The total number of balls in Bag P, Bag Q and Bag R was 46.
38 of the balls from Bag P and 10 balls from Bag Q were removed. More balls were then added into Bag R until the number of balls in it was quadrupled. The ratio of the number of balls in Bag P to Bag Q to Bag R became 5 : 3 : 4.
- How many more balls were there in Bag P than Bag Q at first?
- Find the total number of balls in Bag P and Bag R in the end.
|
Bag P |
Bag Q |
Bag R |
Total |
Before |
8 u |
3 u + 10 |
1 u |
46 |
Change |
- 3 u |
- 10 |
+ 3 u |
|
After |
5 u |
|
4 u |
|
Comparing the balls in the end |
5 u |
3 u |
4 u |
|
(a)
Total number of balls at first
= 8 u + 3 u + 10 + 1 u
= 12 u + 10
12 u + 10 = 46
12 u = 46 - 10
12 u = 36
1 u = 36 ÷ 12 = 3
Number of more balls in Bag P than Bag Q at first
= 8 u - (3 u + 10)
= 8 u - 3 u - 10
= 5 u - 10
= 5 x 3 - 10
= 15 - 10
= 5
(b)
Total number of balls in Bag P and Bag R in the end
= 5 u + 4 u
= 9 u
= 9 x 3
= 27
Answer(s): (a) 5; (b) 27