Question

Pipe P can fill an empty tank in 15 h and pipe Q can fill the same tank in 45 h. Both pipes open alternatively for 1 h each without any time gap. In how many hours 90% of the tank will be filled?
1. \(20\frac{1}{6}\;h\)
2. \(24\frac{1}{7}\;h\)
3. \(21\frac{1}{6}\;h\)
4. \(20\frac{1}{4}\;h\)
5. \(30\frac{1}{4}\;h\)

Answer 1

Correct Answer - Option 1 : \(20\frac{1}{6}\;h\)

Given:

Pipe P can fill the tank in 15 hours.

Pipe Q can fill the tank in 45 hours.

Concept:

Time and efficiency concepts will be used.

Calculation:

Let the total quantity of tank be LCM of (15, 45) = 45 units

⇒ Efficiency of P = 45/15 = 3 units

⇒ Efficiency of Q = 45/45 = 1 unit

Now,

90% of 45 units = 40.5 units

If they are open alternatively then they will fill the 4 units of tank in 2 hours

⇒ In 20 hours they will 40 unit of tank

Remaining quantity = 40.5 – 40 = 0.5 units

⇒ 0.5 unit work left is filled by Pipe P

⇒ Total time = 20 hrs. + 0.5/3

⇒ Total time = 20 hrs. + 1/6

⇒ Total time

∴ In the given condition total tank will be filled in \(20\frac{1}{6}\;\)hours