A, B and C together can complete a certain work in 40 days.
A, B and C together can complete a certain work in 40 days. B and C together can complete the same work in 72 days. B is 50% more efficient than A. A, B and C work together for 16 days. B alone will complete the remaining work in:
A, B और C मिलकर एक निश्चित कार्य को 40 दिनों में पूरा कर सकते हैं। B और C मिलकर उसी कार्य को 72 दिनों में पूरा कर सकते हैं। B की दक्षता, A की दक्षता से 50% अधिक है। A, B और C मिलकर 16 दिनों तक कार्य करते हैं। शेष कार्य को B अकेला कितने दिनों में पूरा करेगा?
Detailed Solution & Logic
36 day
Let total work = 1 unit.
A + B + C complete the work in 40 days.
Their one-day work = $1/40$
B + C complete the work in 72 days.
Their one-day work = $1/72$
So A's one-day work:
$1/40 - 1/72$
Taking LCM 360:
$=\frac{9-5}{360}$
$=\frac{4}{360}=\frac{1}{90}$
B is 50% more efficient than A.
So B's efficiency:
$B=\frac{3}{2}\times\frac{1}{90}$
$=\frac{1}{60}$
Now A, B and C work together for 16 days.
Work done in 16 days:
$16\times\frac{1}{40}=\frac{2}{5}$
Remaining work:
$1-\frac{2}{5}=\frac{3}{5}$
Time taken by B alone:
$\frac{3/5}{1/60}$
$=\frac{3}{5}\times 60$
=36
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