Related Skills
Skill Involving Changing quantities
Ratio
Fraction

# Maths worksheets for challenging problem sums

1) Some scouts prepared 1316 prizes for their games stall. Each stuffed toy cost \$1.10, which was 116 of the cost of each lollipop. Each lollipop cost 23 as much as each puzzle. The ratio of the number of stuffed toys to the number of lollipop to the number of puzzles bought was 5 : 3 : 6. Find the total cost of the prizes.

Ans :- The total cost of the prizes is \$1193.80.

2) 711 of the guests at a party are adults. The ratio of the number of boys to the number of girls is 7 : 13. There are 330 more adults than girls. What is the total number of people at the party?

Ans :- Total 825 people at the party.

3). In a ballroom, the ratio of the number of singers to dancers is
7 : 5. The ratio of the number of male singers to the number of female singers is 8 : 3. Given that 45 of the dancers are females and there are 56 male singers,
(a) What fraction of all the people in the ballroom are male dancers?
(b) How many females are there altogether in the ballroom?

Ans :- a) 112
b) 65 females .

4) Jane had some pens and pencils in 2 boxes.
In Box A, the ratio of the number of pens to the number of
pencils is 2 : 5.
In Box B, the number of pens is three times the number of pencils. Jane transfers 15 of the pens from Box A to Box B. The total number of pens and pencils in Box A becomes 1188 and the ratio of the number of pens to the number of pencils in Box B becomes 21 : 4.
(a) How many pens were transferred from Box A to Box B?
(b) What is the total number of pens and pencils in Box B after the transfer?

Ans :- a) 72 pens
b) 200.

5) John bought some cans of fruit juice and soft drinks in the ratio
of 3 : 5. After making some fruit punch, the ratio of the number of cans of fruit juice to the number of cans of soft drinks became 2 : 5. A total of 24 cans of fruit juice and ¼ of the soft drinks were used to make the fruit punch. A can of fruit juice cost \$1.55 and a can of soft drink cost \$1.20. How much did John pay for the juice and soft drinks altogether?

Ans :- John paid \$170.40.

6) A company paid a total of \$23 600 in salaries to 17 female and some male employees. Each male employee received \$500 more than each female employee. There were 14 more female employees than male employees. Find the difference in the total amount of money received by the male employees and female employees.

Ans :- \$13970

7) Buttercup had a total of 36 wires and strings. Each wire is 4 cm long and each string is 3 cm long. The total length of the wires is 25 cm longer than the total length of the strings. How many more wires than strings did she have?

Ans :- 2 more wires than strings she had.

8) Uncle John had 240 apples, pears and oranges in the ratio
of 4 : 5 : 3 respectively. He bought additional 110 fruits. If the number of apples increased by 25% and the number of pears increased by 60%, find the percentage increase in the number of oranges.

Ans :- 50%.

9) Sanjay had a box of 55 blue, yellow and red marbles in the ratio
of 4 : 2 : 5 respectively. He puts 20 more marbles into the box. As a result, the number of blue marbles is increased by 25% and the number of yellow marbles increases by 50%.
(a) How many red marbles has he in the end?
(b) How many percent more red marbles than blue marbles has he in the end?

Ans :- a) In the end he had 35 red marbles
b) 40% more red marbles than blue marbles.

10) The figure is made up of circle A, triangle B and rectangle C.
½ of A overlaps B and 16 B overlaps C. The ratio of area A to B
is 1 : 3. The ratio of the area of B to C is 2 : 5. Find the ratio of the area of the shaded reigion to the area of the whole figure.

Ans :- 19 : 21.

11) There are two bags of marbles labeled X and Y. in Bag X, there are 350 red marbles and 500 white marbles. In Bag Y, there are 400 red marbles and 100 white marbles. How many red and how many white marbles should be transferred from Bag Y to Bag X so that 50% of the marbles in Bag X and 75% of those in Bag Y are red?

Ans :- 75 white and 175 red.