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Aptitude - Time and Work - Discussion

@ : Home > Aptitude > Time and Work > General Questions - Discussion

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"No one is as deaf as the man who will not listen."
- (Proverb)
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?

[A]. 35[B]. 40
[C]. 45[D]. 50

Answer: Option A

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.
Kishor said: (Tue, Jun 1, 2010 12:32:14 PM)    
 
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
Shehina said: (Wed, Jul 7, 2010 01:18:25 PM)    
 
How 1/40 become 40?
Nagu said: (Thu, Jul 8, 2010 05:30:55 AM)    
 
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..
Nagu said: (Thu, Jul 8, 2010 05:36:26 AM)    
 
Hi Kishor,

you are wrong. This question is correct and the explanation is also correct.
Please refer once again.
Shehina said: (Thu, Jul 8, 2010 01:09:07 PM)    
 
Hi Nagu Thank you
Sneha said: (Sun, Jul 11, 2010 12:25:13 AM)    
 
Please help in solving (i) and (ii).
Nagu said: (Mon, Jul 12, 2010 02:44:19 AM)    
 
You are welcome. Shehina.
Nagu said: (Mon, Jul 12, 2010 02:48:15 AM)    
 
Hi Bhuvi,

if A takes 10 days to complete a work means
A's one day work is 1/10

Same way 10 women's one day work is 1/40 means they will take 40 days to complete the work.

I think you got my point.

Have a nice day
Poonam said: (Thu, Jul 15, 2010 07:30:31 AM)    
 
Hii,

Can you please explain.

How comes.

4x + 6y = 1/8 and 3x + 7y = 1/10.

X = 11/400, why = 1/400.
Vass said: (Mon, Jul 26, 2010 09:58:55 AM)    
 
Hi all,
can you please explain

4x + 6y = 1/8 --(1)
3x + 7y = 1/10 --(2)

From (1) and (2) How it comes
x = 11/400 , y = 1/400
Chan said: (Thu, Sep 9, 2010 06:08:34 AM)    
 
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.
Aravindhan said: (Thu, Sep 9, 2010 08:17:27 AM)    
 
4m+6w=1/8 --(1)

3m+7w=1/10 --(2)

Solve this two we get 10w = 1/40;

So the answer is 40 days.
Karunakaran said: (Mon, Sep 20, 2010 06:50:25 AM)    
 
Hi Poonam,

Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
So 4 man's 1 day's work= 4x and 6 woman's 1 day's work = 6y.
Working together overall work will done in 8 days.
So working together overall work will done in 1 day = 1/8

i.e 4x + 6y = 1/8

So 3 man's 1 day's work= 3x and 7 woman's 1 day's work = 7y.
Working together overall work will done in 10 days.
So working together overall work will done in 1 day = 1/10

i.e 3x + 7y = 1/10

By solving
4x + 6y = 1/8 * 3
3x + 7y = 1/10 * 4
------------------------
12x + 18y = 3/8
12x + 28y =4/10

So 10y = 1/40

y= 1/400
x=11/400
Vijaya said: (Mon, Nov 29, 2010 01:23:21 AM)    
 
Ok I can understand this problem but I want any shortcut method for doing the problem so fast. Because time is precious in competative exams. Dng all these caluclation is waste of time so I sortcut to this one so plzz any one help me.
Priya said: (Thu, Dec 9, 2010 03:02:32 AM)    
 
Can any one say shortcut to this problem.

Thank you in advance.
Saleem said: (Thu, Dec 9, 2010 07:36:08 AM)    
 
how it possible 4x+6/400=1/8

x=11/400

Mr.chan ,could u pls explain
S.P.Velu said: (Fri, Dec 17, 2010 12:59:58 AM)    
 
Can anyone to solve those two equation in step by step?
Ashish said: (Sun, Dec 26, 2010 09:21:22 AM)    
 
Hi all,
(4m+6w)8 = (3m+7w)10...........eq.(1)
2m = 22w
M = 11W
NOW, we put the value of M in eq. 1
(44+6)8= 10X
X = 400/10
X = 40 Ans.
Jyothi said: (Tue, Jan 25, 2011 09:07:48 AM)    
 
Hi ashish. Thanks.
Ashish said: (Sun, Jan 30, 2011 12:40:09 PM)    
 
Hello, Jyothi. It's my pleasure.
Muz said: (Fri, Mar 4, 2011 07:36:56 AM)    
 
Anyone plz tell me, how x in 4x + 6 * 1/400 = 1/8 comes out as "11/400".. i get only "11"
Mani said: (Mon, Apr 11, 2011 10:05:46 AM)    
 
No need to find x value for this question. So don't worry.

