Maths Problems 3 Oct / 4 Oct 09

1. A rectangular tank with dimensions 130 cm by 100 cm by 210 cm was
30% filled with water. 8 identical pails of water, completely filled,
were scooped out from it and this resulted in a drop of the water level
to 38 cm. The remaining amount of water was transferred into a
cubical tank containing 39b of water. The water was then drained
out through a tap at the bottom of the cubical tank at 13b per minute.
(a) What is the capacity of each pail? (2m)
(b) How long did it take to drain the water from the cubical tank completely? (3m)

2. At Carpark P, the number of lorries to that of vans was in the ratio 3 : 7.
At Carpark Q, the number of lorries to that of vans was in the ratio 8 : 9.
When 40% more lorries from an industrial park entered Carpark P, and
20% of the vans at Carpark Q moved to Carpark P, there were 76 fewer
lorries at Carpark P than at Carpark Q. How many vehicles were there
altogether at the two carparks finally? (5m)

3. A bullet train took 5 hours to travel from Patient Town to Honest Town while
an electric train took 4 hours longer to travel from Honest Town to Patient
Town. Both trains set off at the same time and moved towards each other.
Two hours later, they were 255 km apart. What was the speed of the electric
train? (4m)

4. Korey's allowance to Skyler's allowance was in the ratio 10 : 11. Both of
them spent an equal amount. Then Korey’s remaining allowance was 7/9
of Skyler's remaining allowance. What percentage of Skyler's allowance
did she spend? Leave your answer correct to 2 decimal places. (4m)

5. Mrs Ker had a bag of brown sugar. After she used some of the brown sugar,
she had 2/3 of the brown sugar left. Then she distributed 1/4 of what she
had left equally between her neighbours, Mrs Dee and Mrs Bheem. Finally,
Mrs Ker had 437.5 g of brown sugar more than Mrs Bheem. How much
brown sugar did Mrs Ker use? Leave your answer in g. (4m)

6. Shop A sold a party dress for $600. This was 20% more than the price of a similar dress in Shop B. During a sale, both shops offered the same percentage discount on the dress. Mrs Goh bought the dress from Shop B and found that she had paid $70 less than the discounted price in Shop A.
a) Find the price of the dress in Shop B before the sale. (2m)
b) What was the percentage discount given during the sale? (3m)

7. A fruit seller had some oranges, pears and durians. After selling some of them, there were 6 pears for every 5 oranges left and 7 oranges for every 3 durians left. He sold 168 oranges. He had 456 pears and oranges left. The number of pears sold was the same as the number of durians sold.
a) How many oranges had he at first? (2m)
b) If the number of pears was twice the number of durians at first, what was the
total number of pears and durians sold? (3m)

8. Tom and Gary ran in a race. When Gary had completed the run in 20 minutes, Tom had only run 5/8 of the distance.
Tom’s average speed for the race was 75 m/min less than Gary’s.
(a) Find the distance of the race. (2m)
(b) What was Tom’s speed in m/min? (3m)

9. After spending part of his salary on transport and 4/7 of the remainder on food, Ali saved $840.
a) If his salary was $2100, what fraction of his salary did he spend on transport? (2m)
b) If he had the same salary and he had to spend the same amount on transport, what fraction of his salary could he spend on food to save 3/5 of his salary? (2m)

10. Minghua and his sister had 25 stickers altogether at first. After their mother had given them some more stickers, Minghua had 5 times the number of stickers he had before and his sister had 3 times the number of stickers she had before. They had a total of 95 stickers in the end. How many stickers did their mother give each of them?

Ans: Minghua:________________(2m)

Sister:________________(2m)