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