Question:
Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four. Fatima then took one-fourth of what was left but returned three. Eswari then took half of the remainder but threw two back. The bowl had only 17 mints left. How many mints were originally in the bowl?
Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four. Fatima then took one-fourth of what was left but returned three. Eswari then took half of the remainder but threw two back. The bowl had only 17 mints left. How many mints were originally in the bowl?
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Work backwards in step problems to find the original quantity.
Updated On: Aug 4, 2025
- 38
- 31
- 41
- None of these
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The Correct Option is C
Solution and Explanation
Let initial mints = $M$. After Sita: took $\frac13 M$, returned 4, so left = $M - \frac13 M + 4 = \frac23 M + 4$.
After Fatima: took $\frac14$ of that, returned 3, so left = $\frac34(\frac23 M + 4) + 3$.
After Eswari: took half, returned 2, so left = $\frac12(\frac34(\frac23 M + 4) + 3) + 2 = 17$.
Solving yields $M = 41$.
After Fatima: took $\frac14$ of that, returned 3, so left = $\frac34(\frac23 M + 4) + 3$.
After Eswari: took half, returned 2, so left = $\frac12(\frac34(\frac23 M + 4) + 3) + 2 = 17$.
Solving yields $M = 41$.
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