2) A rectangular tank 28cm by 20cm by 40cm was filled to a certain height with water. Water was then drained through a tap at a uniform rate of 240cm3 per minute. If the tap took 35 minutes to empty the tank, what was the water level from the brim of the tank initially?

3) A rectangular tank, 40cm long and 24cm wide, was filled with water to a depth of 12cm. 4.8L of water were poured into the tank. The tank was then 60% full. What was the height of the tank?

4) Tank X and Y were filled completely with water. 1/5 of the volume of water in tank X and 1/3 of the volume of tank Y were equal to 350ml. When 1/5 of the water in tank X was poured out, the total volume of water in both tanks was 1200ml. Find the volume of each tank.

5) A rectangular glass tank, 60cm by 50cm by 45cm, was filled with water to a height of 5cm. The ratio of the volume of the water in the glass tank to that in a container was 5:3. If ¾ of the container was filled with water, find
a) the volume of water in the tank
b) the number of such containers of water needed to fill the rest of the tank completely

6) What is the maximum number of cubes of edge 6cm I can cut from a wooden block, 32cm by 25cm by 21cm?

7) The height of the water in a rectangular tank was 6cm. Water was then poured into it until the water level rose to a height of 25cm. The tank was 50cm long and 40cm wide.
a) How much water had been poured into the tank?
b) What was the new water level if 20L of water were poured out of the tank?

An empty tank of base 50cm by 48cm was being filled with water from tap A and B flowing at the rates of 3L per min and 5L per min respectively. Both taps were turned on at the same time and they took 6 minutes to fill up the tank.
a) How long would it take for tap B to fill up the empty tank on its own?
b) What was the height of the tank?

9) Tap P and Q and Hose R were turned on at the same time and the height of the water in the tank was 2 cm from its brim. How long would it take for the tank to be completely empty?

10) The base of a rectangular tank was 560cm². If 8064cm³ of water were pumped into the empty tank, it became 4/5 full.
a) Find the height of the tank
b) the water was then poured into a cubic tank of edge 30cm. Find the percentage of water in the cubic tank. (Express your answer to 1 decimal place)

For answer, email to maths_problem@hotmail.com the title of the post

Subject: PSLE challenging questions

Content of email:

Name of parent:

Child level(pri 5/pri 6):

22. Andy jogged from town X to town Y at a constant speed. At 10am, he was 84km away from town Y. At 11.30am, he was 48km away from town Y. At what time did andy reach town Y?

23. Ben travels from town A to town B very often. If his average speed is 48km/h, he will reach town B at 1pm. If his average speed is 80km/h, he will reach town B at 11am. Find his average speed so that he would reach town B at 12 noon.

24. Mark and Luke traveled from town X to town Y at a constant speed. Mark took 6h to reach town Y. luke took 4h to cover ¾ of the journey. Find the ratio of Mark’s speed to luke’s speed.

25. Adrian and Bernard were on the same way to town Z. Bernard overtook Adrian when they were 168km from town Z. when Bernard reached town Z, Adrian was still 21km away from it. 20 minutes later, Adrian finally reached town Z. find the average speed of Adrian and Bernard.

26. Victor and Mohan traveled from town X to town Y which was 189km away. Mohan overtook victor on the way and reached town Y, ½ h earlier than victor. When mohan reached town Y, victor was 27km away from town Y. find the average speed of mohan.

27. fandi took 3 h to travel from town A to B. on the way, he passed a motorcyclist who was traveling in the opposite direction at a uniform speed of 48km/h. 1 ¾ later, frandi reached town B while the motorcyclist was still 6 km away from town A. find the distance between the 2 towns.

28. Richard left town A for town B at 10am. ¾ later, Linus left town A for town B and overtook Richard at 12.30pm. Linus arrived at town B at 1.05pm. At what time did Richard reach town B?

29. 2 towns, X and Y were 156km apart. Tom started to travel from town X to town Y at an average speed of 54km/h. At the same time, peter also started to travel from town Y to town X. After traveling for 1 1/3h, they passed each other on the way. Find the average speed of Peter.

a) How long did he take to complete the whole journey?

b) What was his average speed from Town P to Town Q?

