A can complete 40% of a work in 16 days . B is 25% less efficient than C . C takes 16 days less than A to complete the work. In how many days A and B together can complete 84.375% of work together?
Answers
Given :- A can complete 40% of a work in 16 days . B is 25% less efficient than C . C takes 16 days less than A to complete the work. In how many days A and B together can complete 84.375% of work together ?
Solution :-
→ A can complete 40% of a work in = 16 days .
so,
→ A can complete 100% of a work in = (16/40) * 100 = 40 days .
now,
→ Time taken by C to complete the work = 16 days less than A = 40 - 16 = 24 days .
then,
→ Time taken by B to complete the work = (24 * 100)/75 = 32 days .
now,
→ LCM of (40 and 32) = 160 units = Let total work .
so,
→ Efficiency of A = Total work / time taken = 160/40 = 4 units / day
→ Efficiency of B = Total work / time taken = 120/32 = 5 units / day
then,
→ Efficiency of (A + B) = 4 + 5 = 9 units / day.
therefore,
→ Time taken by A and B to complete 84.375% of work together = (160 * 84.375/100) / 9 = 135 / 9 = 15 days (Ans.)
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Given : A can complete 40% of a work in 16 days .
B is 25% less efficient than C .
C takes 16 days less than A to complete the work.
To Find : In how many days A and B together can complete 84.375% of work together?
Solution:
A can complete 40% of a work in 16 days .
=> 100 % can be done in 16 * 100 / 40 = 40 Days
C takes 16 days less than A to complete the work
=> C can complete in 40 - 16 = 24 Days
C' 1 day work = 1/24
B is 25% less efficient than C
=> B's 1 day work = C's 1 day work - 25 % less
= 1/24 - (25/100)(1/24)
= 1/32
A & B together 1 day work = 1/40 + 1/32
= ( 4 + 5)/160
= 9/160
Hence 100 % work will be completed in 160/9 days
=> 84.375% of work will be done = (84.375 / 100 ) (160/9)
= 9,375 * 16 / 10
= 150 /10
= 15 Days
A and B together can complete 84.375% of work together in 15 Days
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