Question

Aman, Bharat, Chitra, and Deepa are four siblings. Their mother gave them some candies. Aman took \( \frac{1}{3} \) of the candies and returned 4. Then Bharat took \( \frac{1}{4} \) of the remaining candies and returned 3. Chitra took \( \frac{1}{2} \) of the remaining candies and returned 2. Finally, Deepa took the remaining 17 candies. How many candies did Bharat and Chitra take altogether?

• A. 25
• B. 23
• C. 19
• D. 17
• E. 22

Hint:

To solve this type of problem, break down the situation step by step, considering the fractions and returns after each sibling’s turn.

Answer 1

The Correct Option is C

Step 1: Starting with Aman’s candies.
Let the total number of candies be \( x \). Aman took \( \frac{1}{3} \) of the candies and returned 4. So: \[ \text{Candies Aman took} = \frac{1}{3}x - 4 \] The remaining candies are: \[ \text{Remaining candies} = x - \left( \frac{1}{3}x - 4 \right) = \frac{2}{3}x + 4 \] Step 2: Bharat’s candies.
Bharat took \( \frac{1}{4} \) of the remaining candies and returned 3. So: \[ \text{Candies Bharat took} = \frac{1}{4} \left( \frac{2}{3}x + 4 \right) - 3 \] The remaining candies after Bharat’s turn are: \[ \text{Remaining candies after Bharat} = \frac{3}{4} \left( \frac{2}{3}x + 4 \right) + 3 \] Step 3: Chitra’s candies.
Chitra took \( \frac{1}{2} \) of the remaining candies and returned 2. So: \[ \text{Candies Chitra took} = \frac{1}{2} \left( \frac{3}{4} \left( \frac{2}{3}x + 4 \right) + 3 \right) - 2 \] Step 4: Deepa’s candies.
Deepa took the remaining 17 candies, which means the sum of the candies taken by Bharat and Chitra equals: \[ \boxed{19} \] Final Answer: \[ \boxed{19} \]