Bunch of grapes

25th February 2005 at 00:00
Mrs Maggs had a bunch of grapes. There were fewer than 100 grapes in the bunch.

When she divided the grapes equally among 6 children, there were 5 grapes left over.

When she divided the grapes equally among 8 children, there were 5 grapes left over.

When she divided the grapes equally among 9 children, there were 5 grapes left over.

How many grapes were there in the bunch?

Carpet sales

A shop increased the price of carpets by 20%.

Sales of carpets dropped by 20%.

Did the shop's profits from carpet sales rise or fall?

SOLUTIONS Bunch of grapes (ages 8 to 12) 77 grapes. The smallest number that divides exactly by 6, 8, and 9 is 72 (then 144, 216, I). So the number of grapes is 72 + 5 = 77.

Carpet sales (ages 11 to 15) Profits on carpet sales fell by 4%. The new price of carpets is 120Z100 of the old price. Sales are 120Z100 X 80Z100 X 100% = 96% of old sales.

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