10 women and 4 men can together finish a machine repairing work in 2 days, while 18 women and 9 men can finish it in a single day. Find the time taken
by 1 woman alone to finish the work, and also that taken by 1 man alone.
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1
Answer:
let one woman can do the same work in w days
in one day, one woman can do 1/w part of work
similarly, let one man can do the same work in m days
in one day...one man....1/m part of work.
first case
10 women + 4 men took 2 days
10 women + 4 men in one day 1/2 part of work
10*1/w + 4*1/m = 1/2
10/w + 4/m = 1/2.......(1)
similarly
18/w + 9/m = 1..........(2(
(1)*9 - (2)*4
90/w + 36/m = 9/2
72/w + 36/m = 4
--------------------------
18/w = 9/2 - 4
18/w = 1/2
w = 18*2
w = 36
putting in (1)
10/36 + 4/m = 1/2
4/m = 1/2 - 10/36
4/m = (18-10)/36
4/m = 8/36
8m = 36*4
m = 36*4/8
m = 18
thus,
a woman can do the same work alone in 36 days
a man can do the same work alone in 18 days
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Please refer to the attached picture
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