The ratio of time taken by Anamika and Bani to complete a work is 1 : 3, respectively. Therefore, Anamika is able to finish a job in 40 days less than Bani. If they work together, they can complete the work in ______ days.

15

Efficiency α \(\frac{1}{Time}\)

             Anamika : Bani

Time              1    :  3

Efficiency       3    :  1

⇒ Anamika is able to finish a job in 40 days less than Bani, therefore

⇒ (3 - 1)T = 40 days

⇒ 2T = 40 days

⇒ T = 20 days.

Therefore time taken by Anamika = 1 x 20 = 20 days,

 and by Bani = 3 x 20 = 60 days.

⇒ Total work = 20 x 3 = 60 units.   ..(Efficiency × Days = Total work)

⇒ Time taken by both of them to complete the work together = \(\frac{60}{3 + 1}\) = \(\frac{60}{4}\) = 15 days.    ..(\(\frac{Work}{Efficiency}\) = Time)