Ben, Perry and Harry had some cards in the ratio of 2 : 3 : 5. Harry gave 40% of his cards to Ben and Perry. As a result, Ben had the same number of cards as Perry and Harry had 47 fewer cards than Ben.
- What was the percentage increase in Ben's cards after receiving from Harry?
- How many cards did Perry have at first?
| Ben |
Perry |
Harry |
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 Harry gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of cards that Ben and Perry each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of cards that Ben had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Ben's cards after receiving from Harry
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 47
3.5 u - 3 u = 47
0.5 u = 47
1 u = 47 ÷ 0.5 = 94
Number of cards that Perry had at first
= 3 u
= 3 x 94
= 282
Answer(s): (a) 75%; (b) 282
