Total unchanged concept.

Using ratio,

First 'if' scenario
Sam : Pravin : Total stamps
1 : 1 : 2


Second 'if' scenario
Sam : Pravin : Total stamps
1 : 8 : 9


Total is unchanged so make the units the same.


Lowest common multiple of 2 and 9 is 18
(9 x 2 = 18, 2 × 9 = 18)

So,

First 'if' scenario
Sam : Pravin : Total stamps
1 : 1 : 2
9 : 9 : 18 (multiply all by 9)



Second 'if' scenario
Sam : Pravin : Total stamps
1 : 8 : 9
2 : 16 : 18 (multiply all by 2)



Now in the first scenario, Pravin gives Sam 25 stamps.

Work backwards,
Pravin actually has (9 units + 25) stamps in the first place.


In the second scenario, Sam gives Pravin 52 stamps.


When this happens, Pravin would have :

9 units + 25 + 52 = 9 units + 77 stamps


So 9 units + 77 stamps = 16 units

16 units - 9 units = 7 units

7 units = 77 stamps

1 unit = 77 stamps ÷ 7 = 11 stamps


Number of stamps they have altogether
= 18 units
= 11 stamps × 18
= 198 stamps

Alternative approach

First scenario : After giving Sam 25 stamps ,

Pravin → 1 unit
Sam → 1 unit

Work backwards,

Pravin at first = 1 unit + 25
Sam at first = 1 unit - 25

Their difference = 25 + 25 = 50



For the second scenario, Pravin gets 52 stamps from Sam.

Pravin → 1 unit + 25 + 52 = 1 unit + 77
Sam → 1 unit - 25 - 52 = 1 unit - 77

Their difference = 77 + 77 = 154
(Or 50 + 52 + 52 = 154)


We see that the ratio is 1 : 8 after the second scenario.

Pravin → 8 parts
Sam → 1 part
Difference = 7 parts

So 7 parts = 154
1 part = 154 ÷ 7 = 22


Total number of stamps
= 1 part + 8 parts
= 9 parts
= 9 × 22
= 198