longer than the other were lit. The longer one was lit at 5.30 pm and the shorter one at 7 pm. At 9.30 pm they were both the same length. The longer one, burned out at 11.30 pm and the shorter one burned out at 11 pm. How long was each candle originally?

A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

Weekly Problem 21 - 2007

Stage: 3 and 4 Challenge Level:

54kg

Let the weights in kilograms of the head and body of the fish be $h$ and $b$ respectively. Then $h = 9 + \frac{1}{3} b$ and $b = h+9$. So $b = 9 + \frac{1}{3} b + 9$, that is, $\frac{2}{3} b = 18$, which gives $b = 27$. Hence $h = 18$, so the whole fish weighed 54kg.

This problem is taken from the UKMT Mathematical Challenges.

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