Question

2 pipes can fill a tank in 10 minutes together. If the efficiency of the first pipe is 8 times the efficiency of the second pipe, find the time required to fill the tank using the second pipe alone.

• A. 88 minutes
• B. 87 minutes
• C. 89 minutes
• D. 90 minutes

Hint:

When efficiency is given as a multiple "n", the time for the slower pipe alone is always \(\text{Together Time} \times (n + 1)\). Here: \(10 \times (8 + 1) = 90\).

Answer 1

The Correct Option is D

Concept: Efficiency is inversely proportional to time. If efficiency ratio is \(x : y\), total combined efficiency is \(x + y\).
Step 1: Assign efficiencies.
Efficiency of 2nd pipe (\(E_2\)) = 1 unit/min.
Efficiency of 1st pipe (\(E_1\)) = 8 units/min (8 times).
Combined efficiency = \(8 + 1 = 9\) units/min.

Step 2: Calculate Total Capacity.
Total Capacity = Combined Efficiency \(\times\) Total Time
Capacity = \(9 \times 10 = 90\) units.

Step 3: Find time for the second pipe alone.
Time = \(\text{Capacity} / E_2 = 90 / 1 = 90 \text{ minutes}\).