# Raj alone can complete 20% of the work in 2.8 days, Sam alone can complete 40% of the work in 4 days and Kavi alone can complete 30% of the work in 3.

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Raj alone can complete 20% of the work in 2.8 days, Sam alone can complete 40% of the work in 4 days and Kavi alone can complete 30% of the work in 3.6 days. They start working together and after 3 days Raj leaves them, then find the time taken by Sam and Kavi together to complete the remaining work?
1. $1\frac{6}{7}{\rm{\;days}}$
2. $1\frac{2}{7}{\rm{\;days}}$
3. $1\frac{4}{7}{\rm{\;days}}$
4. $1\frac{5}{7}{\rm{\;days}}$
5. None of these

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Correct Answer - Option 2 : $1\frac{2}{7}{\rm{\;days}}$

Given:

Raj alone can complete 20% of the work in 2.8 days.

⇒ Raj alone can complete the whole work in 14 days.

Sam alone can complete 40% of the work in 4 days

⇒ Sam alone can complete the whole work in 10 days.

Kavi alone can complete 30% of the work in 3.6 days

⇒ Kavi alone can complete the whole work in 12 days.

Assumption:

Let the total work be L.C.M. of (14, 10 and 12) = 420 units

Calculation:

One day work of Raj = 420/14 = 30 units

One day work of Sam = 420/10 = 42 units

One day work of Kavi = 420/12 = 35 units

According to question,

Let Sam and Kavi takes “d” days to complete remaining work.

3[30 + 42 + 35] + d [42 + 35] = 420

⇒ 321 + 77d = 420

⇒ 77d = 420 – 321

⇒ 77d = 99

⇒ d = 99/77

⇒ d = 9/7

∴ d = $1\frac{2}{7}{\rm{\;days}}$