Question

A can do a certain work in 18 days. B is 25% less efficient than A. A alone worked for a few days and then, B joined him. Both worked together till the completion of the work. The entire work got completed in 12 days. For how many days did A and B work together?

• A. 6
• B. 4
• C. 9
• D. 8

Answer 1

Answer:

D. 8

Let A's efficiency be 100 units/day B's efficiency = (100 × 75/100) = 75 units/day Total work = (100 × 18) = 1800 units work alone by A be x days A and B work together = (12 – x) days (100 × x) + (100 + 75) × (12 – x) = 1800 100x + 1200 – 100x + 900 – 75x = 1800 2100 – 75x = 1800 75x = (2100 – 1800) 75x = 300 x = 4 days Time taken by A and B together to complete the work = (12 – x) = (12 – 4) days = 8 days