Mia and Ria can do a piece of work alone in 15 days and 10 days respectively. Mia started the work alone and then after 5 days Ria joined her till the completion of the work. How long did the work last?

9 days 

Time taken ∝ $\frac{1}{efficiency}$

                    Mia   :   Ria 

Time taken     15   :   10    ⇒   3  :  2

Efficiency         2   :    3

Total Work = LCM of 10, 15 = 30

Work done by Mia in 5 days = efficiency of Mia x No. of days

                                         = 2 x 5 = 10

Work left = 30 - 10 = 20

Efficiency of Mia and Ria together = 2 + 3 = 5

This work will taken Mia and Ria together = $\frac{work}{efficiency}$

                             = $\frac{20}{5}$  = 4 days

Total number of days taken to complete the work = 9 days