Given:
Amar, Samar, and Umesh together can complete a book in 15 days.
Amar and Samar together can complete the same book in 30 days.
Formula Used:
Work rate formula: Work = Number of days × Rate of work
Combined work rate: RateA + RateS + RateU
Calculation:
Let the work rate of Amar be A, Samar be S, and Umesh be U.
From the given data:
A + S + U = 1/15 (since together they complete the book in 15 days)
A + S = 1/30 (since Amar and Samar together complete the book in 30 days)
We need to find U.
Using the combined work rate:
⇒ (A + S + U) - (A + S) = 1/15 - 1/30
⇒ U = 1/15 - 1/30
⇒ U = (2 - 1)/30
⇒ U = 1/30
Therefore, Umesh alone can complete the book in 30 days.
The correct answer is option 4.