simple equations

Three friends returning from a movie, stopped to eat at a restaurant. After the dinner, they paid their bill and noticed a bowl of mints at the front counter. Shikha took 1/3^rd of the mints, but returned four because she had a momentary pang of guilt. Farah then took ¼ of what was remaining but returned three for similar reasons. Aditi then took half of the remaining but threw back two into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?

Answer:

Initial number of mints = y

So, after Shikha’s raid, mints left = y – (y/3 – 4) = 2y/3 + 4

So, after Farah’s raid, mints left = 2y/3 + 4 –{ ¼ (2y/3 + 4) – 3} = 2y/3 – y/6 + 8 = y/2 + 6

So, after Aditi’s raid, mint left = y/2 + 6 – {1/2 (y/2 + 6) – 2} = y/2 – y/4 + 5 = y/4 + 5 = 17

Therefore y = 48.