Abhishek and Abhinandan together can complete a work in 20 days. Abhinandan started to work alone and completes 2/3 work and remaining work is completed by Abhishek alone. They completed the work in total 39 days. Find in how many days Abhinandan alone can complete the work if he works for whole number of days?

Let Abhinandan complete the work alone in x days and Abhishek complete it alone in y days. Working alone, Abhinandan completes 2/3 of the work in 2x/3 days, and Abhishek completes the remaining 1/3 of the work in y/3 days, giving the equation 2x/3 plus y/3 equals 39. Multiplying by 3 gives 2x plus y equals 117. Combining the overall rates of Abhinandan and Abhishek gives 1/x plus 1/y equals 1/20, leading to the relation x times y equals 20 times x plus y. By substituting y equals 117 minus 2x into the second relation and solving the quadratic equation, we find that x equals 36. Since the problem specifies whole number working days, Abhinandan takes 36 days to complete the work alone.

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