Maths worksheets for challenging problem sums

Related Skills
Skill Involving Changing quantities
Ratio
Fraction

* Practice for skill involving changing quantities

1) Andy, Weizhi and Peter had a total of \$4582. After Andy had given 25 of his share to Weizhi, Weizhi then gave \$55 to Peter. As a result, the amount of money Peter had to the amount of money Andy had was 1 : 3. If Weizhi had \$725 at first, find the amount of money Andy had at first.

Ans :- At first Andy had \$3260.

2) The number of balls in Box A is ½ the number of balls in Box B. 10% of the balls in Box A and 10% of the balls in Box B were moved to Box C. As a result, the number of balls in Box C increased by 20%. There are 72 balls in Box C now. How many balls were there in Box B at first?

Ans :- There were 80 Balls in Box B at first.

3) Denise , Ginny and Florence each made some bookmarks for sale. At first, Denise had 1365 bookmarks more than Ginny. Then Denise sold 420 bookmarks and made another 175 bookmarks. Florence sold 140 bookmarks and made another 350 bookmarks. Ginny made some more bookmarks and her number of bookmarks doubled. In the end, the three girls had the same number of bookmarks. Find the total number of bookmarks the three girls had at first.

Ans :- At first they had total 5635 bookmarks.

4) Ronnie and Rachel were each given some money. If Ronnie spent thrice as much money as Rachel, he would still have \$450 when Rachel had spent all her money. If Ronnie spent 13 of what Rachel had spent, he would have \$690 when Rachel had spent all her money.
(a) How much money was Ronnie given?
(b) How much money was Rachel given?

Ans :- a) Ronnie was given \$720
b) Rachel was given \$90

5) Container Y contained 8.3 ℓ of water and Container Z contained 46.79 ℓ of water. An equal amount of water was added to both the containers so that Container Z contained 4 times as much water as Container Y. How much water was added to the containers?

Ans :- 9.06 ℓ water was added to the container.

6) Jason has some chocolate and macadamia nuts cookies. If he sells 16 chocolate cookies and 4 macadamia nuts cookies a day, he would have 65 chocolate cookies left by the time all the macadamia nuts cookies have been sold.
If he sells 8 macadamia nuts cookies and 4 chocolate cookies a day, he would have 289 chocolate cookies left by the time all the macadamia nuts cookies are sold. How many chocolate cookies does he have?

Ans :- Jason has 321 cookies.

7) An MRT train set off from the first station with some passengers on board. The ratio of the number of men to that of women was 5 : 3. At the 2nd station, 37 of the men and some women alighted. The ratio of the number of men to women then became 10 : 7. At the 3rd station, 70 men and 196 women got on the train and the number of men was the same as the number of women.
(a) How many passengers were there on board the train when it set off from the first station?
(b) How many women alighted at the second station?

Ans :- a) At first station, there were 1176 passengers on board.
b) 147 women alighted at the second station.

8) Jug X and Jug Y contain different amounts of water at first. 50% of the water in Jug X was poured into Jug Y. Then 40% of the water in Jug Y was poured into Jug X. The final ratio of the amount of water in Jug X to the amount of water in Jug Y was 7 : 6.
(a) What was the ratio of the amount of water in Jug X to Jug Y at first?
(b) If there were 10 litres of water in Jug X at first, how much water was there in Jug X in the end?

Ans :- a) 6 : 7
b) There was 1123ℓ of water in the end.

9) The ratio of the number of yellow marbles to the total number of green and red marbles was 7 : 13. 40% of the marbles were red marbles. After throwing away 65 red marbles that were chipped, 20% of the remaining marbles were red. How many marbles were there left if another 24 green marbles were found to be chipped and thrown away?

Ans :- 171 marbles were left

10) A company has a total of 168 800 Chinese, Malay, Indian and Eurasian employees. The number of Chinese and Indian employees to the number of Malay and Eurasian employees is in the ratio of
3 : 1. During the economic downturn, 70% of the Chinese and ½ of the Indians were retrenched and a total of 54 600 Chinese and Indian employees remained in the company. What percentage of the total number of employees were the Chinese before the retrenchment? Round off your answer to 1 decimal place.

Ans :- 25.8%.