Question : P, Q, and R alone can do a piece of work in 5, 6, and 4 days, respectively. All three of them began the work together but Q left 1 day before completion of the work. In how many days was the work completed?
Option 1: $\frac{70}{37}$ days
Option 2: $\frac{100}{27}$ days
Option 3: $3$ days
Option 4: $\frac{80}{23}$ days
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Correct Answer: $\frac{70}{37}$ days
Solution : Let the total number of days be t. Rate of P = $\frac{1}{5}$ per day Rate of Q = $\frac{1}{6}$ per day Rate of R = $\frac{1}{4}$ per day ⇒ Combined rate = $\frac{1}{5}$ + $\frac{1}{6}$ + $\frac{1}{4}$ = $\frac{12}{60}$ + $\frac{10}{60}$ + $\frac{15}{60}$ = $\frac{37}{60}$ Q leaves 1 day before the completion of the work. So, P, Q, and R worked together for (t – 1) days, and P and R worked on the last day. Total work = 1 = $\frac{37}{60}$ × (t – 1) + $\frac{9}{20}$ ⇒ 1 – $\frac{9}{20}$ = $\frac{37}{60}$ × (t – 1) ⇒ $\frac{11}{20}$ = $\frac{37}{60}$ × (t – 1) ⇒ $\frac{11×60}{20×37}$ = (t – 1) ⇒ $\frac{33}{37}$ + 1 = t ⇒ t = $\frac{70}{37}$ Hence, the correct answer is $\frac{70}{37}$ days.
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Question : A piece of work can be completed by P and Q together in 24 days, and the same piece of work can be completed by R alone in 60 days. If P and R together can do the same work in 36 days, then find the time taken by Q to complete this piece of work alone.
Option 1: $8\frac{4}{5}$days
Option 2: $29\frac{9}{13}$days
Option 3: $3\frac{6}{7}$days
Option 4: $32\frac{8}{11}$days
Question : C1, C2 and C3 can do work alone in 10, 12, and 15 days respectively. All three of them began the work together but C2 left 2 days before the completion of the work. In how many days was the work completed?
Option 1: 3
Option 2: 7
Option 3: 5
Option 4: 4
Question : Kajal can do a piece of work alone in 24 days, while Neha can do the same work alone in 40 days. Kajal started the work alone, and then after 12 clays, Neha joined her till the completion of the work. How long did the work take to be completed since Kajal started to work on it?
Option 1: $\frac{37}{4}$ days
Option 2: $\frac{39}{2}$ days
Option 3: $\frac{37}{2}$ days
Option 4: $\frac{39}{4}$ days
Question : S alone can do a piece of work in 14 days. T alone can do the same work in 21 days. U alone can do the same work in 28 days. Working together, in how many days will they complete the work?
Option 1: $\frac{84}{13}$ days
Option 2: $\frac{77}{13}$ days
Option 3: $\frac{71}{13}$ days
Option 4: $\frac{87}{13}$ days
Question : A alone can do $\frac{1}{4}$th part of the work in 12 days. B alone can do $\frac{1}{5}$th part of the work in 4 days. In how many days can A and B together can do the same work?
Option 1: $\frac{330}{13}$ days
Option 2: $\frac{240}{17}$ days
Option 3: $\frac{210}{4}$ days
Option 4: $\frac{255}{7}$ days
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