Question

Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is:

• A. \(240\)
• B. \(260\)
• C. \(300\)
• D. \(340\)

Hint:

In work and time problems with different efficiencies, it is often easiest to: \begin{itemize} \item Assume one person's efficiency as a variable, \item Express others' efficiencies in terms of that variable using the given ratios, \item Compute total work done, then divide by an individual’s efficiency for “alone” time. \end{itemize}

Answer 1

The Correct Option is D

Step 1: Let Chandan’s efficiency be \(x\) units of work per day. \[ E_C = x. \] Bipin is twice as efficient as Chandan: \[ E_B = 2x. \] Ankita is twice as efficient as Bipin: \[ E_A = 2 \cdot (2x) = 4x. \]
Step 2: Work done by each person. Total time taken for the job to finish is 60 days. \underline{Bipin:} works for 20 days (then leaves): \[ W_B = E_B \times 20 = 2x \times 20 = 40x. \] \underline{Ankita:} works for all 60 days: \[ W_A = E_A \times 60 = 4x \times 60 = 240x. \] \underline{Chandan:} also works for all 60 days: \[ W_C = E_C \times 60 = x \times 60 = 60x. \]
Step 3: Total work. \[ W_{\text{total}} = W_A + W_B + W_C = 240x + 40x + 60x = 340x. \]
Step 4: Time taken by Chandan alone. If Chandan works alone at efficiency \(x\), then \[ \text{Time} = \frac{W_{\text{total}}}{E_C} = \frac{340x}{x} = 340 \text{ days}. \] Therefore, Chandan would need \(340\) days to complete the job alone.