To complete a job, Abhay alone takes thrice as long as Bittu and Chanakya together. Bittu would take five times as long as Abhay and Chanakya together. All three together complete the work in 10 days. How many days are required by Chanakya to finish the work alone?
1). 120/7 days
2). 129/7 days
3). 106/7 days
4). 85/7 days
Let, Abhay, Bittu and Chanakya can complete the work alone in x, y and z days respectively.
Abhay alone takes thrice as long as Bittu and Chanakya together
1/x = 1/3 (1/y + 1/z)
3/x = 1/y + 1/z ----(1)
Bittu alone takes 5 times as long as Abhay and Chanakya together
1/y = 1/5 (1/x + 1/z)
5/y = 1/x + 1/z ----(2)
All three together complete the work in 10 days
1/x + 1/y + 1/z ----(3)
(3) – (1)
4/x = 1/10
⇒ x = 40
(3) – (2)
6/y = 1/10
⇒ y = 60
Putting this value in (2)
5/60 = 1/40 + 1/z
1/z = 1/12 – 1/40 = 7/120
Z = 120/7 days