Please don't use excel solve in a book

Problem 1. A client invested $100 in a mutual fund at the sstart of the month. After 20 days, the portfolio gained 10% (i.e., value =$110 ), and the client added an extra $50 (total portfolio value $160). From day 20 to day 30 , the portfolio lost 9.09%-the final portfolio value is $160(1 0.0909)=$145.46. Calculate the money-weighted return and time-weighted return. Which rate of should you use to evaluate the performance of the mutual fund manager