Level 3
The area of the triangle to the area of the rectangle in the figure is in the ratio 3 : 2. After the shaded rectangle of length 8 cm is removed from the figure, the ratio of the remaining area of the triangle to the remaining area of the rectangle is 5 : 3. Given that the area of the triangle is 32 cm2 more than the area of the rectangle, find the width of the shaded rectangle that is being removed.
4 m
Level 3
Daniel saved some 50-cent coins and $1 notes in his coin box. The total value of the 50-cent coins to the total value of the $1 notes he had was in the ratio 2 : 5. After $14 worth of 50-cent coins and an equal value of $1 notes were added to the coin box, the ratio of the total value of 50-cent coins to the total value of $1 notes became 5 : 9. How many of each type did Daniel have in the end?

  1. 50-cent coins?
  2. $1 notes?
5 m
Level 2
There was 11 ? of water in a pail and 1.8 ? of water in a basin. Warren then poured in an equal volume of water into each container. Now, the volume of water in the pail is 5 times in the basin. How much water did Warren pour into each container?
2 m
Level 3
At the beginning of the year, the number of members in Club A and Club B were in the ratio 5 : 7. At the end of Term One, some members left Club A to join Club B. The ratio of the number of members in Club A and Club B became 1 : 3. At the middle of Term Two, each club received 54 new members. The ratio of the number of members in Club A and Club B became 2: 3. How many members left Club A to join Club B at the end of Term One?
5 m
Level 3
The number of safety cones along the road was 55% of the number of trees planted along it. After 68 safety cones and 68 trees were added to the stretch of road, the number of trees became 20% more than the number of safety cones. How many trees were there at first?
4 m
Level 3
The average number of mangosteens in Carton C, Carton D and Carton E is 24 and it is 8 more than the average number of papayas in the 3 cartons. 16 of the papayas are in Carton C and the papayas in Carton C is 80% of the number of papayas in Carton D. If each carton has the same number of fruits, what percentage of the fruits in Carton E are mangosteens?
5 m
Level 3
The figure shows an irregular 5-sided figure and a square. The area of the five-sided figure was three times the area of the square. After the shaded part was removed, the area of the remaining square became 15% of the total remaining area of both figures. If the area of the shaded part is 16 cm2, find the remaining area of the 5-sided figure.
4 m
Level 3
Four years ago, Will's age was 25% of Ray's age. Eight years from their current age, Will's age will be 37.5% of Ray's age. How many years is Ray older than Will?
4 m
Level 3
Daniel's age is 19 of his uncle's. His uncle will be 41 years old in 5 years' time. In how many years' time will Daniel's age be 37 of his uncle's?
4 m
Level 3
Mr Poh is 30 years older than his son. 5 years from now, his son will be 13 of his age while his daughter will be 35 of his son's age. Express his daughter's present age as a fraction of Mr Poh's present age. Leave your answer in its simplest form.
4 m
Level 3
At first, there were 410 more men than women at an exhibition. At lunch time, a total of 250 men and women left the exhibition. There were as many men as women who left the exhibition. In the end, there were 3 times as many men as women who remained behind. How many men were at the exhibition at first?
4 m
Level 3
Every week, Mrs. Tan will collect 40% more vitamin pills than Mrs Nurul from the pharmacy. They each consumed 14 vitamins weekly and will leave the rest for their family members to consume the rest. After some time, both ladies consumed a total of 364 vitamin pills and Mrs. Tan's family members consumed 468 more vitamin pills than Mrs. Nurul's family.
  1. How many members are there in Mrs. Tan's family, if they each consume 14 pills weekly?
  2. How many vitamin pills does Mrs Nurul collect from the pharmacy each week?
5 m
Level 3
Fabian's age is 14 that of his father's. His father is 24 years older than him. Find their total age.
4 m
Level 3
Henry is 5 years old now. His sister is 6 years older than him. How old will Henry be when his age is 57 of his sister's?
4 m
Level 3
37 of Caleb's money is equal to 15 of Jake's money. After each of them spent $40, Jake had $120 more than Caleb. How much money does Jake have left after spending?
4 m
Level 3
Three years ago, Greg's age was half of Daniel's age. Fernando is 25 years old now and he is 6 years older than Daniel. How old is Greg now?
4 m
Level 3
2 rectangles A and B, not drawn to scale, overlap at x as shown. x is 18 of rectangle A and 16 of rectangle B. If the length of rectangle B is 9 cm and its breadth is 4 cm, what is the area of the unshaded part of figures A and B?
4 m
Level 3
Mary's father is 75 years old. 15 years ago, he was twice as old as Mary. Express Mary's present age as a fraction of her father's age.
4 m
Level 3
Aunt Susie is now 46 years old and Tanya is 3 years less than half of Aunt Susie's age. How many years later will Aunt Susie be twice as old as Tanya?
4 m
Level 3
Wendy was 9 years old last year. She was 26 years younger than her mother.
  1. How old will her mother be 5 years later?
  2. In how many years' time will Wendy's age be 13 of her mother's age?
4 m