PSLE Jade had a bag of gold marbles and black marbles in the ratio 13 : 7. She removed an equal number of gold marbles and black marbles from the bag. The ratio of the number of gold marbles and black marbles left in the bag became 3 : 1. What percentage of the marbles were left in the bag?
|
Gold marbles |
Black marbles |
Difference |
Total |
Before |
13x1 = 13 u |
7x1 = 7 u |
6x1 = 6 u |
20x1 = 20 u |
Change |
- 4 u |
- 4 u |
|
|
After |
3x3 = 9 u |
1x3 = 3 u |
2x3 = 6 u |
4x3 = 12 u |
When Jade removed an equal number of gold marbles and black marbles, the difference between the number of gold marbles and black marbles at first and in the end remains the same.
LCM of 6 and 2 is 6.
Percentage of the marbles left in the bag
=
1220 x 100%
= 35 x 100%
= 60%
Answer: 60%