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
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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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Question : A, B, and C can complete a work in 10, 12, and 15 days respectively. They started the work together, but A left the work before five days of its completion. B also left the job two days after A left. In how many days was the work completed?
Option 2: 5 days
Option 3: 7 days
Option 4: 8 days
Question : Rimmi and Simmi can together finish a work in 40 days. They worked together for 30 days and then Simmi left. After another 30 days, Rimmi finished the remaining work alone. In how many days Rimmi alone can finish the work?
Option 1: 120 days
Option 2: 30 days
Option 3: 80 days
Option 4: 40 days
Question : A, B, and C together can complete a work in 5 days. A and B together can complete the same work in 6 days. C alone can finish the same work in how many days?
Option 1: 60 days
Option 3: 15 days
Option 4: 20 days
Question : A alone can do a work in 16 days and B alone can do the same work in 12 days. If they worked together on it for 4 days and A left. How long did B take to finish the remaining work?
Option 1: 7 days
Option 3: 6 days
Question : A and B together complete a work in 20 days, B and C together complete the same work in 30 days, and C and A together complete the same work in 24 days. In how many days A, B, and C together can complete the same work?
Option 1: 8 days
Option 2: 16 days
Option 3: 12 days
Option 4: 15 days
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