In order to solve the question, I have changed ‘bought’ to ‘gave away’.

In January, Alice and Ryan had stamps in the ratio 5 : 2. In February, each of them gave away the same number of stamps. Alice then had thrice as many stamps as Ryan. (a) Find the ratio of the number of stamps Ryan had in January to the number of stamps he had in February. (b) Find the ratio of the total number of stamps both had in January to the total number of stamps both had in February.

Method 1 :
In January
Alice : Ryan  difference
5 : 2 : 3
10 : 4 : 6

In February
Alice : Ryan :  difference
3 : 1 : 2
9 : 3 : 6

number of stamps Ryan had in —
January : February
4 : 3

(b)
10 + 4 = 14
9 + 3 = 12
14 : 12
7 : 6

Method 2 :
In January,
Alice : 5u
Ryan : 2u
total : 5u + 2u = 7u

In February,
Alice : 5u – 1p
Ryan : 2u – 1p
total : 5u – 1p + 2u – 1p = 7u – 2p

5u – 1p ——- (2u – 1p) x 3 = 6u – 3p
6u – 5u = 1u ——- 3p – 1p = 2p

2u : 2u – 1p
4p : 3p
4 : 3

(b)
7u : 7u – 2p
14p : 12p
7 : 6

Ans : (a) 4 : 3; (b) 7 : 6