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.
CHAN said:
1 decade ago
Hi All, Let me explain.
8 * 4x + 6y = 1 ( multiplied by 8)
10* 3x + 7y = 1 (multiplied by 10)
32x + 48y = 1 --(1) ----> (1) * 30
30x + 70y = 1 --(2) ----> (2) * 32
Hence
960x+1440y=30/8 (since 30*32 =960)
960x+2240y=32/10 (same)
----------------
800y=1/400
y = 1/400
By substituting the value of y Eqn (1)
You will get 4x+6/400=1/8
x=11/400
REST ARE IN ABOVE WEBSITE'S EXPLANATION.
8 * 4x + 6y = 1 ( multiplied by 8)
10* 3x + 7y = 1 (multiplied by 10)
32x + 48y = 1 --(1) ----> (1) * 30
30x + 70y = 1 --(2) ----> (2) * 32
Hence
960x+1440y=30/8 (since 30*32 =960)
960x+2240y=32/10 (same)
----------------
800y=1/400
y = 1/400
By substituting the value of y Eqn (1)
You will get 4x+6/400=1/8
x=11/400
REST ARE IN ABOVE WEBSITE'S EXPLANATION.
Rishabh nagpal said:
1 decade ago
Don't make it complex, it is so easy.
As given,
4 men and 6 women can do work in 8 days so,
Work done by 4M+6W in 1 day is 1/8.
-> 4M+6W=1/8 -------- (1).
And, work done by 3M and 7W in 1 day is 1/10.
-> 3M+7W=1/10 -------- (2).
Now solve these 2 equations,
Equation (1) *3 different equation (2) *4 to make M equal to solve you will get
10W=1/40.
It means 10W will done work in 40 days.
As given,
4 men and 6 women can do work in 8 days so,
Work done by 4M+6W in 1 day is 1/8.
-> 4M+6W=1/8 -------- (1).
And, work done by 3M and 7W in 1 day is 1/10.
-> 3M+7W=1/10 -------- (2).
Now solve these 2 equations,
Equation (1) *3 different equation (2) *4 to make M equal to solve you will get
10W=1/40.
It means 10W will done work in 40 days.
Hemaharshini T said:
2 years ago
4m + 6w = 8 days.
3m + 7w = 10 days.
10w = Tdays.
4m + 6w = 1/8days --->(1)
3m + 7w = 1/10days ----> (2)
10w = Tdays ----> (3)
1st step is to find the value of m and w with (1)&(2)
32m + 48w = 30m + 70w.
32m - 30m = 70w - 48w.
m/w = 22/2.
m = 11 w = 1.
By product method;
(2)=(3).. you can also take (1) instead of (2).
mw*T = mw*T.
[3(11) + 7(1)] * 10 = 10 * T.
400 = 10T.
T = 40days.
3m + 7w = 10 days.
10w = Tdays.
4m + 6w = 1/8days --->(1)
3m + 7w = 1/10days ----> (2)
10w = Tdays ----> (3)
1st step is to find the value of m and w with (1)&(2)
32m + 48w = 30m + 70w.
32m - 30m = 70w - 48w.
m/w = 22/2.
m = 11 w = 1.
By product method;
(2)=(3).. you can also take (1) instead of (2).
mw*T = mw*T.
[3(11) + 7(1)] * 10 = 10 * T.
400 = 10T.
T = 40days.
(12)
Adnan said:
1 decade ago
One day work by 4M + 6W = 1\8 --- (1).
One day work by 3M + 7W = 1\10 --- (2).
10W = ?
Multiply (1) by 3 and (2) by 4
12M + 18W = 3/8 => 12M = 3/8 - 18W --- (3).
12M + 28W = 4/10 => 12M + 28W = 2/5 --- (4).
Putting 12M value from (3) to (4)
3/18 - 18W + 28W = 2/5.
10W = 2/5 - 3/8.
10W = 1/40.
Since one day work by 10W = 1/40.
Hence, 10 women will complete the work in 40 days.
One day work by 3M + 7W = 1\10 --- (2).
10W = ?
Multiply (1) by 3 and (2) by 4
12M + 18W = 3/8 => 12M = 3/8 - 18W --- (3).
12M + 28W = 4/10 => 12M + 28W = 2/5 --- (4).
Putting 12M value from (3) to (4)
3/18 - 18W + 28W = 2/5.
10W = 2/5 - 3/8.
10W = 1/40.
Since one day work by 10W = 1/40.
Hence, 10 women will complete the work in 40 days.
Karthikeyan said:
4 years ago
4x+6y=1/8 ------> (1)
3x+7y=1/10 ----> (2).
Eqn 1 divided by 3.