12. Arthur and Danny started driving from the same place but in opposite direction along a straight road. After driving for 4 h, they were 548km apart. Arthur’s average speed was 72km/h. What was Danny’s average speed?

13. Town P and Town Q were 720km apart. Alex traveled from town P to town Q at an average speed of 83km/h. At the same time, Freddy traveled from town Q to town P at an average speed of 77 km/h. How far would each of them have traveled when they met on the way?

14. The distance between town X and town Y was 710km. Adam started traveling at 10am at an average speed of 84km/h from town X to town Y. 50 minutes later, Calvin started traveling from town Y to town X at an average speed of 76km/h.

a) How far would Adam have traveled before he met Calvin?

b) At what time did both of them meet?

15. At 8.50am, a car left town P for town Q at an average speed of 75km/h, while a lorry left town Q for town P at an average speed of 67km/h. At 1.50pm, the two vehicles were 70km apart. What was the distance between town P and town Q?

16. At 10am, Bradford started driving at an average speed of 58km/h. At 12.30pm, Calvin started from the same place, traveling on the same road. If calvin took 5 hrs to catch up with Bradford, find the average speed of calvin.

17. Town X and town Y were 650km apart. Gary left town X for town Y and traveled at an average speed of 67km/h. At the same time Henry left town Y for town X. Both of them met 5h later. Find the average speed of Henry.

18. Lenon and Micky were traveling from town X to town Y which were 630km apart. Lenon set off 1 2/3h later than micky but arrive 1 1/3 h earlier. If the average speed of micky was 63km/h, find the average speed of lenon.

19. Adriano, traveling from town A to town B, passed Brandon after completing 1/7 of the journey.
Brandon was traveling in the same direction at an average speed of 77km/h. 7 hours later, Adriano reached town B but Brandon 55 km away from town B. If Brandon had started from town A, how long would he take to travel from town A to town B?

20. At 8am, sean started driving at an average speed of 55km/h. 48 minutes later, oliver started from the same place, driving at an average speed of 67km/h. How long did olive take to catch up with sean?

Send an email with the title “Speed 2″ to maths_problem@hotmail.com to get the answers

11.
Town P and Town Q were 592km apart. Joshua left Town P at an average speed of 77km/h. He drove at this speed for 5h before reducing it by 8km/h for the rest of the journey to Town Q.

a) How long did he take to complete the whole journey?

b) What was his average speed from Town P to Town Q?

12. Arthur and Danny started driving from the same place but in opposite direction along a straight road. After driving for 4 h, they were 548km apart. Arthur’s average speed was 72km/h. What was Danny’s average speed?

13.
Town P and Town Q were 720km apart. Alex traveled from town P to town Q at an average speed of 83km/h. At the same time, Freddy traveled from town Q to town P at an average speed of 77 km/h. How far would each of them have traveled when they met on the way?

14. The distance between town X and town Y was 710km. Adam started traveling at 10am at an average speed of 84km/h from town X to town Y. 50 minutes later, Calvin started traveling from town Y to town X at an average speed of 76km/h.

a) How far would Adam have traveled before he met Calvin?

b) At what time did both of them meet?

15. At 8.50am, a car left town P for town Q at an average speed of 75km/h, while a lorry left town Q for town P at an average speed of 67km/h. At 1.50pm, the two vehicles were 70km apart. What was the distance between town P and town Q?

16. At 10am,
Bradford started driving at an average speed of 58km/h. At 12.30pm, Calvin started from the same place, traveling on the same road. If calvin took 5 hrs to catch up with
Bradford, find the average speed of calvin.

17. Town X and town Y were 650km apart.
Gary left town X for town Y and traveled at an average speed of 67km/h. At the same time Henry left town Y for town X. Both of them met 5h later. Find the average speed of Henry.

18. Lenon and Micky were traveling from town X to town Y which were 630km apart. Lenon set off 1 2/3h later than micky but arrive 1 1/3 h earlier. If the average speed of micky was 63km/h, find the average speed of lenon.

