Ahmad, Asher and Julian had some pens in the ratio of 2 : 3 : 5. Julian gave 40% of his pens to Ahmad and Asher. As a result, Ahmad had the same number of pens as Asher and Julian had 49 fewer pens than Ahmad.
- What was the percentage increase in Ahmad's pens after receiving from Julian?
- How many pens did Asher have at first?
| Ahmad |
Asher |
Julian |
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 Julian gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of pens that Ahmad and Asher each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of pens that Ahmad had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Ahmad's pens after receiving from Julian
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 49
3.5 u - 3 u = 49
0.5 u = 49
1 u = 49 ÷ 0.5 = 98
Number of pens that Asher had at first
= 3 u
= 3 x 98
= 294
Answer(s): (a) 75%; (b) 294
