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## Quiz of the Month (November 2002)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```   1. £203
2. 240
3. 36

Notes

1. The cost of all four chairs = 212 + 220 = 432
So the cost of a Classic and a Luxury = 432-229 = 203

2. Fraction with raincoats only = 3/4 - 1/3 = 5/12
So fraction with raincoats, umbrellas or both = 5/12 + 1/2 = 11/12.
So 1/12 have neither.

3. Suppose M is no. of men and W = no. of women present.
No. of married men = 60 M /100
So no. of men accompanied by wives = 15 M /100
No. of married women = W - 10
So no. of women accompanied by husbands = (W - 10)/2
So 15 M /100 = (W - 10)/2
Also W = 4 M /5
Solving, M = 20, W = 16```

#### THIS MONTH'S QUIZ

1. Jock and Paddy are shovelling gravel into a truck, while Sandy is shovelling it out again. Jock by himself could fill the truck in 60 minutes, while Paddy by himself would take 40 minutes. Sandy could empty the full truck in 30 minutes. How long does it take to fill the truck with all three at work?

2. How many circles of diameter 1 cm can be placed without overlapping in a square 10 cm by 10 cm?

3. How many squares 1 cm by 1 cm can be placed without overlapping in a circle of diameter 10 cm?

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(c) Hector C. Parr (2002)

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