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# Aptitude - Time and Work - 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

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

 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.