Correct Answer - Option 2 : 6
Given:
X and Y can finish a work in 15 days and 30 days respectively. Both of them worked for 5 days and left. The remaining work was completed by Z in 5 days.
Formula:
If A and B can together finish it in t days with A and B finishing the work in a and b days respectively,
1/a + 1/b = 1/t
Calculation:
Let total work be 30 units, LCM of 15 and 30.
Efficiency X = 30/15 = 2
Efficiency Y = 30/30 = 1
Let the efficiency of Z be z
ATQ,
⇒ 5(2 + 1) + 5z = 30
⇒ 15 + 5z = 30
⇒ 5z = 15
⇒ z = 3
∴ Required time = 30/3 + 2 = 30/5 = 6 days.