In January, Mary and Asher had coins in the ratio 6 : 5. In February, each of them gave away the same number of coins. Mary then had thrice as many coins as Asher.

1. Find the ratio of the number of coins Asher had in January to the number of coins he had in February.
2. Find the ratio of the total number of coins both had in January to the total number of coins both had in February.

	Mary	Asher	Difference
Before	6x2 = 12 u	5x2 = 10 u	1x2 = 2 u
Change	- 9 u	- 9 u
After	3x1 = 3 u	1x1 = 1 u	2x1 = 2 u

(a)
Since Mary and Asher gave away the same number of coins, the difference in the number of coins between Mary and Asher at first and in the end remains the same.

Make the difference in the number of coins at first and in the end the same. LCM of 1 and 2 is 2.

Asher's coins in January : Asher's coins in February
10 : 1

(b)
Total number of coins in January
= 12 u + 10 u
= 22 u

Total number of coins in February
= 3 u + 1 u
= 4 u

Total coins in January : Total coins in February
22 : 4 _(÷2)
11 : 2 

Answer(s): (a) 10 : 1; (b) 11 : 2