Question

Four siblings share a jar of candies. Aman took \(\frac{1}{3}\) of the candies and returned 4 to the jar. Bharat then took \(\frac{1}{4}\) of what remained and returned 3. Chitra then took \(\frac{1}{2}\) of what remained and returned 2. Deepa took the remaining 17 candies. How many candies did Bharat and Chitra keep altogether (taken minus returned)?

• A. 25
• B. 23
• C. 19
• D. 17

Hint:

Instead of working backward from the last remainder, try setting up forward equations in terms of the original total and solving for it directly.

Answer 1

The Correct Option is C

Step 1: Let the original total be $N$. Aman takes $\frac{N}{3}$, leaving $\frac{2N}{3}$, then returns 4, so the jar has $J_1 = \frac{2N}{3}+4$.
Step 2: Bharat takes $\frac{J_1}{4}$, leaving $\frac{3J_1}{4}$, then returns 3, so the jar has $J_2 = \frac{3J_1}{4}+3$.
Step 3: Chitra takes $\frac{J_2}{2}$, leaving $\frac{J_2}{2}$, then returns 2, so the jar has $J_3 = \frac{J_2}{2}+2 = 17$ (Deepa's share).
Step 4: Solve forward: $\frac{J_2}{2}+2=17\Rightarrow J_2=30$. Then $\frac{3J_1}{4}+3=30\Rightarrow J_1=36$. Then $\frac{2N}{3}+4=36\Rightarrow N=48$.
Step 5: Bharat kept (taken $-$ returned) $=\frac{J_1}{4}-3 = 9-3=6$. Chitra kept $=\frac{J_2}{2}-2=15-2=13$.
Step 6: Together Bharat and Chitra kept $6+13=19$.
\[\boxed{19}\]