1) There were 490 children altogether in two groups, A and B. Group A consisted of boys only and group B consisted of girls only. There were 2 ½ times as many girls as boys. Later some more girls joined group B, and for every 4 boys in group A, 32 more boys joined the group. The total number of girls was then ^{1}⁄_{3} that of the total number of boys. Express the number of girls who joined group B as a fraction of the number of boys who joined group A.

Ans :- ^{1}⁄_{16}.

2) Pail X had 8 ℓ of water, Pail Y had 6 l of water and Pail Z had 7 ℓ.

^{3}⁄_{4} of the water from X was poured into Z after that, ^{2}⁄_{3} of the water from Y was poured equally into X and Z , finally , ^{4}⁄_{5} of the water from Z , was poured back into X . Find the amount of water in Pail X in the end.

Ans :- In the end pail X has 16 ℓ of water

3) Sally, Yiling and Ali shared a bag of beads. Sally received ¾ of the bag of beads and ¾ of a bead. Yiling received ¾ of the remaining bag of beads and ¾ of a bead. Ali received the last bead in the bag. How many beads did sally receive? (No bead was divided in any way.)

Ans :- Sally received 24 Beads .

4) Rectangle A overlaps with rectangle B. Rectangle A is twice the size of rectangle B. If ^{1}⁄_{3} of rectangle B overlaps with rectangle A, what fraction of rectangle A overlaps with rectangle B

Ans :- ^{1}⁄_{5}.

5) Mrs. Ravi distributed some sweets equally among 9 boys and 11 girls. Each boy gave ^{2}⁄_{3} of what he received to the girls. As a result, the girls received a total of 1020 sweets.

(a) How many sweets did each boy have left?

(b) What was the total number of sweets distributed by Mrs. Ravi?

Ans :- a) 20

b) 1200.

6) Mitchell spent some money on a frying pan and ^{1}⁄_{3} of the remainder on a cooking pot. She then had $128 left. The cost of the cooking pot was ^{4}⁄_{7} of the cost of the frying pan.

(a) How much did the cooking pot cost?

(b) How much did she spend altogether?

Ans :- a) It cost $64

b) She spent $176
.

7) There were 60 pupils in the canteen. ^{3}⁄_{5} of them were girls. When some girls left the canteen, the number of girls who remained in the canteen was ¼ of the total number of pupils who remained in the canteen. How many girls left the canteen?

Ans :- 28 girls left the canteen.

8) In a garden, ^{2}⁄_{5} of the flowers are lilies. ¾ of the remainder are roses and the rest are sunflowers. There are 568 more roses than lilies. After ¾ of the lilies are sold, how many flowers are left in the garden?

Ans :- 7952 flowers.

9) Farmer Dan harvested some apples. He sold to Adam ¾ of the apples and another 105 apples. He sold to Geraldine ¾ of the remainder but took back 55 apples. Farmer Dan had 890 apples left.

(a) How many apples did Geraldine have after returning 55 apples to Farmer Dan?

(b) How many apples did Farmer Dan harvest?

Ans :- a) Geraldine had 2450 apples

b) Farmer Dan harvested 13780 apples
.

10) In the middle of the month, Gary withdrew ^{4}⁄_{5} of his money from the bank. He spent $136 on a computer game and the remaining $224 to buy a tennis racket. When he received his salary at the end of the month, he deposited ^{5}⁄_{8} of it in the bank. As a result, the amount in the bank was increased to $817.50. What is Gary's salary?

Ans :- Gary's salary is $1164.