Solutions
Short Trick:
Total work = 40/2 × 3 = 60
Time taken by Surya and Ramya when they work together
= 60/4 = 15 days
Detailed Solution:
Efficiency ratio of Surya to Ramya = 3 : 1
⇒ Ratio of time taken by Surya and Ramya = 1 : 3 (∵ time α 1/efficiency)
Let the time taken by Surya to complete the work alone be 'x' days and Ramya to complete the work alone be '3x' days.
Given, 3x - x = 40
⇒ 2x = 40
⇒ x = 20
⇒ Time taken by Surya to complete the work alone = 20 days
⇒ Time taken by Ramya to complete the work alone = 60 days
⇒ Total work = Efficiency × No. of days
⇒ Total work = 3 × 20 = 60 units
⇒ One day work Surya = 3 units
⇒ One day work of Ramya = 1 units
∴ When they work together, time taken to complete the work = 60/4 = 15 days