The total number of balls in Box A, Box B and Box C was 172.
58 of the balls from Box A and 4 balls from Box B were removed. More balls were then added into Box C until the number of balls in it was tripled. The ratio of the number of balls in Box A to Box B to Box C became 3 : 5 : 3.
- How many less balls were there in Box B than Box A at first?
- Find the total number of balls in Box B and Box C in the end.
|
Box A |
Box B |
Box C |
Total |
Before |
8 u |
5 u + 4 |
1 u |
172 |
Change |
- 5 u |
- 4 |
+ 2 u |
|
After |
3 u |
|
3 u |
|
Comparing the balls in the end |
3 u |
5 u |
3 u |
|
(a)
Total number of balls at first
= 8 u + 5 u + 4 + 1 u
= 14 u + 4
14 u + 4 = 172
14 u = 172 - 4
14 u = 168
1 u = 168 ÷ 14 = 12
Number of less balls in Box B than Box A at first
= 8 u - (5 u + 4)
= 8 u - 5 u - 4
= 3 u - 4
= 3 x 12 - 4
= 36 - 4
= 32
(b)
Total number of balls in Box B and Box C in the end
= 5 u + 3 u
= 8 u
= 8 x 12
= 96
Answer(s): (a) 32; (b) 96