Question : B and C can complete work alone in 10 days and 30 days respectively. They began the work together but B left the work after some days and C completed the remaining work in 10 days. After how many days from the beginning B left the work?
Option 1: 4 days
Option 2: 6 days
Option 3: 8 days
Option 4: 5 days
Correct Answer: 5 days
Solution :
Let the number of days they worked together be $x$
According to the question
⇒ The efficiency of B = $\frac{1}{10}$
⇒ The efficiency of C = $\frac{1}{30}$
Combined efficiency = $\frac{1}{10}$ + $\frac{1}{30}$ = $\frac{4}{30}$
⇒ Work done for $x$ days = $\frac{4x}{30}$
Remaining work = 1 – $\frac{4x}{30}$ = $\frac{30 – 4x}{30}$
⇒ The remaining work to be done by C in 10 days = $\frac{10}{30}$
⇒ $\frac{30 – 4x}{30}$ = $\frac{10}{30}$
⇒ 30 – 4$x$ = 10
⇒ – 4$x$ = 10 – 30
⇒ $x$ = $\frac{-20}{-4}$ = 5
Hence, the correct answer is 5 days.
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