Question:
A person can complete a work in 30 days. He works for 5 days alone and then leaves. The remaining work is completed by B in 20 days. In how many days can A and B together finish the entire work?
एक व्यक्ति A किसी कार्य को 30 दिनों में पूरा कर सकता है। वह 5 दिन अकेले कार्य करता है और फिर छोड़ देता है। शेष कार्य B द्वारा 20 दिनों में पूरा किया जाता है। A और B मिलकर पूरे कार्य को कितने दिनों में पूरा कर सकते हैं?
Options:
- 13\(\frac{1}{3}\) days
- 15 days
- 12 days
- 14\(\frac{2}{3}\) days
- 13\(\frac{1}{3}\) दिन
- 15 दिन
- 12 दिन
- 14\(\frac{2}{3}\) दिन
Correct Answer: a)
Explanation:
Total work = 60 units (or let work = 1).
A’s daily work = \(\frac{1}{30}\).
Work done by A in 5 days = \(5 \times \frac{1}{30} = \frac{1}{6}\).
Remaining work = \(1 – \frac{1}{6} = \frac{5}{6}\).
B finishes \(\frac{5}{6}\) work in 20 days.
Time for B alone to complete full work = \(20 \times \frac{6}{5} = 24\) days.
Combined daily work of A and B = \(\frac{1}{30} + \frac{1}{24} = \frac{4 + 5}{120} = \frac{9}{120} = \frac{3}{40}\).
Time together = \(\frac{40}{3} = 13\frac{1}{3}\) days.
A’s daily work = \(\frac{1}{30}\).
Work done by A in 5 days = \(5 \times \frac{1}{30} = \frac{1}{6}\).
Remaining work = \(1 – \frac{1}{6} = \frac{5}{6}\).
B finishes \(\frac{5}{6}\) work in 20 days.
Time for B alone to complete full work = \(20 \times \frac{6}{5} = 24\) days.
Combined daily work of A and B = \(\frac{1}{30} + \frac{1}{24} = \frac{4 + 5}{120} = \frac{9}{120} = \frac{3}{40}\).
Time together = \(\frac{40}{3} = 13\frac{1}{3}\) days.
A का 1 दिन का कार्य = \(\frac{1}{30}\)
A द्वारा 5 दिन में किया गया कार्य = \(\frac{5}{30} = \frac{1}{6}\)
शेष कार्य = \(\frac{5}{6}\)
B शेष \(\frac{5}{6}\) कार्य 20 दिन में करता है, अतः B पूरा कार्य करेगा = \(20 \times \frac{6}{5} = 24\) दिन में।
दोनों मिलकर 1 दिन में करेंगे = \(\frac{1}{30} + \frac{1}{24} = \frac{9}{120} = \frac{3}{40}\)
कुल समय = \(\frac{40}{3} = 13\frac{1}{3}\) दिन।
A द्वारा 5 दिन में किया गया कार्य = \(\frac{5}{30} = \frac{1}{6}\)
शेष कार्य = \(\frac{5}{6}\)
B शेष \(\frac{5}{6}\) कार्य 20 दिन में करता है, अतः B पूरा कार्य करेगा = \(20 \times \frac{6}{5} = 24\) दिन में।
दोनों मिलकर 1 दिन में करेंगे = \(\frac{1}{30} + \frac{1}{24} = \frac{9}{120} = \frac{3}{40}\)
कुल समय = \(\frac{40}{3} = 13\frac{1}{3}\) दिन।