Question

Raman can do a piece of work in 16 days, Satish in 8 days, while Ashok can do it in 32 days. All started together but Satish left after 2 days. Raman left 3 days before the completion of the work. How long did it take to complete the entire work?

• A. 8 days
• B. 10 days
• C. 12 days
• D. 14 days

Hint:

In work problems where people leave at different times, always assume total time as a variable and form a single work-equation using individual working durations.

Answer 1

The Correct Option is B

Step 1: Write individual one-day work rates.
Raman can complete the work in 16 days, so his one-day work is \( \frac{1}{16} \).
Satish can complete the work in 8 days, so his one-day work is \( \frac{1}{8} \).
Ashok can complete the work in 32 days, so his one-day work is \( \frac{1}{32} \).
Step 2: Work done by all three in the first 2 days.
Combined one-day work of all three is:
\[ \frac{1}{16} + \frac{1}{8} + \frac{1}{32} \]
\[ = \frac{2 + 4 + 1}{32} = \frac{7}{32} \]
Work done in 2 days is:
\[ 2 \times \frac{7}{32} = \frac{14}{32} = \frac{7}{16} \]
Step 3: Work remaining after 2 days.
\[ 1 - \frac{7}{16} = \frac{9}{16} \]
Step 4: Raman leaves 3 days before completion.
Let total time taken to complete the work be \( x \) days.
Then Raman worked for \( (x - 3) \) days.
Satish worked only for 2 days.
Ashok worked for all \( x \) days.
Step 5: Total work equation.
\[ \frac{x-3}{16} + \frac{2}{8} + \frac{x}{32} = 1 \]
Step 6: Simplify the equation.
\[ \frac{x-3}{16} + \frac{1}{4} + \frac{x}{32} = 1 \]
Multiply entire equation by 32 to clear denominators.
\[ 2(x-3) + 8 + x = 32 \]
Step 7: Solve the equation.
\[ 2x - 6 + 8 + x = 32 \]
\[ 3x + 2 = 32 \]
\[ 3x = 30 \]
\[ x = 10 \]
Step 8: Final conclusion.
Hence, the total time taken to complete the work is 10 days.