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 1/3 of the mints but returned four because she had a monetary pang of guilt. Fatima then took 1/4 of what was left but returned three for similar reasons. Eswari then took half of the remainder but threw 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

Answer: (D)

$48$

Let the mints be $x$.

Mints taken by Sita = $\frac{x}{3}-4$,

Mints remaining = $x-(\frac{x}{3}-4)=\frac{2x}{3}+4$

Mints taken by Fatima =$(\frac{\frac{2x}{3}+4}{4}-3)$,

Mints remaining = $\frac{2x}{3}+4-(\frac{\frac{2x}{3}+4}{4}-3)=\frac{x}{2}+6$

Mints taken by Eswari = $\frac{\frac{x}{2}+6}{2}-2$,

Mints remaining = $\frac{x}{2}+6-(\frac{\frac{x}{2}+6}{2}-2)=\frac{x}{4}+5$ = 17,

$\frac{x}{4}=12,x=48$