Question

Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?

• A. 14
• B. 13
• C. 15
• D. 12

Answer 1

The Correct Option is B

To solve this problem, we begin by calculating the work rates of Anil, Sunil, and Bimal. 

• Anil can finish the job in 20 days → Work rate = \( \frac{1}{20} \) per day
• Sunil can finish it in 40 days → Work rate = \( \frac{1}{40} \) per day
• Bimal contributes 10% of the total work → Bimal's work = \( \frac{1}{10} \)

Step 1: Work by Anil Alone

Anil works alone for the first 3 days.

\[ \text{Work done by Anil} = 3 \times \frac{1}{20} = \frac{3}{20} \]

Step 2: Anil and Sunil Work Together

From Day 4, Sunil joins Anil. Their combined work rate:

\[ \frac{1}{20} + \frac{1}{40} = \frac{3}{40} \]

Let the number of days they work together be \( x \). Then work done by Anil and Sunil together is:

\[ x \times \frac{3}{40} = \frac{3x}{40} \]

Step 3: Total Work Completed

Total work done by Anil and Sunil =

\[ \frac{3}{20} + \frac{3x}{40} \]

Bimal did 10% of the job, so Anil and Sunil together did 90%:

\[ \frac{3}{20} + \frac{3x}{40} = \frac{9}{10} \]

Step 4: Solve the Equation

Convert \( \frac{3}{20} \) to denominator 40:

\[ \frac{6}{40} + \frac{3x}{40} = \frac{36}{40} \] \[ \frac{6 + 3x}{40} = \frac{36}{40} \Rightarrow 6 + 3x = 36 \Rightarrow 3x = 30 \Rightarrow x = 10 \]

Final Answer:

Total days = 3 (Anil alone) + 10 (Anil & Sunil) = 13 days.