Aptitude - Time and Work - Discussion

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.

Here A work is 6days.
B work is 8 days
Together combined work is 3 days right?
So now total work =LCM of 6, 8, 3 = 24.
So A efficiency or one day of work is 24/6 = 4,
B's efficiency or one day work is 24/8 = 3,
A + B + Cs one day work is 24/3 = 8.
So, we want only C one day of work.
We know;
A + B + C = 8, also know that A is 4, B is 3.
4 + 3 + C = 8,
C = 8 - 7 C's one day work is 1.

Now the total money is 32000.
A + B + C together one day work is 8(see above).
So 32000/8=400.
Here, A part is 4, so 4 * 400 = 1600,
B part is 3, so 3 * 400 = 1200,
C part is 1 * 400 = 400
Asking C part,
So, C get 400rupees.

@Pradeep Koney.

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

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.

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.

Why we are taking ratio 3 * 3200 * 1/24 where does this 3 come from can anyone explain me?

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)

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.