We need only Y.

When 10 women works 10*(1/400) becomes 1/40.

So they can complete the work in 40 days.
Mani said: (Sat, Jun 4, 2011 10:02:07 AM)    
 
Thanks evry1 for helping.
Kaushalay said: (Sun, Jul 31, 2011 06:33:16 AM)    
 
Hi Ashish ! Could you please explain the below mentioned part once again?

NOW, we put the value of M in eq. 1
(44+6)8= 10X ( where did we get 10X? )
X = 400/10
X = 40 Ans.
Seshapriya said: (Sat, Sep 3, 2011 01:58:22 AM)    
 
Hi Kaushalay..

why? to confuse with x,

8(44w+6w)=10w
8*50w=10w
when you cancel 50w and 10 w and make it to 8*5

Answer comes as 40.. :)
Yyyy said: (Fri, Sep 9, 2011 03:11:37 PM)    
 
Thanks asish.
Nira said: (Sat, Nov 5, 2011 04:44:54 AM)    
 
How we get 8*50w=10w?
Kalyan said: (Mon, Nov 28, 2011 01:04:18 PM)    
 
Hi can any body say how 11/400 is possible?
Prasant said: (Thu, Dec 8, 2011 03:54:51 PM)    
 
4x+6y = 1/8
=> 4x+6/400 = 1/8 ...as x=1/400
=> 4x = 1/8-6/400
=> 4x = 11/100
=> x = 11/400
Katam Brahmareddy said: (Sat, Feb 11, 2012 08:23:05 PM)    
 
4x + 6y =1/8*3 and 3x + 7y =1/10*4
12x+18y=3/8 and 12x+28y=2/5
subtract them
12x+18y-3/8-12x-28y+2/5=0
ofter
-10y=-3/8+2/5
=-15+16/40
=1/40 (it is work done for day with ten womens)
-10y=1/40*10
=1/40
answer is 40 days..
Adithi said: (Wed, May 9, 2012 01:10:21 AM)    
 
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 !
Mohamed Saleem said: (Thu, Jun 21, 2012 08:22:59 AM)    
 
Let us sahre CHAN HOW 1 BECOMES 30/8

32x + 48y = 1 --(1) ----> (1) * 30
960x+1440y=30/8 (since 30*32 =960)
Srinivas said: (Fri, Jul 20, 2012 08:36:34 PM)    
 
4x+6y=1/8.

3x+7y=1/10.

Here why you are taking days 1/10 and 1/8?

You mean members=1/days ?
Ami said: (Sat, Sep 1, 2012 04:11:20 PM)    
 
4x+6y=1/8 ----(1)
3x+7y=1/10 ----(2)
now,multiply equation 1 with 3 and equ.2 with 4

12x+18y=3/8
12x+28y=2/5
- - -
-------------
-10y=-1/40
10y=1/40 so, 40 become ans
Afia Sharmin said: (Sun, Mar 3, 2013 08:58:39 PM)    
 
Answer for: 6 men and 8 women can do a work in 18 days. How many days will it require to complete the whole work if 3 men and 5 women work together?
Jayalakshmi said: (Wed, Mar 20, 2013 04:10:43 PM)    
 
Can you please explain.

How comes.

4x + 6y = 1/8 and 3x + 7y = 1/10.

X = 11/400, y = 1/400.

In easy method above mentioned methods are very difficult to understand.
Syed said: (Thu, May 2, 2013 11:34:48 PM)    
 
4M+6W=8 ----1
3M+7W=10 ----2
10W = ? ----3

8*4M+8*6w = 10*3M+10*7W
32M+48W = 30M+70W
32M-30M = 70W-48W
2M = 22W
1M = 11W

PUT IN EQ-2.

33W+7W = 10
40W = 10

40*10= 10*?
?= 40.
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