Question:
A and B can do a work in 12 days and 18 days respectively. They work together for 4 days, after which B leaves. C joins A and together they complete the remaining work in 4 days. In how many days can C alone complete the entire work?
A और B किसी कार्य को क्रमशः 12 दिन और 18 दिन में कर सकते हैं। वे 4 दिन तक एक साथ कार्य करते हैं, जिसके बाद B कार्य छोड़ देता है। C, A के साथ जुड़ता है और वे मिलकर शेष कार्य को 4 दिन में पूरा करते हैं। C अकेले पूरे कार्य को कितने दिनों में पूरा कर सकता है?
Options:
- 36 days
- 24 days
- 30 days
- 40 days
- 36 दिन
- 24 दिन
- 30 दिन
- 40 दिन
Correct Answer: a)
Explanation:
Let total work = 36 units.
A’s efficiency = 3 units/day; B’s efficiency = 2 units/day.
In 4 days, A + B do \(4 \times (3 + 2) = 20\) units.
Remaining work = \(36 – 20 = 16\) units.
A and C finish 16 units in 4 days \(\implies\) efficiency of (A + C) = \(16 / 4 = 4\) units/day.
C’s efficiency = \(4 – 3 = 1\) unit/day.
Time for C alone = \(36 / 1 = 36\) days.
A’s efficiency = 3 units/day; B’s efficiency = 2 units/day.
In 4 days, A + B do \(4 \times (3 + 2) = 20\) units.
Remaining work = \(36 – 20 = 16\) units.
A and C finish 16 units in 4 days \(\implies\) efficiency of (A + C) = \(16 / 4 = 4\) units/day.
C’s efficiency = \(4 – 3 = 1\) unit/day.
Time for C alone = \(36 / 1 = 36\) days.
कुल कार्य = 36 इकाई। 4 दिन में A+B द्वारा कार्य = 20 इकाई। शेष = 16 इकाई। (A+C) की क्षमता = 4 इकाई/दिन। C की क्षमता = \(4 – 3 = 1\) इकाई/दिन। C अकेले करेगा = 36 दिन में।