Pinky and Puja together can do a piece of work in 24 days, which puja and Riya can do in 32 days. After Pinky has been working at it for 10 days and Puja for 14 days, Riya finishes it in 26 days. In how many days Riya alone will do the work?

Let P, Pu, R be one-day work of Pinky, Puja, Riya. Given: P + Pu = 1/24, Pu + R = 1/32. After Pinky works 10 days, Puja works 14 days, and Riya finishes in 26 days: 10P + 14Pu + 26R = 1. Substituting P = 1/24 - Pu and solving: 4Pu + 26R = 7/12. Using Pu = 1/32 - R gives 26R - 4R = 7/12 - 1/8, so 22R = 11/24, thus R = 1/48. Therefore Riya alone takes 48 days.