19. Adriano, traveling from town A to town B, passed
Brandon after completing 1/7 of the journey.
Brandon was traveling in the same direction at an average speed of 77km/h. 7 hours later, Adriano reached town B but Brandon 55 km away from town B. If
Brandon had started from town A, how long would he take to travel from town A to town B?

20. At 8am, sean started driving at an average speed of 55km/h. 48 minutes later, oliver started from the same place, driving at an average speed of 67km/h. How long did olive take to catch up with sean?

Send an email with the title “Speed 2″ to maths_problem@hotmail.com to get the answers

2. Mr matthew drove his car to a petrol kiosk from work at an average speed of 50 km/h. The distance between his work place and the petrol kiosk is 15 km. He stopped there for 10 mins to get petrol and some refreshments. He went home after that and reached home 18 minutes later. If he set off from work at 5.30 pm, what time did he reach home?

3. Lewis rode his motorcycle to work at an average speed of 60 km/h. He took 25 mins to reach his work place. However, he forgot his wallet and returned home to get it. What was the total distance Lewis traveled when he reached his office the second time?

4. Alicia can run 80m in 16 seconds. Inez can run 100m in 18 seconds. What is the difference in the time taken if they were to run at their respective speed for a distance of 150m?

5. A car and a motorcycle were 680km apart. At 9.30 am, they moved towards each other. The car moved at the speed of 95km/h and the motorcycle at 65km/h. find the time at which the 2 vehicles passed each other.

6. Angie drove 448 km from town X to town Y at an average speed of 56 km/h. she then took 30 mins to travel from town Y to Town Z at an average speed of 104 km/h. How long would Angie take to travel from town X to town Z at an average speed of 75km/h?

7. Jim traveled at an average speed of 72km/h for the first 5/8 of his journey. He completed the remaining 216km in 4h 30min. How long did he take to complete the whole journey?

8. A car left country A at 11.40pm. It arrived at Country B which was 442km away at 8.10am the next morning. What was its average speed?

9. Rachel drove 190km from Town P to town Q at an average speed of 76km/h. She then drove 231km from Town Q to town R at an average speed of 84km/h. Find the time taken for the whole journey.

10. Gabriel drove at an average speed of 67km/h for the first 2h of the journey. He then drove at an average speed of 72km/h for another 3h before he reached his destination. Find his average speed for the whole journey.

Send email to maths_problem@hotmail.com to get answers

2) Peggy, Amos and Vincent have some stamps. Amos sold 4/7 of the stamps. Peggy sold 1/5 of the number of stamps sold by Vincent. Vincent sold 57 fewer stamps than Amos. How many stamps do they have altogether at first?

3) 1/3 of the people in a wedding banquet were men. The rest were women. When 14 men left the wedding, the number of men decreased to ¼ of the total number of people in the wedding banquet. How many people were there in the wedding banquet at first?

4) In a cinema, there were 72 audiences. Among the children, there were 4 more boys than girls in the cinema. 1/7 of the adult audience and 1/8 of the children audience were equal to 10. How many boys were in the cinema?

5) Lionel spent $399 on a handphone and 2/5 of his remaining salary on a camera. He still had $186 left. How much money did he spend altogether?

6) Alan spent 3/8 of his money, Joseph spent 1/5 of his and Andy spent 1/3 of his. All of them had the same amount of money left. If the 3 persons had spent $378, how much did Joseph have at first?

7) Mary is five times as old as her granddaughter, Alice. In 6 years’ time,
Alice will be ¼ of Mary’s age. How old is Mary now?

James and Doreen have certain number of stickers. James gave 1/5 of his stickers to Doreen. Then Doreen gave 1/6 of what she had back to him. Next James counted all his stickers and gave 1/3 of them to Doreen. In the end, James had 18 stickers and Doreen had 44 stickers. How many stickers did each of them have at first?

9) In a zoo, 5/8 of the visitors were adults. The rest were children. ¼ of the adults were women and 7/8 of the children were boys. If there were 260 more men than women visitors in the zoo, how many boys were there?

10) Julia, Rita and Benjamin had $235 at first. Julia gave ¼ of his money to Rita. She then found out that she had $5 less than Julia. Benjamin had 2/3 of what Julia had left. How much money did Julia and Rita have at first?

send an email with the title (fraction 2) to maths_problem@hotmail.com to get answers

2) There were 121 pupils in a school. 8/9 of the boys and 4/5 of the girls were malaysians. The rest were Singaporeans. If there were 104 malysians pupils, how many malaysians boys were in the school?

