Question : P is thrice as good as a workman as Q and therefore can finish a work in 40 days less than Q. In how many days can they together complete the same work?
Option 1: 20 days
Option 2: 15 days
Option 3: 22.5 days
Option 4: 18 days
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Correct Answer: 15 days
Solution : Let Q finish the work in $D$ days then P will finish the same work in $(D - 40)$ days. So, 1-day work (efficiency) of Q = $\frac{1}{D}$ and 1-day work (efficiency) of P = $\frac{1}{D - 40}$ According to the question ⇒ $\frac{1}{D - 40}$ = 3 × $\frac{1}{D}$ ⇒ D = 3(D – 40) ⇒ D = 60 ⇒ Q's time = 60 days ⇒ P’s time = 60 − 40 = 20 days 1-day work of P and Q together = P’s 1-day work + Q’s 1-day work $=\frac{1}{D – 40}$ + $\frac{1}{D}=\frac{1}{20} + \frac{1}{60} = \frac{4}{60}= \frac{1}{15}$ So, time taken by P and Q together = $\frac{1}{\frac{1}{15}}$ = 15 days Hence, the correct answer is 15 days.
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Question : A is two times as efficient as B. A can complete a work in 20 days less than B. If both of them work together, then in how many days will the same work be completed?
Option 1: $\frac{40}{3}$ days
Option 2: $\frac{27}{2}$ days
Option 3: 20 days
Option 4: 15 days
Question : A is three times as good a worker as B and therefore can finish a job in 40 days less than B. Working together, they can do it in:
Option 1: 14 days
Option 2: 13 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 2: 30 days
Option 3: 15 days
Option 4: 20 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
Question : A can do a piece of work alone in 40 days. A and B together can do the same work in 10 days. C is 50% less efficient than B. In how many days can A and C together complete the same work?
Option 2: 24 days
Option 3: 16 days
Option 4: 12 days
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