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 2 of 11.
Khyati mehta said:
4 years ago
Men=m, Women = w.
4m+6w = 1/8 so 32m + 48w = 1 ---> (1)
3m+7w = 1/10 so 30m + 70w = 1 ---> (2)
Now find the relation between m and w by equating 1 and 2.
We get m=11w.
Now put it in equation 1 we get;
4m+6w.
4*(11w)+6w.
50w complete work in 8 days.
10w complete work in (8*50)/10 = 40 days.
4m+6w = 1/8 so 32m + 48w = 1 ---> (1)
3m+7w = 1/10 so 30m + 70w = 1 ---> (2)
Now find the relation between m and w by equating 1 and 2.
We get m=11w.
Now put it in equation 1 we get;
4m+6w.
4*(11w)+6w.
50w complete work in 8 days.
10w complete work in (8*50)/10 = 40 days.
(7)
Varshini said:
5 years ago
@All.
Please let me know.
How come x=11/400 and y=1/400?
Anybody explain.
Please let me know.
How come x=11/400 and y=1/400?
Anybody explain.
(4)
Jigme said:
5 years ago
Hi,
Could you please show me how did you compute to get x=11/400 & y = 1/400?
Could you please show me how did you compute to get x=11/400 & y = 1/400?
Nayana said:
5 years ago
@All. The Shortcut method:
4m 6w =8days -> 1
3m 7w = 10day -> 2.
(4m+6w)8 = (3m+7w)10
32m+48w = 30m +70w
32m-30m = 70w-48w.
2m = 22w
1m = 11w ---> (3).
Substitute (3) in (1) or(2)
Eq(2)Converting men to women
(3m+7w)10.
((3*11w)+7w)10 = 10x.
40*10 = 10x.
x = 400/10.
x = 40.
Hope it is helpful.
4m 6w =8days -> 1
3m 7w = 10day -> 2.
(4m+6w)8 = (3m+7w)10
32m+48w = 30m +70w
32m-30m = 70w-48w.
2m = 22w
1m = 11w ---> (3).
Substitute (3) in (1) or(2)
Eq(2)Converting men to women
(3m+7w)10.
((3*11w)+7w)10 = 10x.
40*10 = 10x.
x = 400/10.
x = 40.
Hope it is helpful.
(18)
Priya said:
6 years ago
I cannot understand this equation.
4x+6y=1/8.
3x+7y=1/10.
Please explain.
4x+6y=1/8.
3x+7y=1/10.
Please explain.
Harpreet said:
6 years ago
4 x+6y = 1/8 (I)
3x+7y=1/10.
32x+48y=1....(1)
30x+70y=1....(2)
2x-22y=0
X=11y
4*11y + 6y = 1/8
10y = 1/40.
3x+7y=1/10.
32x+48y=1....(1)
30x+70y=1....(2)
2x-22y=0
X=11y
4*11y + 6y = 1/8
10y = 1/40.
Kermiki Bang said:
6 years ago
Then, 4x + 6y =1/8 and 3x + 7y =1/10.
Solving the two equations,
We get: x = 11/400, y =1/400
Can someone help me with this?
Solving the two equations,
We get: x = 11/400, y =1/400
Can someone help me with this?
Eno said:
6 years ago
Please, we have been using 1/n for 1 day's work. How come we are now saying that let 1 man's day be x and 4 days be 4x?
Or are we trying to say we have to cram how each examples are used and not to go by the 1/n always?
Or are we trying to say we have to cram how each examples are used and not to go by the 1/n always?
Santosh K said:
6 years ago
4M+6W=8.
3M+7W=10.
10W=?.
1day work of 4M+6W=1/8,
3M+7W=1/10.
8(4M+6W) = 1.
10(3M+7W) = 1.
Now equate both equations:
32M + 48W = 30M + 70W.
32M - 30M = 70W - 48W.
2M = 22W.
1M = 11W--->3.
Substitute equation 3 in 1.
4 * 11W + 6W = 1/8.
44W + 6W = 1/8,
50W = 1/8; 10W=?
10 * 1/8 * 50 = 1/40.
Therefore 10 women can complete the work in 40days.
3M+7W=10.
10W=?.
1day work of 4M+6W=1/8,
3M+7W=1/10.
8(4M+6W) = 1.
10(3M+7W) = 1.
Now equate both equations:
32M + 48W = 30M + 70W.
32M - 30M = 70W - 48W.
2M = 22W.
1M = 11W--->3.
Substitute equation 3 in 1.
4 * 11W + 6W = 1/8.
44W + 6W = 1/8,
50W = 1/8; 10W=?
10 * 1/8 * 50 = 1/40.
Therefore 10 women can complete the work in 40days.
Sasi Lawandi said:
6 years ago
How to get 1 woman's day work = 1/400.
Can you please explain it clearly? Can't understand about it.
Can you please explain it clearly? Can't understand about it.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers