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 4 of 11.
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.
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)
Daniel Thapa said:
8 years ago
@Aravindhan: Cool bro thats smart way of handling this kinda question, and thanks.
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.
Sangay said:
8 years ago
Superb explanation, thanks @Chan.
Shaheena said:
8 years ago
I don't understand the solving 1 & 2 equations. Please, anyone help me.
Umesh said:
8 years ago
Thanks for the complete solutions.
Anushya said:
8 years ago
I can't understand this solution. Anyone help me to get it.
Anjum BAno said:
8 years ago
In simple way,
4 Man & 6 women complete works in 8 days i.e, 4M+6W=8....(1)
Similarly, 3M+7W=10......(2)
Solve both equations, (4M+6W)*8=(3M+7W)*10, i.e M/W=11/1
According to Qusetion.
Same work done by 10 Women.
(3M+7W)*10=10W * D.
Now put the values of M & W.
(3*11+7*1)*10=10 * 1 D.
33+7=D , i.e = 40.
4 Man & 6 women complete works in 8 days i.e, 4M+6W=8....(1)
Similarly, 3M+7W=10......(2)
Solve both equations, (4M+6W)*8=(3M+7W)*10, i.e M/W=11/1
According to Qusetion.
Same work done by 10 Women.
(3M+7W)*10=10W * D.
Now put the values of M & W.
(3*11+7*1)*10=10 * 1 D.
33+7=D , i.e = 40.
Prasanth said:
9 years ago
4x + 6y = 1/8 and 3x + 7y = 1/10.
How to get x = 11/400 why = 1/400 please explain me.
How to get x = 11/400 why = 1/400 please explain me.
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