3) Mr Wong withdrew 7/9 of his savings. He spent 2/7 of it on games and ¾ of the remainder on food. He put the remaining amount back into his savings account. If he spent $270 on food, how much money did he spend on games?

4) There are 1210 pupils in a school. 3/5 of the boys and ½ of the girls wear spectacles.  There are an equal number of boys and girls wearing spectacles.

a) How many girls are not wearing spectacles?
b) What fraction of the boys in the school wears spectacles? (Express answer in simplest form)

5) There were 240 pupils in the field. 2/5 of them were boys. When some more boys joined them in the field, the fraction of the number of boys increased to 2/3. How many boys joined the field?

6)
Alice savings was 2/5 more than Ben’s. After
Alice had given $800 to Ben, she had 1/5 of Ben’s money. Find their total savings.

7) There are 65 dogs and cats in a pets shop. 2/3 of the dogs are equal to 1/5 of the cats in the pet. How many dogs are there in the pet shop?

If James was given $32, he had 1/3 as much money as
Adrian. Peter had twice as much money as James’s original sum of money. If the 3 persons had $378 altogether at first, how much money did Peter have at first?

9) John and Mary had a sum of $720. John received ¼ of Mary’s money. He then gave 1/4 of the money he had to Mary. Finally, each of them had the same amount of money. Find the original amount of money that John had.

10) 3/8 of my salary was spent on food. I gave 1/3 of the remainder to my mother. Then I kept the rest in a box. Two days later, I took out 7/10 of the money in the box and had $210 left.

a) How much money did I give to my mother?

b) How much spent on food?

Send an email and include the title (fraction) for the answer to maths_problem@hotmail.com

2) Ahmad and Jack together stood on a weighing scale and saw that their total mass was 48kg. Ahmad knew that he was g kg heavier than Jack. What was Jack’s mass in terms of g?

3) 2/3 of Ben’s money is equal to 2/5 of
Tracy’s money. If
Tracy has $35z, how much money do they have altogether in terms of z?

4) Andrew travelled 42h km in 6 hours. How far could he travel in an hour if he travelled at a uniform speed?

5) Eddie is (r-4) years old now. Mary is 5 years older than him. What will be their total age in 10 years’ time in terms of r?

6) Doreen bought 4 books at $3d each and had $6d left. How many pens could he buy with the original amount of money that he had if each pen cost $1.50 each?

7) The ratio of Amanda’s money to Tony’s money was 5:3. When Amanda spent $(4h)/5, Tony had thrice as much money as he had left. How much money did Tony have at first in terms of h?

Karren spent ¼ of her money on some fruit and had $30a left. Then she spent the remaining amount of money on 15 similar red pens. How many red pens could she buy with his original sum of money?

9) The square has a diagonal 4b cm long. Find its area in terms of b

10) John, Ali and Peter spent a certain sum of money. John and Ali each spent 25% of it. Peter spent $16a.
How much did John spend?

Email the title to maths_problem@hotmail.com to get the answers

2) Daniel is (6+p) years old now. Mary is 6 yrs older than Daniel. How old were they 5 years ago?

3) Box A is thrice as heavy as Box B. Box C is half as heavy as boxes A and B together. What is the mass of box C if box B is n kg?

4) If n=3, find the value of 5n²-10

5) The water from a tap flows at a rate of 3 litres per minute. A tank has a volume of 45x litres. How long will the tap take to fill up the tank?

6) Bobby had 5a marbles. He had 12 more marbles than Andy. Ali had twice as many marbles as Andy. How many marbles do Andy and Ali have altogether?

7) A string is b cm long. If the string is used to form a square, what is the area of the square in terms of b?

Simplify 21a -4 -3a +19

9) Joan bought 8 blouses at $t each. She gave the cashier $50 and received $18 change. Find the value of t.

10) The square has an area of 36x² cm2. Find the length of the square.

Email the title to maths_problem@hotmail.com to get answers