Question

Amit can do a work in 12 days and Sagar in 15 days. If they work on it together for 4 days, then the fraction of the work that is left is:

• A. \(\,\,3\\20\)
• B. \(3\\5\)
• C. \(2\\5\)
• D. \(\,\,2\\20\)

Answer 1

The Correct Option is C

To determine the fraction of work left after Amit and Sagar work together for 4 days, we first calculate their individual work rates.

Amit can complete the work in 12 days, so in one day, he completes \(\frac{1}{12}\) of the work. 

Sagar can complete the work in 15 days, so in one day, he completes \(\frac{1}{15}\) of the work.

When Amit and Sagar work together, their combined work rate per day is:

\(\frac{1}{12} + \frac{1}{15}\). To add these fractions, we find a common denominator:

\(\frac{1}{12} = \frac{5}{60}\)and \(\frac{1}{15} = \frac{4}{60}\)

So, their combined work rate is \(\frac{5}{60} + \frac{4}{60} = \frac{9}{60} = \frac{3}{20}\) of the work per day.

Thus, in 4 days, they can complete:

\(4 \times \frac{3}{20} = \frac{12}{20} = \frac{3}{5}\) of the work.

The fraction of the work that is left is:

\(1 - \frac{3}{5} = \frac{2}{5}\)

Therefore, the fraction of work left after 4 days is \(\frac{2}{5}\). The correct option is \(\frac{2}{5}\).