Eduardo, Abraham and Xavier can finish a certain piece of work in 12, 10 and 15 days, respectively. All three of them started the work together. Eduardo left the work after 2 days and Abraham left just three days before the work was completed. Find the total number of days taken for the work to be completed.

Correct option is C

Given:

Eduardo can complete the work in 12 days → Work per day = $$\frac{1}{12}$$​​

Abraham can complete the work in 10 days → Work per day =$$\frac{1}{10}​$$​​

Xavier can complete the work in 15 days → Work per day =$$\frac{1}{15}​$$​​

Eduardo leaves after 2 days

Abraham leaves 3 days before the work is completed 

Formula used:

Total Work = Efficacy$$\times$$ Time  

Solution: 

Combine work;

​$$\frac{1}{12} + \frac{1}{10} + \frac{1}{15}$$ 

= $$\frac{5}{60} + \frac{6}{60} + \frac{4}{60} = \frac{15}{60} = \frac{1}{4}$$ 

Work done in 2 days: 

​$$2 \times \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$$ 

$$1 - \frac{1}{2} = \frac{1}{2}$$ 

Abraham leaves 3 days before the work is completed, so he works for $x-5$ days.

​$$\frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6}$$   

= $$(x - 5) \times \frac{1}{6}$$ 

Work done by Xavier alone in the last 3 days 

= $$3 \times \frac{1}{15} = \frac{3}{15} = \frac{1}{5}$$ 

$$\frac{1}{6}(x - 5) + \frac{1}{5} = \frac{1}{2}$$ 

$$\frac{x - 5}{6} + \frac{6}{30} = \frac{15}{30}\newline$$ 

$$\frac{x - 5}{6} = \frac{9}{30}\newline$$ 

$$\frac{x - 5}{6} = \frac{3}{10}$$ 

x - 5  =  $$\frac{18}{10}$$ 

x - 5 = 1.8

x = 6.8 days

Efficiency of Xavier=115\text{Efficiency of Xavier} = \frac{1}{15}

​

2×14=24=122 \times \frac{1}{4} = \frac{2}{4} = \frac{1}{=$$(x - 5) \times \frac{1}{6}$$