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"We cannot solve our problems with the same thinking we used when we created them."
- Albert Einstein
5. 

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

[A]. Rs. 375[B]. Rs. 400
[C]. Rs. 600[D]. Rs. 800

Answer: Option

Explanation:

C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 1 .
3 6 8 3 24 24

A's wages : B's wages : C's wages = 1 : 1 : 1 = 4 : 3 : 1.
6 8 24

C's share (for 3 days) = Rs. 3 x 1 x 3200 = Rs. 400.
24


Vishnu said: (Fri, Jul 30, 2010 02:49:29 PM)    
 
How did you calculated the wages ratio?

Dhanush said: (Fri, Aug 13, 2010 01:43:34 AM)    
 
A's wages : B's wages : C's wages =
=A's 1 day's work:B's 1 day's work:C's 1 day's work
=1/6 : 1/8 : 1/24
=4 : 3 : 1.(multiple by 24..:1/6*24 : 1/8*24 : 1/24*24)

Shaju said: (Sat, Sep 11, 2010 09:37:36 AM)    
 
Can anyone help me with the last step?

If we need to calculate (3 x 1/24 x 3200) then what was the use of finding the ratio.

Chethu said: (Thu, Sep 30, 2010 04:04:58 PM)    
 
Good Question Shaju,

With the ratio you would get to know the share of A, B and C.

A:B:C = 4:3:1

So the wages can be calculated easily (4*400:3*400:1*400) which is equal to (1600:1200:400) if we add it, it would give us the total amount if 3200.

Shyam said: (Sun, Oct 3, 2010 12:58:02 PM)    
 
It is simple, A's share is (4/8)*3200

B's share is (3/8)*3200

C's share is (1/8)*3200

Harish said: (Mon, Oct 25, 2010 02:09:10 AM)    
 
1/6:1/8:1/24==4:3:1 how its came give me the logic

Ravi said: (Thu, Nov 4, 2010 02:17:12 AM)    
 
The highest among the denominators is 24..so multiply the ratios by 24..
24/6:24/8:24/24
4:3:1

Sandy said: (Wed, Nov 10, 2010 06:00:24 AM)    
 
From where did 1/24 come?

Sandy said: (Wed, Nov 17, 2010 12:19:23 PM)    
 
@Sandy that is c's one day work.. ok.... @dhanush has clearly explained...

Vinita said: (Wed, Dec 8, 2010 05:14:23 AM)    
 
Sir pls explain me this step 1/3-7/24= 1/24
How is it?

Guna said: (Fri, Dec 10, 2010 05:25:31 AM)    
 
@Vinita

Its simple L.C.M
24-21/24*3=3/72=1/24...

Siddharth said: (Fri, Jan 21, 2011 02:57:26 AM)    
 
IN 3*1/24*3200...FROM WHERE 3 IS COME

Sahil Kapoor said: (Fri, Jan 21, 2011 01:35:54 PM)    
 
I agree with siddharth, either the 3 should be removed or they should mention that A,B,C charge Rs 3200 "PER DAY"

Aatif said: (Wed, Feb 2, 2011 05:10:55 AM)    
 
1/24 is the work done by C in one day. For three days "3" is used.

Jagjeet said: (Thu, Feb 10, 2011 01:55:18 PM)    
 
I agree in question they should mention 3200 per day.

Shashank A said: (Tue, Apr 19, 2011 05:27:53 AM)    
 
The last step of calculating 3*1/24*3200 is wrong as C would alone earn 3200 that way at the end of 24 days..:).The idea should be 1 part of 8 parts earned amongst A ,B and C is earned by C.Hence its 400....

Vandhanasuberwal said: (Sat, May 7, 2011 09:51:03 AM)    
 
We can solve it as 1/8 multiply 3200.

