a does 8/ 15 of the given work in 8 days and remaining work is finish with the assistance of B in 4 days how long will b
to take the work alone
Answers
Answer :-
B alone takes 20 days to complete the work.
Explanation :-
In 8 days A completes = (8/15) of the given work
In 1 day A completes = (8/15) ÷ 8 = (8/15) × (1/8) = 1/15 of the given work
i.e A's 1 day work = 1/15
Remaining work done by A with the assistance of B = 1 - Work done by A in 8 days
= 1 - (8/15)
Taking LCM
= (15 - 8)/15
= 7/15
i.e Remaining work done by A with the assistance of B = 7/15
Given
Remaining work is finished by A with the assistance of B in 4 days
We know that
Number of Days worked × (A's 1 day work + B's 1 day work) = Remaining work done by A with the assistance of B
⇒4(1/15 + B) = 7/15
⇒ (1/15) + B = (7/15) ÷ 4
⇒ (1/15) + B = (7/15) × (1/4)
⇒ (1/15) + B = 7/60
⇒ B = (7/60) - (1/15)
Taking LCM
⇒ B = (7 - 4)/60
⇒ B = 3/60
⇒ B = 1/20
i.e B's 1 day work = 1/20
So B alone takes 20 days to complete the work.
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