P can complete five - eighths of a work in 15 days and Q can complete three - fourths of the same work in 30 days. They worked together for 8 days and then P left. How much time will Q working alone, take to complete the remaining work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 18 days 16 hours.
Concept Used:
Total work = Time × Efficiency
Explanation:
According to the given question,
P can complete five - eighths of a work in 15 days,
P can complete total work in 24 days
Also, Q can complete three - fourths of the same work in 30 days.
Q can complete total work in 40 days
Let the total work to be done be LCM of (24, 40) = 120 units
Efficiency of P = = 5 units/day
And, efficiency of Q = = 3 units/day
Total work done by (P + Q) in 8 days = (5 + 3) × 8 = 8 × 8 = 64 units
Remaining work = 120 - 64 = 56 units
Q will complete the remaining work alone in = 18 days hours = 18 days 16 hours
Hence the required answer is 18 days and 16 hours.