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?
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
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.
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.
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.
To solve this problem, we can start by considering the rates at which each individual man and woman works.
Let M be the rate at which a man works (in terms of the fraction of work completed per day) and W be the rate at which a woman works. Since the number of men and women varies in each scenario, let's find the combined rates of men and women in completing the work for each scenario.
In Scenario 1, where 4 men and 6 women complete the work in 8 days, the combined rate is given by:
4M + 6W = 1/8 (since the total work is completed in 8 days)
In Scenario 2, where 3 men and 7 women complete the work in 10 days, the combined rate is given by:
3M + 7W = 1/10
Now that we have two equations, we can solve them simultaneously to find the values of M and W.
Multiplying the equation from Scenario 1 by 3 and the equation from Scenario 2 by 4 gives:
12M + 18W = 3/8
12M + 28W = 2/5
Subtracting the first equation from the second equation eliminates M, leaving:
10W = 2/5 - 3/8
To simplify, find a common denominator:
10W = (16 - 15) / 40
10W = 1 / 40
Dividing both sides by 10 gives:
W = 1 / (10 * 40)
W = 1 / 400
We have found the rate at which a single woman works. Now we need to determine how many days it will take for 10 women to complete the work.
Since the combined rate of the 10 women is 10 times the rate of a single woman, the equation becomes:
10 * (1/400) = 1 / D
Simplifying, we have:
1 / 40 = 1 / D
Cross multiplying gives:
D = 40
Therefore, it will take 10 women 40 days to complete the work.