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.
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
ok.
so 4 men & 6 women takes = 8 days,
3 men & 7 women takes = 10 days.
and 10 women takes = 400 days.
thankyou sir.
Both answers are incorrect. Let me explain the correct solution.
Given:
4 men + 6 women = complete work in 8 days (equation 1)
3 men + 7 women = complete work in 10 days (equation 2)
To find the number of days it takes for 10 women to complete the work, we need to calculate the rate at which each man and woman works.
Let the rate at which a man works be m, and the rate at which a woman works be w.
From equation 1:
4/m + 6/w = 8
Multiply both sides by mw to eliminate the fractions:
4w + 6m = 8wm (equation 3)
From equation 2:
3/m + 7/w = 10
Multiply both sides by mw to eliminate the fractions:
3w + 7m = 10wm (equation 4)
Now, we can solve equations 3 and 4 simultaneously to find the values of w and m.
Multiply equation 3 by 3 and equation 4 by 4 to eliminate the m terms:
12w + 18m = 24wm (equation 5)
12w + 28m = 40wm (equation 6)
Subtract equation 5 from equation 6:
28m - 18m = 40wm - 24wm
10m = 16wm
m = 1.6w (equation 7)
Now, substitute equation 7 into either equation 3 or 4 to solve for the value of w.
Using equation 3:
4w + 6(1.6w) = 8w(1.6w)
4w + 9.6w = 12.8w^2
13.6w = 12.8w^2
12.8w^2 - 13.6w = 0
w(12.8w - 13.6) = 0
w = 0 (not admissible) or w = 13.6/12.8 = 1.0625 (equation 8)
Therefore, the rate at which a woman works (w) is approximately 1.0625.
To find the number of days it takes for 10 women to complete the work, divide the work by the total rate of the women:
Number of days = Work / (10*w)
Number of days = 1 / (10*1.0625)
Number of days = 1 / 10.625
Number of days = 0.0941 (approximately)
So, 10 women will take approximately 0.0941 days to complete the work, which is equivalent to about 2 hours and 15 minutes.