Aptitude - Time and Work - Discussion

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.

Total amount is 3200,
Ratio 4:3:1,

4*x+3*x+1*x = 3200.

8x = 3200.

x = 400.

If A=1/6 ,B=1/8 and A+B+C = 1/3 ----(1).

A+B = 1/6 + 1/8 = 7/24.

Put the value of A+B in Eq.(1).

Than C = 1/8 - 7/24 = 1/24.

The Value of C' is 1/24.

Now the Ratio of A:B:C =1/6:1/8:1/24 (The L.C.M Of 1/6+1/8+1/24 is 24)
A:B:C =4:3:1.

Than Amt.is Rs.3200.

So the C' will be paid = 3200 X 1/8.

= Rs. 400.00 Answer.

Yes, I agree that amount 3200 in the question is not clearly mentioned. Is that for per day?

The ratio obtained is 4:3:1. Then why did you multiply 3*1/24*3200? we should not multiply with 1?

Actually, havent got the ratios we could have also found proportionate share of their wages as follows:

4+3+1 = 8.

Hence c's wage would've been 1/8*3200 = 400.

take LCM of A and B work, then get:

A+B=7/24.

WHERE:
A+B+C = 1/3 (given).

So 7/24+C=1/3.

C=1/24.

With the ratio you would get to know the share of A, B and C.

Now the Ratio of A:B:C =1/6:1/8:1/24 (The L.C.M Of 1/6+1/8+1/24 is 24)
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.

It is simple, A's share is (4/8)*3200.
B's share is (3/8)*3200.
C's share is (1/8)*3200 (because 4+3+1=8).

Can we solve the problem without calculating ratio?

No need to calculate the ratios its just wast of time.

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 = 7/24 works.....(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.