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:

Question

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

Answer 1

Working directly with fractions of the job avoids picking an LCM at all.

In one day, Amit does $\frac{1}{12}$ of the work and Sagar does $\frac{1}{15}$ of the work.
Together, in one day they do $\frac{1}{12}+\frac{1}{15}=\frac{5}{60}+\frac{4}{60}=\frac{9}{60}=\frac{3}{20}$ of the work.
In 4 days, they complete $4 \times \frac{3}{20} = \frac{12}{20} = \frac{3}{5}$ of the work.
The fraction left is $1 - \frac{3}{5} = \frac{2}{5}$.

So the correct answer is option C, 2/5.

Answer 2

Working directly with fractions of the job avoids picking an LCM at all.

In one day, Amit does $\frac{1}{12}$ of the work and Sagar does $\frac{1}{15}$ of the work.
Together, in one day they do $\frac{1}{12}+\frac{1}{15}=\frac{5}{60}+\frac{4}{60}=\frac{9}{60}=\frac{3}{20}$ of the work.
In 4 days, they complete $4 \times \frac{3}{20} = \frac{12}{20} = \frac{3}{5}$ of the work.
The fraction left is $1 - \frac{3}{5} = \frac{2}{5}$.

So the correct answer is option C, 2/5.

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:

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The Correct Option is C

Solution and Explanation

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