QOTD | Quantitative Aptitude | Time and work

Question of The Day09-03-2020

A and B alone can complete a piece of work in 16 days and 24 days respectively. A starts the work and does it for the first half of the time, then A and B together do the remaining work to complete it in the rest half of the time. What will be the total time taken to complete the work in such a manner?

Answer

Correct Answer : d ) 12 days

Explanation :

Let us assume the total work will be completed in T days

Now, according to the question

A alone can complete a piece of work in 16 days

One day work of A = \({1 \over 6}\)

The amount of work done by A in T/2 days =\({T\over 32}\) ..... (1)

B alone can complete a piece of work in 24 days

One day work of B = \({1 \over 24}\)

Thus, one day work of A and B together will be equal to one day work of A and one day work of B

⇒\({1 \over 6} + {1 \over 24} ={5 \over 48}\)

Now, the amount of work done by A and B together in T/2 days will be =\({5T \over 96}\)..... (2)

We know that in total T time all the work gets completed

Thus, from equation (1) and (2) we get

\({T \over 32} + {5T \over 96}=1\)=1

\({3T + 5T\over 96}=1\)

\(T={96 \over 8}=12 \) days

Hence, (d) 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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