A, B and C can complete a task together in 8 days. A and B would need 16 days if only the two of them worked, while A and C would take 12 days if only the two of them worked. If A worked alone, how many days would A take to compete the task?a)30b)48c)60d)45Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
A, B, and C can complete a task together in 8 days.
A and B would need 16 days if only the two of them worked.
A and C would take 12 days if only the two of them worked.

To find:
How many days would A take to complete the task alone?

Assumption:
Let's assume that the amount of work done by each person per day is constant.

Solution:

Let's start by assuming that the total work required to complete the task is 1 unit.

Step 1: Calculate their individual efficiencies:
Let's assume that A's efficiency is 'x', B's efficiency is 'y', and C's efficiency is 'z'.

Therefore, the amount of work done by A, B, and C in 1 day respectively would be:
A: x units
B: y units
C: z units

Step 2: Calculate the combined efficiency of A and B:
We are given that A and B can complete the task together in 16 days. So, their combined efficiency would be:
A + B = 1/16 units per day

Step 3: Calculate the combined efficiency of A and C:
We are given that A and C can complete the task together in 12 days. So, their combined efficiency would be:
A + C = 1/12 units per day

Step 4: Calculate the combined efficiency of A, B, and C:
We are given that A, B, and C can complete the task together in 8 days. So, their combined efficiency would be:
A + B + C = 1/8 units per day

Step 5: Form equations:
From Step 2, we have A + B = 1/16
From Step 3, we have A + C = 1/12
From Step 4, we have A + B + C = 1/8

Step 6: Solve the equations:
By solving these equations simultaneously, we can find the values of A, B, and C.

A + B = 1/16
A + C = 1/12
A + B + C = 1/8

Subtracting the first equation from the second equation, we get:
(A + C) - (A + B) = 1/12 - 1/16
C - B = 1/48

Subtracting the second equation from the third equation, we get:
(A + B + C) - (A + C) = 1/8 - 1/12
B - C = 1/24

Adding the two equations obtained, we get:
C - B + B - C = 1/48 + 1/24
0 = 3/48
0 = 1/16

This implies that the equations are inconsistent and do not have a valid solution. However, we can still find the individual efficiency of A.

Step 7: Calculate A's efficiency:
From Step 2, we have A + B = 1/16
Substituting B = 1/16 - A into Step 3, we get:
A + (1/16

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