Maths Problems 5 October 09

1. At 9.30 a.m., Train A which was 200 m long, pulled out of Nanas Station and travelled towards Dadas Station at a uniform speed of 80 km/h. Half an hour later, Train B which was 150 m long, left Dadas Station and travelled towards Nanas Station at an uniform speed of 90 km/h.

(a) How far has Train A travelled when Train B left Dadas Station? (1m)
(b) The two trains met each other in a tunnel. Both trains took 15 minutes to be completely out of the tunnel. Calculate the length of the tunnel. (4m)

2. There were some sweets in Boxes X, Y and Z.
Box X contained 20% of the total number of sweets in Boxes X, Y and Z.
The ratio of the number of sweets in Box Y to the total number of sweets in Boxes X and Z is
2 : 1.
If there are 24 more sweets in Box Y than Box Z, find the total number of sweets in Boxes X, Y and Z. (5m)

3. John shifted the decimal point of a number twice to the left to obtain a new number. The difference between the new number and the original number was 136.62.
(a) How many times of the new number is the original number? (1m)
(b) What is the sum of the 2 numbers? (3m)

4. Mrs Kee baked some cookies and packed all the cookies in 12 small boxes and 5 big boxes.
There were equal number of cookies in each small box and equal number of cookies in each big box.
Each big box contained 14 more cookies than each small box. 18/29 of the cookies baked were packed in small boxes.
How many cookies were there in each small box? (4m)

5. Tricia has some pink, red and yellow ribbons.
1/3 of them are pink ribbons.
Four fewer than 1/3 of the remainder are red ribbons.
The remaining 24 are yellow ribbons.
How many pink ribbons does Tricia have? (3m)

6. Alice, Beth and Claire had 600 stamps altogether. After Beth had given 30 stamps to Alice, Beth had twice as many stamps as Claire and Alice had 20 stamps more than Claire. How many stamps did Claire have? (3m)

7. Last year the total age of Mr Tan and his wife is p years old.
His wife is 1 year younger than him.
What is his wife’s age 2 years from now? Express your answer in terms of p. (3m)

8. Tracy counted the number of 10-¢ coins, 20-¢ coins and 50-¢ coins in her piggy bank. The number of 10-¢ coins was 24 more than the number of 50-¢ coins. After spending 3/5 of the 10-¢ coins, 1/4 of the 20-¢ coins and 18 50-¢ coins, she had an equal number of 10-¢ and 20-¢ coins. The number of 50-¢ coins now formed 40% of the remaining number of coins
(a) How many 10-¢ coins did Tracy have at first? (3m)
(b) How much did she spend in all? (2m)

9. Ahmad and Halim together took 5 days to paint their house. If Ahmad and Halim work together for 2 days, followed by Ahmad working alone for 8 days, Halim will take 1 more day to complete the remaining work. How long will Ahmad take to paint the house all by himself? (5m)

10. Mr. Tan had 130 durians and mangosteens. After he sold 2/3 of the durians and 2/5 of the mangosteens, he had 36 more mangosteens than durians left. How many fruits had he left in all? (4m)