Working 10 hours a day, Jagan can complete a work in 12 days while working 8 hours a day, Magan can complete the same work in 9 days. If Jagan and Magan work together 6 hours a day, then in how many days will they complete the original work ?

Correct option is C

Given:

Jagan works 10 hours a day to complete the work in 12 days.

Magan works 8 hours a day to complete the work in 9 days.

Jagan and Magan work together 6 hours a day.

Solution:

$$\text{Jagan's work rate} = \frac{1}{10 \times 12} = \frac{1}{120} \text{ (per hour)} \\ \ \\\text{Magan's work rate} = \frac{1}{8 \times 9} = \frac{1}{72} \text{ (per hour)} \\ \ \\\text{Total work rate} = \frac{1}{120} + \frac{1}{72} \\ \ \\\text{Total work rate} = \frac{3}{360} + \frac{5}{360} = \frac{8}{360} = \frac{2}{90} \text{ (per hour)}$$​​

Total work done per day when both work together for 6 hours:
​$$\text{Total work done per day} = \frac{2}{90} \times 6 = \frac{12}{90} = \frac{2}{15}$$​​

So, Jagan and Magan together complete $$\frac{2}{15}$$​ of the work each day.

Total time taken to complete the work:
​$$\text{Total time} = \frac{1}{\frac{2}{15}} = \frac{15}{2} = 7\frac12$$​ days

Alternate Method:

One day work (Magan +Jagan) = (5 + 3) ×6 = 48hours.

Taken time complete original work =$$\frac{360}{48}=\frac{15}2$$​​

=7$$\frac12$$​ days.