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?

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!!

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.