Jeevana said: (Thu, May 12, 2011 02:37:14 AM)    
 
Can anyone help me with the first step?
why do like that only

Krishna said: (Wed, May 18, 2011 07:20:34 PM)    
 
See jeevana ,

a,b,c can complete work in 3 days
so a,b,c can complete a work in 1 days=1/3...........(1)
a and b can complete work in 1 day=1/6+1/8=7/24works.....(2)

c's one day works =a's and b's one day works is subtracted from a b c one days work that is(1-2)

So 1/24 works done by c
c 's 3 days work is 3/24=1/8
so c's share is = 3200/8=400

Anil said: (Wed, Jun 8, 2011 05:52:38 AM)    
 
Wages is necessary for this question ?

Kiran said: (Fri, Jun 17, 2011 08:10:04 AM)    
 
In the end, why we have multiplied 3200 with C's 3 day work whereas it is the salary of both A and B ?

Satheesh said: (Fri, Jun 24, 2011 09:58:38 AM)    
 
What is the need to multiply 3 in last step = 3*1/24*3200 (since we already subtracted (1/3) ?

Balaram said: (Tue, Jun 28, 2011 04:02:53 AM)    
 
Hi Satheesh.

From the step 1/c+1/6+1/8=1/3, you can get the work that can be done by the c in one day.

So, the part of work that is contributed by c in 3 days, is 3*work done in one day. Hence, the step 3*1/24 is the total work done by c in 3 days. Now, the wage that has to come to c is just multiplication of his work to the total wage for the whole work.

Hope, you would get the logic now.

Ramya said: (Wed, Jul 6, 2011 03:42:27 AM)    
 
Why we have to multiply with 24 to get the ratio as 4:3:1?

Venky said: (Tue, Jul 19, 2011 09:53:09 PM)    
 
No need to calculate wages ratios.

C's part of work for 1 day is 1/24. So the contribution for 3 days is 3/24. As per contribution his share will be 3/24*3200=400.

Arnab said: (Fri, Jul 22, 2011 12:04:56 AM)    
 
A lot simpler method --
A does 1/6 in 1 day.. B does 1/8 in one day..So they both do (1/6+1/8=7/24)in 1 day.. Hence they will finish the work in 24/7 days..
they get paid 3200 for 24/7 units of work..hence they'll be paid 3200*7/24 for 1 units of work..which is equal to 2800/3..
now A and B were finishing it in 24/7 days but on C's help they do it in 3 days..hence they are saved 24/7-3 units of work which is equal to 3/7 units of works and C will be paid for this..now 1 unit's pay was 2800/3..hence 3/7 units pay is (2800*3)/(3*7) = 400!!

Anandhakumar said: (Fri, Jul 29, 2011 03:07:54 PM)    
 
Let us take total work as the L.C.M of 6,8,3 i.e 24.

So A's per day work is 24/6=4, B's =24/8=3, a+b+c's=24/3=8.

So C's Ability is= 8-(4+3)=1 ie(a+b+c-a-b).

So the amount has to be divided into 4:3:1

So C's share is (1/8)*3200=400

Preeti2009_Delhi@Yahoo.Com said: (Tue, Aug 2, 2011 09:49:24 PM)    
 
If both a and b work together on the single piece than in how many days they will complete their work and how?

Pradeep Koney said: (Fri, Aug 5, 2011 07:50:03 PM)    
 
No need to do all this hard work dudes......

A works 6days and gets 3200,i.e.,for one day=3200/6=1600/3

B works 8days and gets 3200,i.e.,for one day=3200/8=400

A&B&C worked for 3days

That is A gets 3*1600/3 for 3days=1600

B gets 3*400 for 3days=1200

A+B wages=1600+1200=2800

C wages=3200-2800=400

Kavitha said: (Tue, Aug 9, 2011 10:31:03 PM)    
 
One day work of A+B = (1/6)+(1/8) = 7/24
3 days work of A+B = (7/24)*3 = 7/8

Total amount=3200
3 days work of A+B with the amount 3200 = (7/8)*3200 = 2800

(A+B)'s share is 2800
C's share is = 3200-2800 = 400.

Kartik M. said: (Tue, Aug 9, 2011 10:48:00 PM)    
 
@pradeep koney

Your method is nice.

