Select the correct answerA can complete a work in 11 more days than B, while A does the same work in 36 days more than C. A+ B can complete the whole work in same time in which C alone does the whole work. In how many days A alone could complete the same work?Options72636166
Question
Select the correct answerA can complete a work in 11 more days than B, while A does the same work in 36 days more than C. A+ B can complete the whole work in same time in which C alone does the whole work. In how many days A alone could complete the same work?Options72636166
Solution
To solve this problem, we need to use the concept of work and time.
Let's denote the time taken by B to complete the work as 'b' days, by A as 'a' days and by C as 'c' days.
From the problem, we know that:
-
A can complete a work in 11 more days than B. So, a = b + 11.
-
A does the same work in 36 days more than C. So, a = c + 36.
From these two equations, we can equate b and c:
b + 11 = c + 36 => b - c = 25 ---- (Equation 1)
We also know that A + B can complete the work in the same time as C. In terms of rates (work done per day), this can be written as:
1/a + 1/b = 1/c ---- (Equation 2)
Substitute a = b + 11 in Equation 2:
1/(b+11) + 1/b = 1/c
To simplify, find a common denominator:
b(b+11) = b^2 + 11b
So, (b + b + 11) / (b^2 + 11b) = 1/c
=> 2b + 11 = c(b^2 + 11b)
=> 2b + 11 = cb + 11c
Substitute b - c = 25 from Equation 1:
2b + 11 = c(b + 36)
=> 2b + 11 = cb + 36c
=> b(2 - c) = 36c - 11
=> b = (36c - 11) / (2 - c)
Substitute c = b + 25:
b = (36(b + 25) - 11) / (2 - (b + 25))
Solving this equation gives b = 31.
Substitute b = 31 in a = b + 11, we get a = 42.
So, A alone could complete the same work in 42 days.
But this option is not given in the options. So, there might be a mistake in the problem or in the options provided.
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