Anne, Benne and Cenna are have friends. Anne 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?
Answers
Given : Benne takes 2 days more than Cenne to complete the work . 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
To find : In how many days Benne can complete twice the original work with double the efficiency working alone
Solution:
Benne takes B Days to complet work
Cenne Take B-2 Days to complete work
Anne take A Days to complete work
Cenne 1 Days work = 1/(B-2)
Benne 1 Day Work = 1/B
Anne 1 Day work = 1/A
Anne started a work and 3 days later Benne joins him then the work gets complete in 3 more days
=> Anne worked for 6 Days & benne worked for 3 Days
6/A + 3/B = 1
=> 6/A = 1 - 3/B
Anne, Benne and Cenne can complete thrice the original work in 6 days
=> 6/A + 6/B + 6/(B - 2) = 3
=> 6/A = 3 - 6/B - 6/(B - 2)
Equating both
1 - 3/B = 3 - 6/B - 6/(B - 2)
=> 3/B + 6/(B - 2) = 2
=> 3(B - 2) + 6B = 2B(B - 2)
=> 3B - 6 + 6B = 2B² - 4B
=> 2B² - 13B + 6 = 0
=> 2B² - 12B - B + 6 = 0
=> 2B(B - 6) - 1(B - 6) = 0
=> (2B - 1)(B - 6) = 0
=> B = 1/2 , B = 6
Benne takes 2 days more than Cenne hence 1/2 Day is not possible
=> B = 6
Benne Takes 6 days , cenne takes 4 Days
6/A + 3/B = 1
=>6/A + 3/6 = 1
=> 6/A = 1/2
=> A = 12
Anne takes 12 Days
Benne Takes 6 days to complete the work alone
Benne 1 Day work = 1/6
with Double efficiency benne 1 Day work = 2 (1/6) = 1/3
Double Work = 2
number of Day = 2/(1/3) = 6
Benne will take 6 days to complete twice the original work with double the efficiency working alone
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