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 $ \dfrac{1}{3} $ of the mints but returned four because she had a monetary pang guilt. Fatima then took $ \dfrac{1}{4} $ of what was left but returned three for similar reasons. Eswari then took half of the remainder but three two back into the bowl. The bowl had only $ 17 $ mints left when the raid was over. How many mints were originally in the bowl?
 $
  A.\,\,38 \\
  B.\,\,31 \\
  C.\,\,41 \\
  D.\,\,48 \\
  $

Answer 1

Hint: To find this type of problem we first let total numbers of mint in bowl as ‘x’ then calculating numbers of mint taken by first by Sita and then calculating remaining mints left in bowl and then calculating numbers of mints taken by Fatima and then calculating remaining mints left in bowl and finally calculating numbers of mints taken by Eswari and then remaining numbers of mints left in bowl and finally equating number of mints left in bowl equal to $ 17 $ to form an equation and on solving it to find value of ‘x’ and hence required solution of given problem.

Complete step-by-step answer:
Let total number of mint originally in bowl = x
First Sita took $ \dfrac{1}{3} $ of total mint and then put four back in the bowl.
Therefore, mint left in the bowl after what Sita had taken is given as:
 $
\Rightarrow x - \dfrac{1}{3}x + 4 \\
   = \dfrac{{3x - x}}{3} + 4 \\
   = \dfrac{2}{3}x + 4 \;
  $
Hence, number of mint left in bowl are $ \dfrac{2}{3}x + 4 $
Now, Fatima took $ \dfrac{1}{4} $ of mint left in the bowl but she returned three.
Therefore, number of mint left in bowl can be written as:
 $
  \left[ {\dfrac{2}{3}x + 4 - \dfrac{1}{4}\left( {\dfrac{2}{3}x + 4} \right)} \right] + 3 \\
   \Rightarrow \dfrac{2}{3}x + 4 - \dfrac{1}{6}x - 1 + 3 \\
   \Rightarrow \dfrac{{4x - x}}{6} + 6 \\
   \Rightarrow \dfrac{{3x}}{6} + 6 \\
   \Rightarrow \dfrac{x}{2} + 6 \\
  $
Therefore, we see that numbers of mints left in bowl are $ \left( {\dfrac{x}{2} + 6} \right) $
Now, Eshwari took half of the mint left in the bowl and put two back.
Therefore, number of mint left in bowl can be given as:
 $
  \left[ {\left( {\dfrac{x}{2} + 6} \right) - \dfrac{1}{2}\left( {\dfrac{x}{2} + 6} \right) + 2} \right] \\
   \Rightarrow \dfrac{x}{2} + 6 - \dfrac{x}{4} - 3 + 2 \\
   \Rightarrow \dfrac{{2x - x}}{4} + 5 \\
   \Rightarrow \dfrac{x}{4} + 5 \;
  $
Therefore, from above we see that numbers of mints left in the bowl are $ \left( {\dfrac{x}{4} + 5} \right) $ .
But it is given that number of mints left in bowl are $ 17. $
Therefore, from above we have,
 $
  \dfrac{x}{4} + 5 = 17 \\
   \Rightarrow \dfrac{x}{4} = 17 - 5 \\
   \Rightarrow \dfrac{x}{4} = 12 \\
   \Rightarrow x = 48 \;
  $
Therefore, we see that number of mints originally in bowl was $ 48 $ .
So, the correct answer is “48”.

Note: We can also find the solution of given problem in other way. In this way we first calculate numbers of mints taken by Eswari from given number of mints left in bowl which was $ 17 $ and then doing so we can calculate numbers of mint taken by Fatima and numbers of mints by Sita and hence from all these we can calculate total numbers of mints originally was there in bowl.