Given:
A and B can do a piece of work in 14/3 days, B and C in 12/5 days, and C and A in 16/3 days.
Concept Used:
To find the work done by A, B, and C together, we need to find their individual work rates and combine them.
Formula Used:
If A and B can complete a work in x days, then their combined work rate is 1/x work per day.
Similarly, for B and C, and C and A.
To find the individual rates, we use the principle of superposition and solve the system of equations.
Calculation:
Let the work rates of A, B, and C be a, b, and c respectively.
From the given data:
⇒ a + b = 3/14 ----(1)
⇒ b + c = 5/12 ----(2)
⇒ c + a = 3/16 ----(3)
Adding equations (1), (2), and (3):
⇒ (a + b) + (b + c) + (c + a) = 3/14 + 5/12 + 3/16
⇒ 2a + 2b + 2c = 3/14 + 5/12 + 3/16
⇒ 2(a + b + c) = 3/14 + 5/12 + 3/16
⇒ a + b + c = 1/2 (3/14 + 5/12 + 3/16)
⇒ a + b + c = 1/2 (72/336 + 140/336 + 63/336)
⇒ a + b + c = 1/2 (275/336)
⇒ a + b + c = 275/672
Work done by A, B, and C together in 1 day = 275/672
Work done by A, B, and C together in 2 days:
⇒ 2 × 275/672
⇒ 550/672
⇒ 275/336
∴ The correct answer is option 1: 275/336.
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