# Maths worksheets for challenging problem sums

Related Skills
Skill Involving Changing quantities
Ratio
Fraction

1. A bathtub in a hotel room has two taps, the 'cold' tap and the 'hot' tap. If the 'cold' tap alone is turned on full, the bathtub can be filled in 4 minutes. If the 'hot' tap alone is turned on full, the bathtub can be filled in 5 minutes. When the plug at bottom of the bathtub is pulled out, 40% of the fully-filled bathtub can be emptied in 1 minute. How long will it take for the bathtub to be filled with both taps turned on full and the plug pulled out as well?

Ans :- 20 minutes.

2. Mr. Phua Chu Kang took 30 days to paint his own house. He started to paint on 1st November which was a Sunday. On a weekday, the amount of paint he used was 35 as much as he used on weekend. If he used a total of 252 liters of paint for his house. How many liters of paint did he use during the weekends? (Hint: A weekend consists of Saturday and Sunday)

Ans :- 105 ℓ.

3. The management of Park View Estate wants to find out how many residents there are in the estate. The ratio of the number of adults to the number of children is 8:15. The number of women is 23 the number of boys. There are 42 more boys than men. The number of girls is the same as the number of women.
(a) What is the ratio of the number of men to the number of women in the estate?
(b) How many residents are there in the estate?

Ans :- a) 1 : 3
b) 138 residents

4. Mary and Tom had the same amount of money. Mary bought a badminton racket and had \$86 left. Tom bought a pair of roller blades and had ¼ of what Mary had left. If the roller blades cost 3 times as much as the racket, how much did Tom have at first?

Ans :- At first Tom had \$118.25.

5. The 3 jars below contain twenty-cent and fifty-cent coins only. The number of coins in the 3 jars is the same. The ratio of the number of twenty-cent coins to the number of fifty-cent coins in jars A, B and C is 1:1, 7:2 and 11:7 respectively.
(a) What is the ratio of the total number of twenty-cent coins to the number of fifty-cent coins?
(b) If there are \$600 in jar B, find the total number of fifty-cent coins in jar B.

Ans :- a) 17 : 10
b) 500 50¢ coins.

6. A train travels at 30 km/h and a car travels at a certain uniform speed. The train left town U 3 hours before the car, but the car overtook the train 6 hours after it had set off and arrived at town V 2 hours before the train.
(a) What is the speed of car?
(b) Find the distance between town U and town V.

Ans :- a) 45 km/h
b) 450 km .

7. A square WXYZ is divided into 4 smaller squares. The shaded region in each smaller square is formed by 2 quadrants. Given that the perimeter of the whole shaded region is 352 cm, find the radius of a quadrant. (Take π = 227 )

Ans :- 28 cm.

8. A box of stamps was equally divided among 18 children. 6 of those children gave up 34 of their share. As a result, the remaining children received 21 more each. How many stamps were there in all?

Ans :- In all there were 1008 stamps.

9. A farmer has 9m rabbits, 35 ducks and 8m chickens. He sold m rabbits, 19 ducks and 5m chickens. How many legs do the remaining animals on his farm have together?

Ans :- (38m + 32) legs

10. Mr. Lee has some sweets. He wants to give them to his pupils. If he gives 5 sweets to each of his pupils, he will have 20 sweets left. If he gives 6 sweets to each of his pupils, he will need 16 more sweets. How many pupils are there?

Ans :- There are 36 pupils.