Am I interpreting the question correctly or is the solution provided wrong?
Originally Ravind was carrying (r+f)kgs and Pranas was carrying (p+f)kgs.
Now, if they were carrying luggage twice the weight than the original then
Ravind would be carrying 2(r+f)kgs and
Pranas would be carrying 2(p+f)kgs
Then their excess weights would be 2r+f and 2p+f respectively. Why does the question state 2r-f and 2p-f
The solution has assumed the new wait to be 2r+f and 2p+f kgs I believe but nowhere in the question has it been mentioned that we have to take double of the excess weight only.
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You are wrong in assuming that the new weights become 2(r + f) and 2(p + f). In the solution, r and p are already defined as the total luggage weights carried by Ravind and Pranas. The free allowance is f kg, so the chargeable excess luggage is calculated as total luggage minus the free allowance, which is (r − f) and (p − f). That is why the original charge is based on (r − f)k and (p − f)k.
When the question says they carried twice the weight they actually did, it simply means their total luggage becomes 2r and 2p. The free allowance f does not change because the airline’s free allowance is fixed. Therefore, the new excess weights become (2r − f) and (2p − f). Your interpretation adds f again by writing 2r + f, which is incorrect because r already includes the free allowance portion of the luggage.