Question : 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?
Option 1: 5 days
Option 2: 9 days
Option 3: 12 days
Option 4: 4 days
Correct Answer: 9 days
Solution :
Given: Mia and Ria can do a piece of work alone in 15 days and 10 days, respectively.
Mia in 1 day can do $\frac{1}{15}$ part
Ria in 1 day can do $\frac{1}{10}$ part
After 5 days Mia can do $\frac{5}{15}$ = $\frac{1}{3}$ part
So, the remaining part = ($1-\frac{1}{3}$) = $\frac{2}{3}$
Ria and Mia together in 1 day can do ($\frac{1}{15}+\frac{1}{10}$) = $\frac{2+3}{30}$ = $\frac{1}{6}$ part
They can do $\frac{1}{6}$ part in 1 day
So, they can do $\frac{2}{3}$ part in ($\frac{2}{3}\div \frac{1}{6}$) = 4 days
Therefore, the work lasted (5 + 4) = 9 days
Hence, the correct answer is 9 days.
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