8 men with 2 boys can do a piece of work in 7 days, which 25 men with 13 boys can do in two days. what fraction of the whole can be done in One Day by 11 men with 20 boys
Answers
Answer:
let,
the work done by 1 man in a day ( no of units by a man/day) be m,
the work done by 1 boy in a day ( no of untis by a boy / day ) be b.
Given
(8 m + 2 b ) can do a piece of work in 7 days
(25 m + 13 b ) can do a piece of work in 2 days
we know that efficiency * time = work
from this we can say that (8 m + 2 b ) * 7 = work done
(25 m + 13 b ) * 2 = work done
to make our calculation part easy we’ll consider the lcm (7,2) as the work done i.e., 14
=> ( 8 m + 2 b ) * 7 = 14 units
= > ( 8 m + 2 b ) = 2 units/ day ……………eq ( a )
( from the above equation we can say that 8 men and 2 boys will do 2 units per day)
and
(25 m + 13 b ) * 2 = 14 units
=> ( 25 m + 13 b ) = 7 units / day …………..eq ( b)
if we solve eq ( a) and eq (b ) we get
m = 2/9 units/day
b = 1/9 units/day
we need to find 11 men and 20 boys
i.e., ( 11 m + 20 b ) units /day
=> 11 * 2/9 + 20 * 1/9 units /day
=> 42/9 units/day
and total units to be completed is 14 so the the time taken by 11 men and
20 boys to complete the work is 14/(42/9) i.e., 3 days
in one day the can complete 1/3 of the work.
Answer:
Step-by-step explanation:
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