Jack, Ryan and Xavier had some cards in the ratio of 2 : 3 : 5. Xavier gave 40% of his cards to Jack and Ryan. As a result, Jack had the same number of cards as Ryan and Xavier had 40 fewer cards than Jack.
- What was the percentage increase in Jack's cards after receiving from Xavier?
- How many cards did Ryan have at first?
| Jack |
Ryan |
Xavier |
Total |
| 2 u |
3 u |
5 u |
10 u |
| + 2 u |
- 2 u |
|
| 3.5 u |
3.5 u |
3 u |
10 u |
(a)
Number of cards that Xavier gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of cards that Jack and Ryan each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of cards that Jack had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Jack's cards after receiving from Xavier
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 40
3.5 u - 3 u = 40
0.5 u = 40
1 u = 40 ÷ 0.5 = 80
Number of cards that Ryan had at first
= 3 u
= 3 x 80
= 240
Answer(s): (a) 75%; (b) 240
