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 5 of 11.
Cln reddy said:
9 years ago
Please explain it in units method.
Wasif said:
9 years ago
Why we use days in fraction?
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)
Shyam said:
9 years ago
Hi, Here I'm solving the equation in detail.
4x + 6y = 1/8 --------> equation (1).
3x + 7y = 1/10 -------> equation (2).
Now we need to cancel one term. Choose either x or y. I chose x. So I'll multiply equation 1 with 3 and equation 2 with 4.
(4x + 6y = 1/8) *3
(3x + 7y = 1/10) *4
The new values will be:
12x + 18y= 3/8 ----------> (1)
12x + 28y= 4/10 --------> (2)
Now subtract 1 from 2.
12x - 12x will be 0.
18y - 28y = -10y.
3/8 - 4/10 = -1/40.
So, -10y = -1/40.
y = -1/40/-10
y =1/400
Now Put the value of y in equation 1 or 2. I choose 1.
So, 4x + 6*1/400 = 1/8.
= 4x + 6/400 = 1/8.
= 4x = 1/8 - 6/400.
= 4x = 11/100.
x = 11/100/4.
=11/400.
So x = 11/400 and y= 1/400.
4x + 6y = 1/8 --------> equation (1).
3x + 7y = 1/10 -------> equation (2).
Now we need to cancel one term. Choose either x or y. I chose x. So I'll multiply equation 1 with 3 and equation 2 with 4.
(4x + 6y = 1/8) *3
(3x + 7y = 1/10) *4
The new values will be:
12x + 18y= 3/8 ----------> (1)
12x + 28y= 4/10 --------> (2)
Now subtract 1 from 2.
12x - 12x will be 0.
18y - 28y = -10y.
3/8 - 4/10 = -1/40.
So, -10y = -1/40.
y = -1/40/-10
y =1/400
Now Put the value of y in equation 1 or 2. I choose 1.
So, 4x + 6*1/400 = 1/8.
= 4x + 6/400 = 1/8.
= 4x = 1/8 - 6/400.
= 4x = 11/100.
x = 11/100/4.
=11/400.
So x = 11/400 and y= 1/400.
Ashok said:
9 years ago
Please learn how solve this equations?
Rohit pal said:
10 years ago
Easiest way:
We want only 10 women value right so just take equation like:
4m + 6w = 1/8.....(1) *3.
3m + 7w = 1/10......(2) *4.
We get -10w = 3/8 - 2/5.
Solve w = 1/400.
So 10 women = (1/400*10) = 40.
We want only 10 women value right so just take equation like:
4m + 6w = 1/8.....(1) *3.
3m + 7w = 1/10......(2) *4.
We get -10w = 3/8 - 2/5.
Solve w = 1/400.
So 10 women = (1/400*10) = 40.
Sekhar said:
10 years ago
4 men + 6 women = 8 days.
3 men + 7 women = 10 days.
10 women = ?
8(4 men + 6 women) = 10(3 men + 7 women).
32 men + 48 women = 30 men+70 women.
So 2 men = 22 women. Then 1 man = 11 women.
Now convert men into women. 4 men + 6 women = 8 days.
Now instead of 4 men write 44 women. So 44 women + 6 women = 8 days.
50 women ------- 8 days.
10 women -------- ?
m1 d1 = m2 d2.
50*8 = 10*?
So 10 women can do work in 40 days!
3 men + 7 women = 10 days.
10 women = ?
8(4 men + 6 women) = 10(3 men + 7 women).
32 men + 48 women = 30 men+70 women.
So 2 men = 22 women. Then 1 man = 11 women.
Now convert men into women. 4 men + 6 women = 8 days.
Now instead of 4 men write 44 women. So 44 women + 6 women = 8 days.
50 women ------- 8 days.
10 women -------- ?
m1 d1 = m2 d2.
50*8 = 10*?
So 10 women can do work in 40 days!
Gananathan said:
10 years ago
M = 11 W.
4m+6w = 8 -----> 4*11+6 = 50 (women) = 8 (days) /// assume work =1 /////.
10w = ?
Apply formula: Women 1*day 1/work 1 = Women 2*day 2/work 2.
50*8/1 = 10*d2/1.
50*8/10 = d2.
400/10 = d2.
40/1 = d2.
So women do work for 40 days.
4m+6w = 8 -----> 4*11+6 = 50 (women) = 8 (days) /// assume work =1 /////.
10w = ?
Apply formula: Women 1*day 1/work 1 = Women 2*day 2/work 2.
50*8/1 = 10*d2/1.
50*8/10 = d2.
400/10 = d2.
40/1 = d2.
So women do work for 40 days.
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.
Bhupendra kumbhare said:
1 decade ago
Hello friends.
Can anyone explain if any other examples in which 3 persons like man, woman and boy replacing by other?
Can anyone explain if any other examples in which 3 persons like man, woman and boy replacing by other?
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