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03 Dec 2020, 01:15
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A
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Difficulty:
75%
(hard)
Question Stats:
65% (03:10) correct
35%
(03:13)
wrong
based on 135
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A, B and C, can complete a piece of work individually in 15, 30 and 40 days respectively. They started the work together and the A and B let 2 days and 4 days before the completion of the work respectively. In how many days was the work completed?
A. 10 2/15
B. 10 13/15
C. 12
D. 15
E. 16
A. 10 2/15
B. 10 13/15
C. 12
D. 15
E. 16
05 Dec 2020, 00:18
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Bunuel
Since C is the person finishing the work, assume he worked for x days
So, A worked for x - 2 days and B worked for x - 4 days
Work done by A in 1 day = \(\frac{1}{15}\)
Fraction of work done in (x - 2) days = \(\frac{x - 2}{15}\)
Work done by B in 1 day = \(\frac{1}{30}\)
Fraction of work done in (x - 4) days = \(\frac{x - 4}{30}\)
Work done by C in 1 day = \(\frac{1}{40}\)
Fraction of work done in x days = \(\frac{x}{40}\)
Sums of the fraction of work done by all of them = 1 (As work is completed)
Then \(\frac{x - 2}{15} + \frac{x - 4}{30} + \frac{x}{40} = 1\)
LCM (15, 30, 40) = 120
\(\frac{8(x - 2) + 4(x - 4) + 3x}{120} = 1\)
8x - 16 + 4x - 16 + 3x = 120
15x = 142
x = \(\frac{152}{15} = 10\frac{2}{15}\) days
Option A
Arun Kumar
31 Aug 2025, 01:48
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