Aptitude - Time and Work - Discussion

It is very simple;

A's 1day work = 1/6.
B's 1day work = 1/8.
A&B&C's 1day work=1/3.

C's 1day work=A+B+C'S 1day work-(A+B's 1day work)=(1/3)-(1/6)-(1/8) = 1/24.

A will do a complete work that is 1 full work in 6 day's means how much work he will do in 3 days given by;

6days--------->1 complete work
3days--------->?

Cross multiply then we get 1/2 work that is half of the work total work done by A.
Similarly, B ' s work done in 3 days is given by;

8 days-------->1 complete work,
3------------------?

Cross multiply we get 3/8 part of 1 complete work done by B.
Similarly, C's part of work is given by;
24 days --------->1 complete work
3 days ------------>?

By cross multiply, we get 1/8.
So,
For 1 complete work they get ------------>3200.
Then for A's (1/2) part of that work------>?
Cross multiply we get 1600.

Similarly for B
1 complete work------->3200
B's (3/8) part of the work--->?
By cross multiply, we get 1200.
Similarly for C.

1 Complete work ------>3200
C's part of (1/8) part of the work--->?
We get by cross multiply 400.

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.

@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.

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.

A = 6days.
B = 8days.

A+B+C=3days.
C's no of days required to complete the work.
(1÷6)+(1÷8)+(1÷C)=(1÷3).
Therefore C=24 day's.

Now the ratio of no of days taken by each member to complete the work comes(6:8:24).

But, we know that A is somewhat a fast worker than B and C therefore he must be paid more and C is taking more time he must be paid less,

Now let's considers these people's each day of work ie A=(1÷6), B=(1÷8), C=(1÷24).

Therefore the total units of work=(1÷6)+(1÷8)+(1÷24)=( 1÷3) by taking lcm
Now ,

The total amount to is 3200.
3200/(1÷3)=9600.
Therefore 9600/24 is 400.

From given:

A+B+C can complete a work in 3 days and they will get amount 3200 for 3 days.

So A, B, C work for 3 days.

A one day work is 1/6.

B one day work is 1/8.

C one day work is, we have to find out.

A+B+C one day work is 1/3 because A, B, C complete a work in 3 days.

So A+B+C one day work = 1/6+1/8+1/C.

1/3 = 1/6+1/8+1/C.

1/C = 1/24 so "C" one day work is 1/24.

A's 3 days work is 3/6 and he will get the amount is 3/6*3200 = 1600.

B's 3 day work is 3/8 and he will get 3/8*3200 = 1200.

C's 3 day work is 3/24 and he will get 3/24*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).

A lot simpler method --
A does 1/6 in 1 day.. B does 1/8 in one day..So they both do (1/6+1/8=7/24)in 1 day.. Hence they will finish the work in 24/7 days..
they get paid 3200 for 24/7 units of work..hence they'll be paid 3200*7/24 for 1 units of work..which is equal to 2800/3..
now A and B were finishing it in 24/7 days but on C's help they do it in 3 days..hence they are saved 24/7-3 units of work which is equal to 3/7 units of works and C will be paid for this..now 1 unit's pay was 2800/3..hence 3/7 units pay is (2800*3)/(3*7) = 400!!

1. A can do in 6 days => 6
2. B can do in 8 days => 8 LCM of 6,8,3 is 48
3. A+B+C an do in 3 days => 3
=>Individual efficiency is;
A's 48/6 => 8 , B's 48/8 => 6 , A+B+C's =>48/3 => 16
=> Now the ratio is A:B:C = 8:6:16.
i.e .., A:B:C = 4:3:8.
Since the above ratio, C's is (4+3)-8=1.
=> New ratio is A:B: C = 4:3:1.
We have to find out how much to be paid for work.
1/8*3200 => 400.

A 1 day work = 1/6.

B 1 day work = 1/8.

(A + B + C) complete work in = 3 days.

A + B + C one day work = 1/3.

1/6 + 1/8 + (C one day work) = 1/3.

C one day work = 1/3 - (1/6 + 1/8) = 1/24.

Total money = 3200.

So A, B, C share in the whole money is depend on their work ratio.

A work : B work : C work = 1/6 : 1/8 : 1/24.

Or 4 : 3 : 1 (multiply 24 in each).

A share = (4/8) *3200 = 1600.

B share = (3/8) * 3200 = 1200.

C share = (1/8) *3200 = 400.