Aptitude - Time and Work - Discussion

See,

I hope everyone gets dout on how 1/6 : 1/8 : 1/24 = 4 : 3 : 1.
So first consider this 1/6:1/8:1/24
LCM will be 24 so, then
1/6 × 24 = 4.
1/8 × 24 = 3.
1/24 × 24 = 1.
So, it's 4 : 3 : 1.

A's 3day ways = (1/6)*3*3200 = 1600.
B's 3day ways = (1/8)*3*3200 = 1200.
C's 3day ways = 3200-(1600+1200).

3(1/6+1/8+1/x) = 1
=> 1/x = 1/24,
1/6:1/8:1/24= 4:3:1,

3200 * 1/8 = 400.

A 1 Day Work-->1/6.
B 1 Day Work-->1/8.
Total Amount = 3200.

For 3 Days Work With the help of C.
Now,
Finding the Share of A&B.
(1/6+1/8) * 3,
(7/24)*3 = 7/8.

Share of A&B = (7/8) * 3200 = 2800.
Finding share of C = 3200 - 2800 = 400.
So,
C = 400.

@Pradeep Koney.

It's very simply elaborated and easy to understand. Thanks.

The easiest solution to this question is to find the efficiency of a + b + c - (a + b). You would be getting 1 as c's efficiency.

So, the total work done by a + b + c is 8.
i.e. 1 is divided by 8 * 3200. And You'll get 400.

Work done by A in one day = 1/6.
Like this of B = 1/8.
The work done by both A and B is 1/6 + 1/8 = 7/24.
3 days work of A and B is 3 * 7/24 = 7/8.

A and B complete 7 parts (for 7/8) of the total work (as we consider the total work is 1),
So, C does 1/8 (which means 1 part of the total work)
So 3200/8 = 400(for each part),
c will be paid 400.

Thanks everyone for explaining the answer.

How did you calculated the wages ratio?

@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.