# Maths worksheets for challenging problem sums

Related Skills
Skill Involving Changing quantities
Ratio
Fraction

## * Practice for skill involving changing quantities

1. Roslan had a total of 84 green, blue and yellow pencils. She gave 9 green pencils and 13 of the blue pencils to her friend. She then bought 2 more yellow pencils. If the ratio of the green, blue and yellow pencils became 1 : 2 : 3, find the number of yellow pencils that she had at first.

Ans :- She had 31 yellow pencils at first.

2. Zoe, Fann, May and Ann had 85 beads altogether. Zoe gave away half her beads and Fann gave away 7. May increased her beads by 12 and Ann doubled hers. They each finally had the same number of beads. How many beads did Zoe and Fann have altogether at first?

Ans :- 67.

3. At a carpark, the ratio of cars to lorries was 4 : 1. When 25% of the cars and 50% of the lorries left the carpark, 80 more cars than lorries remained. Find the total number of cars and lorries at the carpark at first.

Ans :- At first there were total 160 cars and lorries at the car park.

4. Ali had half as many green marbles as blue marbles. After giving away 10 green marbles and 60 blue marbles, he was left with thrice as many green marbles as blue marbles. How many green marbles did he have at first?

Ans :- At first Ali had 34 green marbles.

5. Ali and Baba had \$790. Baba had more money than Ali. After each of them spent half of what they had originally, the difference between them was \$98.
(a) How much did Baba have at first?
(b) How much money did they have in the end?

Ans :- a) At first Baba had \$493
b) In the end they had \$395.

6. Edwin and Shawn had the same amount of stickers. After Edwin had given away 77 of his stickers and Shawn had given away 9 of his, Shawn had 3 times as many stickers as Edwin. How many stickers did each of them have at first?

Ans :- At first each of them had 111 stickers.

7. 20 girls and 10 boys shared a box of sweets equally. When the 10 boys gave up ¼ of their share of sweets, the girls had 3 extra sweets each. How many sweets were there in the box at first?

Ans :- At first there were 720 sweets in the box.

8. Nancy and Jane baked 1800 muffins altogether. After Nancy sold 680 of her muffins, Nancy still had 20 more muffins than Jane. How many muffins did Nancy bake?

Ans :- Nancy baked 1250 muffins .

9. John and Bob are given some money each. If John spends twice as much as Bob, he will still have \$600 than Bob has spent all his money. If John half as what Bob spends, he will still have \$ 1800 when Bob has spent all his money.
(a) How much money is given to John?
(b) How much money is given to Bob?

Ans :- a) \$2200 given to John
b) \$800 is given to Bob .

10. A box contains only red balls and white ball. 80% of the balls are red balls. 28 red balls and 2 white balls are removed from the box and the remaining balls are put into group of 9 balls. In each group of 9 balls, there are 7 red balls. Find the least possible number of balls in the box at first.

Ans :- At first there were 168 red balls and 42 white balls and total 210 balls in the box.