Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 12)
12.
4 men and 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?
Answer: Option
Explanation:
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
| Then, 4x + 6y = | 1 | and 3x + 7y = | 1 | . |
| 8 | 10 |
| Solving the two equations, we get: x = | 11 | , y = | 1 |
| 400 | 400 |
 1 woman's 1 day's work = |
1 | . |
| 400 |
 10 women's 1 day's work = |
 |
1 | x 10 |  |
= | 1 | . |
| 400 | 40 |
Hence, 10 women will complete the work in 40 days.
Discussion:
106 comments Page 8 of 11.
Shaheena said:
8 years ago
I don't understand the solving 1 & 2 equations. Please, anyone help me.
Sangay said:
8 years ago
Superb explanation, thanks @Chan.
N.nagachandu said:
8 years ago
Here we can use m1*d1=m2*d2 formulae.
m1=(4m+6w), d1=8d, m2=(3m+7w), d2=10d,
here we convert all mens are into women's
(4m+6w)*8=(3m+7w)*10,
(4m+6w)*4=(3m+7w)*5,
16m+24w=15m+35w,
1m=11w,
Use this one first equation.
4(11w)+6w=50w.
So 50 women's can do the work =8days.
So 10 womens can do the work=50/10*8=40days.
m1=(4m+6w), d1=8d, m2=(3m+7w), d2=10d,
here we convert all mens are into women's
(4m+6w)*8=(3m+7w)*10,
(4m+6w)*4=(3m+7w)*5,
16m+24w=15m+35w,
1m=11w,
Use this one first equation.
4(11w)+6w=50w.
So 50 women's can do the work =8days.
So 10 womens can do the work=50/10*8=40days.
Daniel Thapa said:
8 years ago
@Aravindhan: Cool bro thats smart way of handling this kinda question, and thanks.
Dhiru said:
8 years ago
(4m+6w)8 ---> (i)
(3m+7w)10 ---> (ii)
As per question.
(4m+6w)8=(3m+7w)10.
32m+48w=30m+70w.
2m=22w.
m/w=22/2 or 11/1.
Putting m=11 and w= 1 in eq(i)
(4*11+6*1)8 =400.
10 women complete work in 400/10 =40.
(3m+7w)10 ---> (ii)
As per question.
(4m+6w)8=(3m+7w)10.
32m+48w=30m+70w.
2m=22w.
m/w=22/2 or 11/1.
Putting m=11 and w= 1 in eq(i)
(4*11+6*1)8 =400.
10 women complete work in 400/10 =40.
(3)
Bipul Muntasir said:
7 years ago
4 men and 6women can do the work in 8 days.
3 men and 7women can do that work in 10 days.
...........................................
So, 1men can be replaced by 1women with extra 2 days work.
4men can be replaced by 4 women with 2*4=8 extra days work.
Now total men worker '0' & total women workers 6+4=10,
This 10 women can do that work in 8+8(extra days) =16 days.
so, the answer should be 16 days.
3 men and 7women can do that work in 10 days.
...........................................
So, 1men can be replaced by 1women with extra 2 days work.
4men can be replaced by 4 women with 2*4=8 extra days work.
Now total men worker '0' & total women workers 6+4=10,
This 10 women can do that work in 8+8(extra days) =16 days.
so, the answer should be 16 days.
Vishal Pardhi said:
7 years ago
8*(4M+6W) = 10*(3M+7).
32M + 48W = 30M + 70W,
32M - 30M = 70W - 48 W,
2M = 22W,
M = 22/2 W,
M= 11W,
IT MEANS 1 man = 11 women.
So, 4 Man = 4*11 = 44 Women,
Now, 44 + 6 = 50 Women.
Then 50 Women work done in 8 days...so those work 10 women compleat in how many days ?
So, 50*8/10 = 40 days.
32M + 48W = 30M + 70W,
32M - 30M = 70W - 48 W,
2M = 22W,
M = 22/2 W,
M= 11W,
IT MEANS 1 man = 11 women.
So, 4 Man = 4*11 = 44 Women,
Now, 44 + 6 = 50 Women.
Then 50 Women work done in 8 days...so those work 10 women compleat in how many days ?
So, 50*8/10 = 40 days.
Abhi Samrat said:
7 years ago
(4m + 6w)x8 = (3m +7w)x 10.
2m =22w,
1m= 11w,
M/w = 11/1,
Put value
(3m + 7w) x 10.
(3x11 + 7x1) x10.
(33+7)x10.
400.
(10wx1)xd = 400.
D = 400/10.
40days.
2m =22w,
1m= 11w,
M/w = 11/1,
Put value
(3m + 7w) x 10.
(3x11 + 7x1) x10.
(33+7)x10.
400.
(10wx1)xd = 400.
D = 400/10.
40days.
Suchi said:
7 years ago
Thanks @Chan and @Ashish.
Sonu said:
7 years ago
Can anyone solve the equation clearly?
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