Perry, Ivan and Nick had some pens in the ratio of 2 : 3 : 5. Nick gave 40% of his pens to Perry and Ivan. As a result, Perry had the same number of pens as Ivan and Nick had 41 fewer pens than Perry.
- What was the percentage increase in Perry's pens after receiving from Nick?
- How many pens did Ivan have at first?
| Perry |
Ivan |
Nick |
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 pens that Nick gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of pens that Perry and Ivan each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of pens that Perry had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Perry's pens after receiving from Nick
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 41
3.5 u - 3 u = 41
0.5 u = 41
1 u = 41 ÷ 0.5 = 82
Number of pens that Ivan had at first
= 3 u
= 3 x 82
= 246
Answer(s): (a) 75%; (b) 246
