► Skill Involving Two or more Quantities With Fixed Total
1. The ratio of the boys to girls in a hall was 2 : 3. After 20% of the boys and 60% of the girls left the hall, the boys then outnumbered the girls by 60. How many children were in the hall at first?
Ans :- At first there 750 children in the hall.
2. In April, Tom saved 40% of his salary and spent the the rest of $600. In May, he saved $100 more. In June, he saved 3⁄5 of the amount he saved in May. Find his monthly average savings in the three months.
Ans :- $400.
3. Jenny spent 0.6 of her money on 4 towels. She bought another 2 towels and 3 cakes of soap with the rest of her money. If one free cake of soap is given for every 5 purchased, how many cakes of soap would Jenny get if she spent all her money on soap?
Ans :- 36 cakes of soap.
4. Fann had a bottle full of Coke. She filled 4 mugs with 5⁄9 of it. She found that the remaining Coke could still fill 2 mugs and 3 glasses. Find how many glasses could a bottle full of Coke fill.
Ans :- 18 glasses.
5. The body of a cat is as long as its head plus ½ the length of its tail. The tail is as long as the combined length of the head and body. If the head is 8 cm long, find the length of the whole cat.
Ans :- Cat is 64 cm long.
6. Alvin, Bobby and Calvin shared a box of clips equally. Alvin divided clips into 3 equal packets. Bobby divided his share into 4 equal packets and Calvin divided his share into 6 equal packets. If 1 of Alvin's packets and 1 of Bobby's packets had 30 more clips than 2 of Calvin's packets, how many clips did they share?
Ans :- They shared 360 clips.
7. Rachel bought 20 mugs and glasses. She was given a discount of $1 per mug and $0.30 per glass. She saved $10.20 altogether. How many mugs did she buy?
Ans :- 6.
8. Jerry poured 1⁄4 of a full bottle of water into 2 mugs and 3 glasses. He poured the rest into 7 mugs and 6 glasses. How many mugs can a full bottle fill?
Ans :- 12.
9. Box A and Box B contain some apples and oranges. The number of apples in Box A and Box B are in the ratio of 1 : 3 respectively. The number of oranges in Box A and Box B are in the ratio of 3 : 7 respectively. When 2⁄3 of the apples in Box B are transferred to Box A, The number of fruits in both boxes become equal. If there are 20 apples less than oranges altogether, Find the number of apples in Box B at first.
Ans :- 60.
10. Each month, Mrs Tan receives 0.4 of her daughter's monthly salary and 4⁄9 of her son's salary. Find the salary of her son if she receives equal amount of money from both her son and daughter and her daughter earns $100 more than her son.
Ans :- $900.
11. 37% of the beads in a box are yellow. The rest are red and blue beads in the ratio 3 : 4. There are 20 more yellow beads than red beads. How many beads are there altogether?
Ans :- 200 beads.