Eqn 2 divided by 4.
12x+18y=3/8----(3).
12x+28y=4/10---(4).
-------------------------
-10y=1/40.
Y=1/40*10.
y=1/400.
Y value substitute in eqn (1).
4x+6(1/400) =1/8,
4x+6/400=1/8,
4x=1/8-6/400,
4x=44/400,
X=44/400*4,
X=11/400.
1 women complete a work=1/400*10.
1/40.
Hence, 10 women
3x+7y=1/10 ----> (2).
Eqn 1 divided by 3.
Eqn 2 divided by 4.
12x+18y=3/8----(3).
12x+28y=4/10---(4).
-------------------------
-10y=1/40.
Y=1/40*10.
y=1/400.
Y value substitute in eqn (1).
4x+6(1/400) =1/8,
4x+6/400=1/8,
4x=1/8-6/400,
4x=44/400,
X=44/400*4,
X=11/400.
1 women complete a work=1/400*10.
1/40.
Hence, 10 women
(11)
Adithi said:
1 decade ago
4 men + 6 Women completes 1/8 of the work
i.e., 4m + 6w = 1/8 --- equation I
3 men + 7women completes 1/10 of the work
i.e ., 3m + 7w = 1/10 --- equation II
Multiply Equation I*3 and Equation II * 4 we get
12m + 18w =3/8
12m + 28w =4/10 ( now subtract)
------------------------------
0 + 10 w = 3/8 -4/10 = 1/40
------------------------------
hence 10 women takes 40 days !
i.e., 4m + 6w = 1/8 --- equation I
3 men + 7women completes 1/10 of the work
i.e ., 3m + 7w = 1/10 --- equation II
Multiply Equation I*3 and Equation II * 4 we get
12m + 18w =3/8
12m + 28w =4/10 ( now subtract)
------------------------------
0 + 10 w = 3/8 -4/10 = 1/40
------------------------------
hence 10 women takes 40 days !
Kishor said:
2 decades ago
If 4 men and 6 women can complete a work in 8 days
4 men and 1 women can complete a work in=6* 8 days
1 men and 1 women can complete a work in=4*6* 8 days
1 men and 7 women can complete a work in=4*6*8/7 days
3 men and 7 women can complete a work in=4*6*8/(3*7) days
=64/7days
which is not 10 days as given in the question
4 men and 1 women can complete a work in=6* 8 days
1 men and 1 women can complete a work in=4*6* 8 days
1 men and 7 women can complete a work in=4*6*8/7 days
3 men and 7 women can complete a work in=4*6*8/(3*7) days
=64/7days
which is not 10 days as given in the question
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.
Likitha Ganta said:
2 years ago
Given:
4m + 6w = 8 days ---> (1)
3m + 7w = 10 days ---> (2)
Total work = Efficiency × days.
By solving equation (1) and (2).
(4m + 6w) × 8 = (3m + 7w) × 10.
16m + 24w = 15m + 35w,
16m - 15m = 35w - 24w,
m = 11w.
Total work = (4 × 11 + 6) × 8.
Total work = 400 unit.
Time taken by 10 women = 400/10.
Time taken by 10 women = 40 days.
4m + 6w = 8 days ---> (1)
3m + 7w = 10 days ---> (2)
Total work = Efficiency × days.
By solving equation (1) and (2).
(4m + 6w) × 8 = (3m + 7w) × 10.
16m + 24w = 15m + 35w,
16m - 15m = 35w - 24w,
m = 11w.
Total work = (4 × 11 + 6) × 8.
Total work = 400 unit.
Time taken by 10 women = 400/10.
Time taken by 10 women = 40 days.
(17)
Kavya said:
10 years ago
Given 4m 6w = 8 days.
3m+7w = 10 days.
Next step: (4m+6w) 8 days = 32m+48w.
(3m+7w) 10 days = 30m+70w.
Next step: 32m+48w = 30m+70w.
32m-30m = 70w-48w.
2m = 22w.
2(1m = 11w) therefore 1m = 11w.
Take any relation given in question 4m+6w = 8 days.
4(11)+6w = 44+6 = 50w.
Finally 50w-8 days.
So, 50w*8 days/10w = 40 days.
3m+7w = 10 days.
Next step: (4m+6w) 8 days = 32m+48w.
(3m+7w) 10 days = 30m+70w.
Next step: 32m+48w = 30m+70w.
32m-30m = 70w-48w.
2m = 22w.
2(1m = 11w) therefore 1m = 11w.
Take any relation given in question 4m+6w = 8 days.
4(11)+6w = 44+6 = 50w.
Finally 50w-8 days.
So, 50w*8 days/10w = 40 days.
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