Aitya said: (Thu, Aug 18, 2011 12:36:30 AM)    
 
A very simple method is :-

The total complition money of the job is 3200.

A completes the job in 6 day's..

So his per day fees is 3200/6=533.33

B completes the job in 8 day's..

So his per day fees is 3200/8=400

a,b & c complets the job in 3days..

(3*A'per day fees + 3*B'per day fees )=3200

(3*533.33+3*400+3*c'per day fees)=3200

3*c'per day fees=3200-(1600+1200)
=3200-2800

C' full fee of the work is=400

Ramkumar said: (Sun, Sep 18, 2011 05:08:46 PM)    
 
Pradeep Koney method is easily understood.

Naman said: (Thu, Oct 6, 2011 01:42:56 PM)    
 
This is very easy to understand .....

in last line....
there wages is 4:3:1 ....so wage of c is..
===1*3200/(4+3+1)====3200/8===400

Parvatraj said: (Wed, Oct 12, 2011 12:54:59 PM)    
 
According the quetion,

A can do in 1 day 1/6 work. in 3 days 3/6 work.
B can do in 1 day 1/8 work. in 3 days 3/8 work.
So C has done (1-(3/6+3/8)) work. That is 1/8 work.
So he has to get 1/3 of total amount. i.e, 3200/8=400 rs.

But the calculation they have given is wrong. but answer is right unfortunately.

Sekhar said: (Sun, Nov 6, 2011 11:40:26 AM)    
 
Pradeep koni explains very very good.

Sri said: (Mon, Nov 14, 2011 07:25:35 PM)    
 
@Pradeep koney.

Thanks Pradeep your method is easy.

Ess said: (Thu, Dec 22, 2011 02:08:47 AM)    
 
Why you are multiplying 3200 in c's 3 day work ?

Prasad said: (Sun, Feb 5, 2012 11:59:58 AM)    
 
C's share is=[1/(4+3+1)]*3200;
Is it ok to solve by this method

Tabish said: (Sat, Feb 18, 2012 07:23:35 AM)    
 
Why multiplied by 24 to the A,B,C's one day work as it is the work completed by C in one day?

Shro said: (Mon, Feb 20, 2012 10:22:54 PM)    
 
Why to subtract C's work from (A and B) in 1st step?

Adithya said: (Mon, Mar 26, 2012 08:15:01 PM)    
 
A's wages : B's wages : C's wages = 4 : 3 : 1.
so
total wages(4+3+1)
3200/8 =400
for A = 400*4 = 1600....B = 3*400=1200.
for C =400

Muhammad Akmal said: (Mon, May 28, 2012 11:11:09 PM)    
 
Please explain that how (1/3 -7/24) = C's one day's work?
What is the logic?

Chandana said: (Mon, Jul 23, 2012 03:20:18 PM)    
 
C's one days work is 1/3.

A and B's one day work is 1/6 and 1/8 respectively.

Now to know the amount of work done by C, we have to calculate the work done by A and B, i.e.,

1/6 + 1/8= 7/24, now we have to calculate how much work C alone has alone done so, 1/3 - 7/24 take LMC you will get 8-7 / 24 you will get 1/24

And now 3*1/2*3200 = 400.

Srisha said: (Mon, Jul 30, 2012 03:55:16 PM)    
 
A very simple method is :

The total completion money of the job is 3200.

A completes the job in 6 day's.

So his per day fees is 3200/6=533.33

B completes the job in 8 day's.

So his per day fees is 3200/8=400

a,b & c completes the job in 3days.

(3*A'per day fees + 3*B'per day fees )=3200

(3*533.33+3*400+3*c'per day fees)=3200

3*c'per day fees=3200-(1600+1200)=3200-2800

C's full fee of the work is = 400

Rahul Chourasia said: (Sun, Aug 19, 2012 01:23:01 AM)    
 
Wages ratio is not important short method is
c work in 3 days
a & b money =3200
c work ratio is 1/24 by method (1/3-(1/6+1/8))
last calculation is 3*1/24*3200
ans is 400

Ayan Sett said: (Mon, Sep 3, 2012 09:43:44 PM)    
 
@pradeep koney

thanks..

