Meenu alone can do a work in 16 days. Simi alone can do it in 12 days. If Raj joins them, they three together can complete the work in 4 days. How long will Raj alone take to finish the work?

Correct option is C

Simi can complete the work in $12$ days ​112\frac{1}{12}

All three (Meenu, Simi, and Raj) together can complete the work in 444 days

Solution:

Let Raj's work rate = $$\frac{1}R$$​ (work per day)  

Work done by Meenu in one day = $$\frac{1}{16}$$​

Work done by Simi in one day =  $$\frac{1}{12}$$​
Total work done by all three in one day = $$\frac{1}{4}$$​

So, their total combined work rate is :

$$\frac{1}{16}+\frac{1}{12}+\frac{1}{R}=\frac{1}{4}$$

$$\frac{3}{48}+\frac{4}{48}+\frac{1}{R}=\frac{1}{4}$$​     

​$$\frac{7}{48}+\frac{1}{R}=\frac{1}{4}$$​​

​$$\frac{1}{R}=\frac{5}{48}$$​​

Raj alone will take $$\frac{48}{5}$$ days to complete the work.485\frac{48}{5}​​​​

14=1248\frac{1}{4} = \frac{12}{48}

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