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03 Feb 2021, 09:30
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C
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Difficulty:
15%
(low)
Question Stats:
85% (01:49) correct
15%
(02:15)
wrong
based on 188
sessions
History
Date
Time
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Not Attempted Yet
Rahul can finish a job in 30 days. He worked for 15 days alone and completed the remaining job working with Gaurav in 3 days. How many days would both Gaurav and Rahul together take to complete the entire job ?
(A) 4 days
(B) 5 days
(C) 6 days
(D) 10 days
(E) 12 days
(A) 4 days
(B) 5 days
(C) 6 days
(D) 10 days
(E) 12 days
Method: Using efficiency
Finding the efficiecny of R and G
From the problem statement, Rahul(\(R\)) can complete the total work in \(30\) days and \(R\) worked for \(15\) days. Remaiing work is \(30-15 = 15\) which was completed by Gaurav (\(G\)) and Rahul working together in \(3\) days.
Therefore, the efficiency of R and G as follows:
\(15R=3(R+G)\Longrightarrow 15R = 3R+3G\)
\(12R=3G\)
\(\dfrac{R}{G}= \dfrac{1}{4}\)
From the above equation, the efficiency of \(R=1\) and \(G=4\).
Finding total work
To find the total work, we can subtitute the efficieny of \(R\). Therefore, the \(\texttt{Total Work}\) \(= 30 \times 1 (\texttt{efficiency of Rahul}) = 30\)
Working together they completed the work in \(3\) days, where the efficiency of R and G gets combined i.e., \(R+G= 1+4 =5\)
Therefore, time to complete the total work working together \(= \dfrac{\texttt{Total Work}}{\texttt{Combined Efficiency}} = \dfrac{30}{5} = 6\) days
ANS C
Finding the efficiecny of R and G
From the problem statement, Rahul(\(R\)) can complete the total work in \(30\) days and \(R\) worked for \(15\) days. Remaiing work is \(30-15 = 15\) which was completed by Gaurav (\(G\)) and Rahul working together in \(3\) days.
Therefore, the efficiency of R and G as follows:
\(15R=3(R+G)\Longrightarrow 15R = 3R+3G\)
\(12R=3G\)
\(\dfrac{R}{G}= \dfrac{1}{4}\)
From the above equation, the efficiency of \(R=1\) and \(G=4\).
Finding total work
To find the total work, we can subtitute the efficieny of \(R\). Therefore, the \(\texttt{Total Work}\) \(= 30 \times 1 (\texttt{efficiency of Rahul}) = 30\)
Working together they completed the work in \(3\) days, where the efficiency of R and G gets combined i.e., \(R+G= 1+4 =5\)
Therefore, time to complete the total work working together \(= \dfrac{\texttt{Total Work}}{\texttt{Combined Efficiency}} = \dfrac{30}{5} = 6\) days
ANS C
26 Mar 2021, 11:35
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Rahul can finish a job in 30 days. He worked for 15 days alone and completed the remaining job working with Gaurav in 3 days. How many days would both Gaurav and Rahul together take to complete the entire job ?
Rahul can complete the job in 30 days
He worked for 15 days, therefore he completed half the job
Rahul and Gaurav completed half the job in 3 days. They would complete the full job in 6 days
Rahul can complete the job in 30 days
He worked for 15 days, therefore he completed half the job
Rahul and Gaurav completed half the job in 3 days. They would complete the full job in 6 days
