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 3 of 11.
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.
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.
Mk sai gopala krishna said:
9 years ago
LCM METHOD:
LCM8, 10) = 40 units.
4M + 6W -> 8 days -> 5 units per day.
3M + 7W -> 10days -> 4 units per day.
3 * (4M + 6W) = 5 units per day -----> (1).
4 * (3M + 7W) = 4 units per day -----> (2).
Solving eq (1) and eq (2);
We get 10W =1 unit per day.
Therefore, 40 units/(1 unit per day) = 40 days.
LCM8, 10) = 40 units.
4M + 6W -> 8 days -> 5 units per day.
3M + 7W -> 10days -> 4 units per day.
3 * (4M + 6W) = 5 units per day -----> (1).
4 * (3M + 7W) = 4 units per day -----> (2).
Solving eq (1) and eq (2);
We get 10W =1 unit per day.
Therefore, 40 units/(1 unit per day) = 40 days.
(3)
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)
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.
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)
Sharad said:
1 decade ago
@Manu.
4x+6y = 1/8.............1.
3x+7y = 1/10............2.
For canceling term x we can multiply 1 by 3 and equation 2 by 4. Then we got:
12x+18y = 3/4...........3.
12x+28y = 4/10.........4.
Then subtract equation 4 by equation 3.
y = 1/100.
Put y in equation 1.
y = 1/400.
4x+6y = 1/8.............1.
3x+7y = 1/10............2.
For canceling term x we can multiply 1 by 3 and equation 2 by 4. Then we got:
12x+18y = 3/4...........3.
12x+28y = 4/10.........4.
Then subtract equation 4 by equation 3.
y = 1/100.
Put y in equation 1.
y = 1/400.
Nagu said:
2 decades ago
Hi Shehina,
10 women's 1 day's work = 1/40 means they will take 40 days to complete a work
for example a man can do a work in 10 days means we will take his one day work as 1/10
like that one day work is 1/40 they should complete it in 40 days.
i think you understood..
10 women's 1 day's work = 1/40 means they will take 40 days to complete a work
for example a man can do a work in 10 days means we will take his one day work as 1/10
like that one day work is 1/40 they should complete it in 40 days.
i think you understood..
Abdul said:
1 decade ago
How can this problem be solved if the supporting statement isn't given, that is "3 men and 7 women complete work in 10 days. ".
What if the question is "4 men and 6 women can complete the work in 8 days then how many days it will take for 10 women to finish the work?".
What if the question is "4 men and 6 women can complete the work in 8 days then how many days it will take for 10 women to finish the work?".
Avinash Singh said:
1 decade ago
I have a best answer:
4M + 6W = 8 days.
32M + 48W = 1 day --- 1.
3M + 7W = 10 days.
30M + 70W = 1 day ----2.
From 1 and 2, we get.
2M = 22W.
1M = 11W.
and also 3M = 33W.
Subs in 3M + 7W = 10 days.
we get, 33W + 7W = 10 days.
40W = 10 days.
Then,
10W = 40 days.
4M + 6W = 8 days.
32M + 48W = 1 day --- 1.
3M + 7W = 10 days.
30M + 70W = 1 day ----2.
From 1 and 2, we get.
2M = 22W.
1M = 11W.
and also 3M = 33W.
Subs in 3M + 7W = 10 days.
we get, 33W + 7W = 10 days.
40W = 10 days.
Then,
10W = 40 days.
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