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27 Apr 2021, 07:15
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (01:57) correct
28%
(01:59)
wrong
based on 148
sessions
History
Date
Time
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Not Attempted Yet
A and B can do a work in 10 days. B and C in 12 days, while C and A in 15 days. How long would they take if all the three work together?
(A) 4 days
(B) 5 days
(C) 7 days
(D) 8 days
(E) 9 days
(A) 4 days
(B) 5 days
(C) 7 days
(D) 8 days
(E) 9 days
27 Apr 2021, 19:51
Kudos
Bookmarks
Given: A and B can do a work in 10 days. B and C in 12 days, while C and A in 15 days.
Time taken by all of them together?
Let rate of A = a, rate of B = b, rate of C = c, Work done = w, time taken by all three of them = t.
We want the value of t in:
(a + b + c) * t = w
From data:
(a + b) * 10 = w
(b + c) * 12 = w
(a + c) * 15 = w
From above three equations:
(a + b) + (b + c) + (a + c) = \(\frac{w}{10}\) + \(\frac{w}{12}\) + \(\frac{w}{15}\) = \(\frac{w}{4}\)
=> 2 * (a + b + c) = \(\frac{w}{4}\)
=> (a + b + c) * 8 = w
=> t = 8 days.
So, correct answer is option D.
Time taken by all of them together?
Let rate of A = a, rate of B = b, rate of C = c, Work done = w, time taken by all three of them = t.
We want the value of t in:
(a + b + c) * t = w
From data:
(a + b) * 10 = w
(b + c) * 12 = w
(a + c) * 15 = w
From above three equations:
(a + b) + (b + c) + (a + c) = \(\frac{w}{10}\) + \(\frac{w}{12}\) + \(\frac{w}{15}\) = \(\frac{w}{4}\)
=> 2 * (a + b + c) = \(\frac{w}{4}\)
=> (a + b + c) * 8 = w
=> t = 8 days.
So, correct answer is option D.
