Question

‘A’ while working 40% more efficiently can complete a piece of work in 25 days and ‘B’ while working 25% more efficiently can complete the same work in 21 days. While working with their original efficiencies ‘A’ and ‘B’ together worked for 9 days, then find the time taken by ‘A’ alone to complete the remaining work with his original efficiency.

• A. 7 days
• B. 14 days
• C. 12 days
• D. 6 days

Answer 1

Answer: (B)

14 days

Answer 2

Let total amount of work be 525 units
Amount of work done by ‘A’ in one day (with increased efficiency) = $\frac{525}{25}$ = 21 units
Original efficiency of ‘A’ = $\frac{21}{1.40}$ = 15 units per day
Amount of work done by ‘B’ in one day (with increased efficiency) = $\frac{525}{21}$ = 25 units
Original efficiency of ‘B’ = $\frac{25}{1.25}$ = 20 units per day
Amount of work completed by ‘A’ and ‘B’ together in 9 days = 35 × 9 = 315 units
Remaining work = 525 – 315 = 210 units
Desired time = $\frac{210}{15}$ = 14 days
So, the correct option is (B) : 14 days.