Aptitude - Time and Work - Discussion

Here, 1 day's work of a and b is(50/10) = 5.
1 day work of c is(50/50) = 1
a+b+c=(5+1)=>6->(1).
Given that a's time=sum of b's and c's time so,a=b+c
we can write a=b+c as b=a-c and then substitute this in (1)
that is a+b+c=6.
a+a-c+c=6=>2a=6->a=3.
Then later in that (1).
a+b+c = 6.
b = 6 - a - c,
b = 6 - 3 - 1,
b = 2.
That is 50/2=>25days.

A = B+C ,
A - C = B ---> (i).

Then,

A + B + C = 1/10 + 150 = 3/25.
From (i) putting a value of B
A+B+C= 3/25,
A+A - C + C = 3/25.
2A = 3/25.
A = 3/50.
Now, A+B = 1/10,
Putting A = 3/50,
B = 1/10-3/50.
B = 1/25 (B one day work) then total days is 25.

If A = B+C.
So A-B =C.

i,e A-B = 1/50 ----> eq 1
And
A+B = 1/10 ----> eq 2.
From eq 2 - eq 1 we will get the answer.
.

Great, Thanks everyone for explaining.

Time taken by A and B =10 days and Time taken by C =50 days

Total work=50 units

Efficiency of A and B = 5
The efficiency of C =1

A=B+C is given

A+B=5 => B+C+B=5 => 2B+C=5
2B+1=5 =>2B=4
B=2 is the efficiency

Time taken by B= work /efficiency of B =>50/2 =25.

Therefore, B can complete the work in 25days.

A+B can finish work in 10 days so its efficiency is 5 unit per day.
c can finish work in 50 days so its efficiency will be 1 unit per day.
So from here, we can calculate the total work, which will be 50 unit.
now according to the question,

Efficiency of A =efficiency of B+C
Adding B both sides,
A+B=2B+C
5=2B+1.

Therefore the efficiency of B will be,2 unit per day.

Now since the total work is 50 unit,we can calculate the time,
Time = total work/efficiency
Time=25 days.

Total work is = 50
C's efficiency = 50/50=1.
A+B's Efficiency = 50/10=5.
A+B+C's Efficiency = 5 + 1 = 6.

A = B+C,
B+C+B+C=6,
2(B+C)=6,
B+C= 6/2 =3,
A's Efficiency = 3,
So B's Efficiency =5-3 =2.
Hence B alone do it in 50/2 = 25 Days.

1/A+1/B=1/10 ---> EQN1.

Given that,
1/C = 1/50,
1/A=1/B+1/C ---> EQN2.

From EQN1 and EQN2 we get,
1/B + 1/B+1/C = 1/10,
2/B + 1/C = 1/10,
2/B + 1/50 = 1/10,
2/B = 2/25,
1/B = 1/25.

Hence B alone can do it in 25 Days.

They gave A = B+C, A+B = 10Days, C=50 Days;
A+B = 1/10;
since A = B+C;
B+C+B = 1/10;
2B+C = 1/10;
2B+1/50 = 1/10;
therefore B = 1/25;
B can complete in 25 days.

A = B + C,
A+B = 10 or A and B's one day work A+B=1/10.
C=50 or C=1/50.

A+B=1/10 (Since A=B+C),
B+C+B=1/10,
2B+1/50=1/10,
2B=1/10-1/50,
2B=2/25,
B=2/25*1/2.
B=1/25 (Which is one day's work).
B would take 25 days to complete certain work.