Question of The Day11-05-2020

A and B starts working on a project such that they work on it in alternate months starting from B. The work gets completed in \(19 {1 \over 5}\) months. If A alone can complete the project in 23 months, then in how many months B alone can complete the work?

Answer

Correct Answer : b ) \(16 {2 \over 3}\)

Explanation :

As total work gets completed in \(19 {1 \over 5}\) months  and B started doing the work for first month

So, Number of months B had worked upon the project = 10 months

And, Number of months A had worked upon the project will be

\(=19 {1 \over 5} -10=19-10+15=9 {1 \over 5}\) months

A alone can complete the project in 23 months

Part of work completed by A in 1 month = \({1 \over 23}\)

Part of work completed by A in 915 month = \( {1 \over 23}*(9 {1 \over 5})={1 \over 23} * {46 \over 5}={2 \over 5}\)

Now, remaining work = \(1- {2 \over 5}= {3 \over 5}\)

Therefore, \(( {3 \over 5})\)th of the work is completed by B in 10 months

So, total work is completed by B in=\(10* {5 \over 3}= {50 \over 3}=16 {2 \over 3}\)months

Hence, (b) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS etc.

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