In May, Diana and Harry had beads in the ratio 13 : 10. In June, each of them gave away the same number of beads. Diana then had thrice as many beads as Harry.
- Find the ratio of the number of beads Harry had in May to the number of beads he had in June.
- Find the ratio of the total number of beads both had in May to the total number of beads both had in June.
| |
Diana |
Harry |
Difference |
| Before |
13x2 =
26 u |
10x2 =
20 u |
3x2 =
6 u |
| Change |
- 17 u |
- 17 u |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
2x3 =
6 u |
(a)
Since Diana and Harry gave away the same number of beads, the difference in the number of beads between Diana and Harry at first and in the end remains the same.
Make the difference in the number of beads at first and in the end the same. LCM of 3 and 2 is 6.
Harry's beads in May : Harry's beads in June
20 : 3
(b)
Total number of beads in May
= 26 u + 20 u
= 46 u
Total number of beads in June
= 9 u + 3 u
= 12 u
Total beads in May : Total beads in June
46 : 12
(÷2)23 : 6
Answer(s): (a) 20 : 3; (b) 23 : 6
