Time and Work Practice Question

Question of The Day15-02-2021

A, B and C together can complete a work in 12 days. B, C, and D together can complete the same work in 15 days. C, D and A together can complete the same work in 12 days. D, A and B together can complete same work in 10 days. In how many days all of them together can complete the work?

Answer

Correct Answer : c ) \(9\) days

Explanation :

Let us assume the total work that needs to be done be (LCM of 12, 15, 12, and 10) = 180 units

As, total work done = (Time taken × Efficiency of person who is doing the work)

Now, depicting the given data

From the above figure,

Efficiency of A + B + C = 15………(1)

Efficiency of A + B + C = 12……….(2)

Efficiency of A + B + C = 15………..(3)

Efficiency of A + B + C = 18…………(4)

Now, adding equation 1, 2, 3, and 4 we get

3 (Efficiency of A + B + C + D) = 15 + 12 + 15 + 18 = 60

Efficiency of A + B + C + D = 20 units/day

Thus,

Time taken by A, B, C, and D together to complete the work=\(Total \ work \over Efficiency \)

⇒\(180 \over 20\)=9 days

Hence, (c) 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, UPSC NDA, etc.

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