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 6 of 11.
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.
Saurabh said:
1 decade ago
@Narasingarao please explain your method?
Deepika said:
1 decade ago
Please explain how to solve these two equations? Explain with it in step by step?
Raman said:
1 decade ago
Can anyone please solve this by LCM method?
Priya said:
1 decade ago
Can any one solve this by work equivalence (man days) or by normal equation method?
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.
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?
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.
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.
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!
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers