Aptitude - Time and Work - Discussion

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.

C's one day work=1/24.
so C's 3 days work is=1/8.
C will take 1/8 part of 3200 which is equal to 1/8*3200=400.

We are multiplying 3200 with 3 because of this reason:

See, A and B worked together and got 3200 for their work. But with the help of C, they could finish their work in 3 days. So, as we can see" with the help of C", so, C 's share is also given by both A and B as A and B has taken help from C.

So, C's share is calculated like this:-.

C's 1 day's work=1/24.

But if we do this:- 3200*1/24; this will be wrong as C will get wages for his 1 day work only.

But given in question that C has worked for 3 days, so 3200*1/24*3= i.e. 3 will also be multiplied, so to give C's share to him completely.

So, answer is 3200*1/24*3=400.

400 is the correct answer.

It's more like the ratio n proportion. The ratio of A:B:C's 1-day work is 1/6:1/8:1/24
24 is multiplied for simplified calculation. If you multiply 24 in the numerator of each, it'd give 4:3:1.

(Because 24/6=4, 24/8=3, 24/24=1).
Sum of the proportion 4:3:1 = 4+3+1 = 8.

Now, A gets = 4/8 of 3200 = 1600,
B gets = 3/8 of 3200 = 1200,
C gets = 1/8 of 3200 = 400.

C's 1day work=total work-(A'a 1day work+B's1day work).
C's work is=1/3-(1/6+1/8).
It's simple.