Latest RRB Aptitude Question SOLUTION: Anna, Benne and Cenna are have friends. Anna and Benne are twins. Benne takes 2 days more than Cenne to complete the work. If Anne started a work and 3 days later Benne joins him t

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(#M40166149) RRB Numerical Ability question Keep an EYE

Anna, Benne and Cenna are have friends. Anna and Benne are twins. Benne takes 2 days more than Cenne to complete the work. If Anne started a work and 3 days later Benne joins him then the work gets complete in 3 more days. Working together . Anne, Benne and Cenne can complete thrice the original work in 6 days. In how many days Benne can complete twice the original work with double the efficiency working alone?

Asked In RRB Ram Kumar (5 years ago)

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Devendra Marghade  (5 years ago)

Ans: 6 days

Working alone, let Anna, Benne and Cenna can complete the work in A, B & C days respectively, then

Statement I) : Benne takes 2 days more than Cenne => B=C+2 ---(i)

Statement II) : Anne started a work and 3 days later Benne joins him then the work gets complete in 3 more days => When Anne worked for 6 days & Benne for 3 days, work gets completed.
=> 6/A + 3/B = 1 ---(ii)

Statement III) : Anne, Benne and Cenne can complete thrice the original work in 6 days.
=> Together they can complete the original work in 2 days.
=> 1/A + 1/B + 1/C = 1/2 ---(iii)

Now solving (ii) & (iii), we get 3/B + 6/C = 2 ---(iv)
Substituting C=B-2 from (i) in eqn (iv), 3/B + 6/(B-2) = 2
3B - 6 + 6B = 2(B² - 2B)
2B² - 13B + 6 = 0
(2B-1) (B-6) = 0
B=1/2, 6. Considering whole number of days, B=6

Now B's 1 day work=1/6. With twice efficiency 1 day's work = 2/6 = 1/3
Therefore, days required for twice the original work = 2/(1/3) = 6

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