PSLE Penelope had a box of brown marbles and purple marbles in the ratio 13 : 7. She removed an equal number of brown marbles and purple marbles from the box. The ratio of the number of brown marbles and purple marbles left in the box became 9 : 4. What percentage of the marbles were left in the box?
|
Brown marbles |
Purple marbles |
Difference |
Total |
Before |
13x5 = 65 u |
7x5 = 35 u |
6x5 = 30 u |
20x5 = 100 u |
Change |
- 11 u |
- 11 u |
|
|
After |
9x6 = 54 u |
4x6 = 24 u |
5x6 = 30 u |
13x6 = 78 u |
When Penelope removed an equal number of brown marbles and purple marbles, the difference between the number of brown marbles and purple marbles at first and in the end remains the same.
LCM of 6 and 5 is 30.
Percentage of the marbles left in the box
=
78100 x 100%
= 3950 x 100%
= 78%
Answer: 78%