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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?

1. $14$
2. $13$
3. $15$
4. $12$

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.

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