CAT 2019 Set-2 | Question: 71

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

Given that, Anil alone can do a job in $20$ days, and Sunil alone can do a job in $40$ days.

• Anil $\rightarrow 20$ days
• Sunil $\rightarrow 40$ days

LCM of $20$ and $40 \Rightarrow 40\;\text{units}$ (Total work)

• Anil efficiency  $=\frac{40}{20} \Rightarrow 2$
• Sunil efficiency $= \frac{40}{40}\Rightarrow 1$

Work done by Anil in $3$ days $ = 2 \times 3 = 6\;\text{units}$

Now, remaining work $ = 40 – 6 = 34\;\text{unit}$

Let the number of days Anil and Sunil done the work together be $x$ days.

 Bimal has done $10\%$ of the work $ = 40 \times \frac{10}{100} = 4\;\text{units}$

Remaining  work done by Anil and Sunil $ = 34-4=30\;\text{units}$

The number of days Anil and Sunil did the work together $ x = \frac{30}{(2+1)} = \frac{30}{3} = 10$ days.

$\therefore$ The total time to complete the work $ = x + 3 = 10 + 3  = 13$ days.

Correct Answer : B