Aptitude - Time and Work - Discussion

@all.

A takes 6 days to complete the job. So a one day work is 1/6 and for 3 days it is 3/6 ie 1/2.

Similarly for B for 3 days work is 3/8 now A's share is 1/2 of 3200= 1600 B's share 3/8 of 3200=1200.

So C's share 3200--- (1600+1200) = 40.

Option A is the right answer if you perfectly have understood the question.
Here in the question, it is given that A & B undertook to do the work for 3200 then how C can earn his wages from the first day.
Here Supposed A & B if do the work in 3 days then they will able to do - 21 work
But they did it in 3 days with the help of C.

So the method is here that;
For the first two days, A+B do - 14 work.
Then with the help of C they able to finish it in 3 days so A+B+C do last day - 10 work.
That means one-day work of C is - 3.
Then the work ratio of A+B for two days with A+B+C in one day is - 14:10 = 7:5.
Then (3200 ÷12) * 5 = 1250.
Then bye one-day work ratio of A B&C = 4:3:3.
Then (3200÷10) * 3 = 375,
Hence the answer is 375.

Why we need to multiply 3200*1/8?

@All.

It is simple by solving this way.

Work = efficiency*time ----> 1
Efficiency = work/time. ----> 2
Time = work/efficiency ----> 3

Acc to question;

A can do work in 6 days.
B can do work in 8 days.
(A+B+C) Can do work in 3 days.

Taking LCM of 6,8,3 is 24.
Hence Let Work =24 units.

Now efficiency of A=24/6= 4units/day ----> using(2)
Efficiency of B=24/8= 3 units/day ----> using(2)
Efficiencyof (A+B+C) = 24/3=8unit/day ----> using(2)

Hence efficiency of C=Efficiency of (A+B+C)-Efficiency of A -Efficiency of B= 8-4-3=1unit/day.

Now we know A:B:C::4:3:1.
Let x be the price for 1 unit of work.

SO 4x+3x+x=3200.
8x=3200.
X=3200/8 =400.

As we know C can do 1unit/day.
Hence wages for C =1x(and x=400).
Hence it's 400.

LCM 24.
A4
B3
ABC 8
So, c=1.
3200*1/8=400.

Why should we multiply the wages with 24 to get the ratio?

Why here 1/3 is subtracted? Please explain.

Assume W=24 unit because multiple of 6 and 8 days.

A- 6days - 24/6=4u/d
B- 8 Days - 24/8=3u/d
C-?
A&B&C=24/3=8u/d.

So, C= 1u/d because A&B&C take 8u/d so subtract the total minus - individual A and B.

Pa: Pb: Pc = Wa: Wb: Wc
=Ra: Rb: Rc.

so Rc=3*1/24*3200=400.

Easier way to work it out.

(3/8+3/6) -1 x 3200 = 400.

A -6 Days (24/6=4).
B -8 Days (24/8=3).
A+B+C -3 Days (24/3=8) Take L.C.M of 3,6,8 is 24 and 24 is divide each work Day of A,B, A+B+c, to find 1 Days work.
A+B+C=8, (8 unit=3200, then 1 unit =3200/8=400).
we know A+B=7.
Then C=1 We know =400 Rs. only.