Bitu said: (Tue, Feb 12, 2013 12:42:01 PM)    
 
According to the question 3200.00 was given to be the amount taken by both A & B collectively for completing the work together. Then how could it be treated as the total amount obtained by the three to be distributed among.

Ranjeet Singh said: (Tue, Mar 12, 2013 09:58:10 AM)    
 
Because lastly A, B, C are working together for completing the work and we all know that no one work for free of cost so we will have to involve C in 3200 distribution. Initially only A and B working that's why 3200 distributed between A and B.

Maruthupandian said: (Thu, Mar 28, 2013 11:51:31 AM)    
 
@Arnab.

In your explanation how do you do this (24/7-3) for calculating days of C alone?

won't it be (3-24/7) ?

because (A+B+C)-(A+B) = C.

Somesh said: (Fri, Apr 12, 2013 01:32:12 PM)    
 
If one person A takes "x" days to complete a work alone and another person B takes "y" days to complete the same work alone, then the number days both A and B take working together is : x y/ (x + y).

I hope you will surely understand what you have to do.

Sangeethavimalraj said: (Tue, Apr 23, 2013 09:52:29 AM)    
 
Total amount is 3200,
Ratio 4:3:1,

4*x+3*x+1*x = 3200.

8x = 3200.

x = 400.

Vinod Anand said: (Wed, May 22, 2013 04:47:00 PM)    
 
If A=1/6 ,B=1/8 and A+B+C = 1/3 ----(1).

A+B = 1/6 + 1/8 = 7/24.

Put the value of A+B in Eq.(1).

Than C = 1/8 - 7/24 = 1/24.

The Value of C' is 1/24.

Now the Ratio of A:B:C =1/6:1/8:1/24 (The L.C.M Of 1/6+1/8+1/24 is 24)
A:B:C =4:3:1.

Than Amt.is Rs.3200.

So the C' will be paid = 3200 X 1/8.

= Rs. 400.00 Answer.

Hema said: (Tue, Jul 2, 2013 12:38:00 PM)    
 
Yes, I agree that amount 3200 in the question is not clearly mentioned. Is that for per day?

B.Indirasouajyaan said: (Mon, Jul 8, 2013 11:37:23 PM)    
 
The ratio obtained is 4:3:1. Then why did you multiply 3*1/24*3200? we should not multiply with 1?

Dave said: (Thu, Jul 11, 2013 12:21:51 AM)    
 
Actually, havent got the ratios we could have also found proportionate share of their wages as follows:

4+3+1 = 8.

Hence c's wage would've been 1/8*3200 = 400.

Seema Duhan said: (Sun, Jul 14, 2013 11:33:07 AM)    
 
take LCM of A and B work, then get:

A+B=7/24.

WHERE:
A+B+C = 1/3 (given).

So 7/24+C=1/3.

C=1/24.

With the ratio you would get to know the share of A, B and C.

Now the Ratio of A:B:C =1/6:1/8:1/24 (The L.C.M Of 1/6+1/8+1/24 is 24)
A:B:C =4:3:1.

So the wages can be calculated easily (4*400:3*400:1*400) which is equal to (1600:1200:400) if we add it, it would give us the total amount if 3200.

It is simple, A's share is (4/8)*3200.
B's share is (3/8)*3200.
C's share is (1/8)*3200 (because 4+3+1=8).

Soumya said: (Sat, Aug 24, 2013 07:58:34 PM)    
 
Can we solve the problem without calculating ratio?

Vikas said: (Wed, Aug 28, 2013 08:31:17 PM)    
 
No need to calculate the ratios its just wast of time.

Prince Dubey said: (Fri, Aug 30, 2013 07:43:53 PM)    
 
A, B, C can complete work in 3 days.

so A, B, C can complete a work in 1 days = 1/3...........(1).

