Asked by kumar

posted by kumar Thursday, March 15, 2018 at 11:51am.

4 men & 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

maths - Reiny Thursday, March 15, 2018 at 1:50pm
man's rate ---- m
woman's rate --- w

4/m + 6/w = 8
4w + 6m = 8wm
2w + 3m = 4wm ---> wm = (2w + 3m)/4

3/m + 7/w = 10
3w + 7m = 10wm ---> wm = (3w + 7m)/10

(2w + 3m)/4 = (3w + 7m)/10
20w + 30m = 12w + 28m
8w = -2m
m = -4w

in 2w + 3m = 4wm
2w + 3(-4w) = 4w(-4w)
2w - 12w = -16w^2
16w^2 - 10w = 0
2w(8w - 5) = 0
w = 0 , not admissable
w = 5/8

for 10 women, time = 10/(5/8) = 80/5 = 16 days

maths - kumar yesterday at 3:17am
ok. Thank you sir. I have a doubt.

4m+6w=8 ........[1]
3m+7w=10 ......[2]

[2]*4 = 12m+28w=40
[1]*3 = 12m+18w=24
.........................................
[2]-[1]= 0 + 10W = 16 Days. Is it correct ? plz advice.

maths - kumar yesterday at 6:35am
I have one more doubt.
if the work is same,
then
[ 4m+6w]8 = [3m+7w]10
32m+48w = 30m+70w
2m=22w : 1m=11w
put it in equation
3m+7w=10 33w+7w=40w=10days
so,10 women = 40 days.

out of these 2 answers which one is correct ?
Sir, plz advice.
Answered by scott
the work takes ... 32 man-days plus 48 woman-days ... or ... 30 man-days plus 70 woman-days

the loss of 2 man-days is balanced by the addition of 22 woman days
... 1 man-day = 11 woman-days

the work takes 400 woman-days ... (30 * 11) + 70
Answered by kumar
ok.
so 4 men & 6 women takes = 8 days,
3 men & 7 women takes = 10 days.
and 10 women takes = 400 days.
thankyou sir.
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