Zane, Luke and Neave had some pens in the ratio of 2 : 3 : 5. Neave gave 40% of his pens to Zane and Luke. As a result, Zane had the same number of pens as Luke and Neave had 32 fewer pens than Zane.
- What was the percentage increase in Zane's pens after receiving from Neave?
- How many pens did Luke have at first?
| Zane |
Luke |
Neave |
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 Neave gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of pens that Zane and Luke each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of pens that Zane had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Zane's pens after receiving from Neave
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 32
3.5 u - 3 u = 32
0.5 u = 32
1 u = 32 ÷ 0.5 = 64
Number of pens that Luke had at first
= 3 u
= 3 x 64
= 192
Answer(s): (a) 75%; (b) 192
