PSLE Gwen had a basket of red marbles and purple marbles in the ratio 13 : 7. She removed an equal number of red marbles and purple marbles from the basket. The ratio of the number of red marbles and purple marbles left in the basket became 9 : 4. What percentage of the marbles were left in the basket?
|
Red 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 Gwen removed an equal number of red marbles and purple marbles, the difference between the number of red 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 basket
=
78100 x 100%
= 3950 x 100%
= 78%
Answer: 78%