In March, Zara and Henry had buttons in the ratio 10 : 7. In April, each of them gave away the same number of buttons. Zara then had thrice as many buttons as Henry.
- Find the ratio of the number of buttons Henry had in March to the number of buttons he had in April.
- Find the ratio of the total number of buttons both had in March to the total number of buttons both had in April.
| |
Zara |
Henry |
Difference |
| Before |
10x2 =
20 u |
7x2 =
14 u |
3x2 =
6 u |
| Change |
- 11 u |
- 11 u |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
2x3 =
6 u |
(a)
Since Zara and Henry gave away the same number of buttons, the difference in the number of buttons between Zara and Henry at first and in the end remains the same.
Make the difference in the number of buttons at first and in the end the same. LCM of 3 and 2 is 6.
Henry's buttons in March : Henry's buttons in April
14 : 3
(b)
Total number of buttons in March
= 20 u + 14 u
= 34 u
Total number of buttons in April
= 9 u + 3 u
= 12 u
Total buttons in March : Total buttons in April
34 : 12
(÷2)17 : 6
Answer(s): (a) 14 : 3; (b) 17 : 6
