Pipes and Cisterns – Two inlets and one outlet complete the tank in a target time: Pipe A fills the tank in 1 hour and pipe B in 75 minutes. With an outlet C also open, the tank becomes full in 50 minutes. How long would pipe C alone take to empty a full tank?

Introduction / Context:
We are given the individual filling times of two inlets and the combined completion time when an outlet is also open. The goal is to deduce the outlet’s emptying time by working with rates.

Given Data / Assumptions:

• A alone: 1 h ⇒ 1.0 per h.
• B alone: 75 min = 1.25 h ⇒ 0.8 per h.
• All three together: 50 min = 5/6 h ⇒ net rate = 1 / (5/6) = 1.2 per h.

Concept / Approach:
Net rate = A + B − C. Solve for C, then invert to get C’s emptying time.

Step-by-Step Solution:
A + B = 1.0 + 0.8 = 1.8 per h.Net rate (with outlet) = 1.2 per h.Outlet rate C = (A + B) − net = 1.8 − 1.2 = 0.6 per h.C’s time = 1 / 0.6 h = 5/3 h = 100 min.

Verification / Alternative check:
Recombine: 1 + 0.8 − (1/ (5/3)) = 1.8 − 0.6 = 1.2 per h ⇒ 50 min total, as given.

Why Other Options Are Wrong:
150, 200, 125, and 90 minutes give outlet rates that fail to hit the 50-minute net target.

Common Pitfalls:
Converting 75 minutes incorrectly or using minutes and hours inconsistently.

Final Answer:
100 min