A and B can complete work in 1 day = 1/6+1/8 = 7/24 works.....(2).

C's one day works = A's and B's one day works is subtracted from A B C one days work that is(1-2).

So 1/24 works done by C.

C 's 3 days work is 3/24 = 1/8.

So C's share is = 3200/8 = 400.

Prince Dubey said: (Fri, Aug 30, 2013 07:45:20 PM)    
 
Wages ratio is not important short method is.

C work in 3 days.

A & B money = 3200.

C work ratio is 1/24 by method (1/3- (1/6+1/8) ).

Last calculation is 3*1/24*3200.

Answer is 400.

Karun said: (Tue, Sep 10, 2013 11:50:29 AM)    
 
A efficiency 16.66.

B efficiency 12.50.

So total work of A+B is 29.16 remaining 70.84.

So 70.84/3 = 24(C efficency )

Satyakrishna said: (Mon, Sep 16, 2013 08:59:11 PM)    
 
Is there any shortcut method to find this, by directly substituting the values?

Vinod Rathod said: (Mon, Sep 23, 2013 11:33:27 AM)    
 
Leave every method go for simple method.

A alone can do the work in 6 days.

B alone can do the work 8 days.

They took the work at Rs 3200 with the help of C.

Lets take a per day work of A at Rs x.

Total = 3200/6 days.

= 533.33*3 days.

A = 1599.99 = 1600.

B = 3200/8 days.

= 400 * 3 days.

B = 1200.

A+B = 1600+1200 = 2800 And left 3200 -2800 = 400.

C = 400 Answer.

Rohan said: (Wed, Oct 9, 2013 02:20:51 PM)    
 
1/6 : 1/8 : 1/24 and ratio 4:3:1.

Answer above says highest number is 24 so multiply all by 24... is that the logic?

Alby said: (Thu, Oct 24, 2013 07:09:30 PM)    
 
From the ratio itself we can calculate.

A's wages:B's wages:C's wages = 4:3:1.

Then to calculate C's wages from 3200 = 1/(4+3+1) * 3200.

= 1/8 of 3200.

= 400.

Sai Mounika said: (Mon, Dec 30, 2013 04:26:34 PM)    
 
Why we are multiply all by 24? I think C's 1 day work is 1/24 so we have to multiply all by 24 in order to get the 3 days work. Am I right?

Vivek Jasele said: (Fri, May 9, 2014 12:09:31 PM)    
 
4:3:1.

C share will be simply as already we have count for 3 days work.
1/4+3+1*32000 = 1/8*3200 = 400.

Answer.

Vinnu said: (Mon, Jun 9, 2014 05:33:21 PM)    
 
See from the problem we can calculate c's 1 day work = 1/24.

It means he can complete work in 24 days.

So for calculating wage of c we can say for 24 days he is to be paid 3200. But for 3 days he is to be paid?

Cross multiply we get (3*3200) /24=400.

Its easy.

Hemanth said: (Tue, Jul 1, 2014 07:36:52 PM)    
 
The question is actually not clear. Its should say A, B and C undertook the work for Rs.3200. The questions as it is stated may imply that A and B took Rs.3200 individually. Correct me if im wrong.

Kumar said: (Thu, Aug 21, 2014 09:23:23 PM)    
 
The question is actually not clear. Its should say A, B and C undertook the work for Rs.3200. The questions as it is stated may imply that A and B took Rs.3200 individually. Correct me if I'm wrong.

Nisha said: (Sun, Sep 7, 2014 11:20:27 AM)    
 
Ya The question is actually not clear. Its should say A, B and C undertook the work for Rs. 3200. The questions as it is stated may imply that A and B took Rs. 3200 individually. Correct me if I'm wrong.

Divakar said: (Mon, Sep 22, 2014 08:45:03 PM)    
 
Last step can be written as C's share = 1/8*3200 = 400.

Dumbass said: (Mon, Oct 20, 2014 04:15:15 PM)    
 
Please help.

Where did the number 8 come from in 1/8*3200 = 400?

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