Arijit and Brajesh, working together, can complete a task in 10 days, whereas Brajesh and Chandan can finish the same job in 15 days working together. If Arijit works for 5 days and Brajesh works for 8 days, it takes Chandan 9 days to complete the rest of the task. How many days will Chandan take to finish the same job alone?a)10 daysb)20 daysc)30 daysd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given Information:
- Arijit and Brajesh can complete a task in 10 days.
- Brajesh and Chandan can finish the same job in 15 days.
- Arijit worked for 5 days and Brajesh worked for 8 days.
- Chandan took 9 days to complete the remaining task.

To Find: How many days will Chandan take to finish the same job alone?

Solution:
Let's assume that the total work is 'W' and the efficiency of Arijit, Brajesh, and Chandan is 'a', 'b', and 'c' respectively.

From the given information,
- Arijit and Brajesh can complete the task in 10 days,
So, their combined efficiency is given by:
a + b = W/10 --------(1)

- Brajesh and Chandan can finish the same job in 15 days,
So, their combined efficiency is given by:
b + c = W/15 --------(2)

Now, we need to find the efficiency of Chandan, i.e. 'c'.
Let's assume that Chandan takes 'x' days to complete the whole task alone.
So, his efficiency is given by:
c = W/x

Also, it is given that:
- Arijit worked for 5 days and Brajesh worked for 8 days,
So, the amount of work done by them is:
5a + 8b = (5+8) (a+b) = 13(a+b) --------(3)

- Chandan took 9 days to complete the remaining task,
So, the amount of work done by him is:
c x 9 = W - 13(a+b) --------(4)

Substituting equation (1) and (2) in equation (3), we get:
5a + 8b = 13[(W/10) - b] [Using equation (1)]
=> 5a + 8b = (13W/10) - 13b
=> 18b = (13W/10) - 5a
=> b = (13W/180) - (5a/18) --------(5)

Substituting equation (2) and (5) in equation (4), we get:
(c/15) x 9 = W - 13(a+b)
=> (c/15) x 9 = W - 13[a + {(13W/180) - (5a/18)}]
=> c = (15W/52) [Solving further]

Therefore, Chandan can complete the whole task alone in:
x = W/c = (52/15) days

Hence, the correct answer is option (b) 20 days.

Answer

Given:
Arijit + Brajesh = 10 days
Brajesh + Chandan = 15 days
Arijit works for 5 days and Brajesh works for 8 days
Chandan completes the rest of the task in 9 days

To find:
How many days will Chandan take to finish the same job alone?

Solution:
Let's assume that the total work is 1 unit.
Let's also assume that Arijit's efficiency is 'a', Brajesh's efficiency is 'b', and Chandan's efficiency is 'c'.

From the given information, we can form the following equations:

Equation 1: (a + b) x 10 = 1
Equation 2: (b + c) x 15 = 1
Equation 3: 5a + 8b + 9c = 1

We need to find the value of 'c' from these equations.

Let's solve these equations one by one.

From Equation 1, we get:
a + b = 1/10

From Equation 2, we get:
b + c = 1/15

Adding the above two equations, we get:
a + 2b + c = 1/10 + 1/15
a + 2b + c = 1/6

Substituting the value of 'a + b' from Equation 1, we get:
1/10 + c = 1/6
c = 1/6 - 1/10
c = 1/15

So, Chandan's efficiency is 1/15.

Now, let's use Equation 3 to find the value of 'b'.
5a + 8b + 9c = 1
Substituting the values of 'a' and 'c', we get:
5a + 8b + 9(1/15) = 1
5a + 8b = 4/15

Substituting the value of 'a' from Equation 1, we get:
5/10 + 8b = 4/15
8b = 1/30
b = 1/240

So, Brajesh's efficiency is 1/240.

Now, let's find the total time taken by Arijit and Brajesh to complete the task:
(a + b) x T = 1
(1/10 + 1/240) x T = 1
T = 24 days

Since Arijit and Brajesh worked for a total of 5 + 8 = 13 days, they completed (a + b) x 13 = (1/10 + 1/240) x 13 = 31/240 of the task.

So, the remaining work is 1 - 31/240 = 209/240.

Chandan can complete this remaining work in 9 days, working alone.
So, his efficiency is (209/240) / 9 = 23/320.

Finally, we can find the time taken by Chandan to complete the whole task:
c x T = 1
(23/320) x T = 1
T = 320/23 days

Therefore, Chandan will take 320/23 days to complete the same job alone

Answer

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