How many days can Amar and Anthony finish it?

Question

Amar and Akbar can do a work in 8 days, Akbar and Anthony do the same work in 12 days and Amar, Akbar and Anthony complete it in 6 days.
In how many days can Amar and Anthony finish it?

Answer 1

8 days

---

Amar-m, Akbar- k, Anthony- n
Given:
1/m+1/k=1/8 ---------> (1)
1/k+1/n=1/12 ---------> (2)
1/m+1/k+1/n=1/6 ---------> (3)
1/m+1/n=1/x, x=?

---

(1)+(2)= 1/m+1/n+2*1/k=1/8+1/12=5/24 ---------> (4)
2*(3)=2*1/m+2*1/m+2*1/k=1/3 ---------> (5)
(5)-(4)=1/m+1/n=1/3-5/24=1/8 ---> x=8 days