Direction : Read the given below table carefully and answer the following…
2021
Direction : Read the given below table carefully and answer the following questions.
The data shows volume and height of 4 right circular tanks P, Q, R and S. The given data also depicts time taken to fill or empty the tank by inlet pipe A, B and outlet pipe C.
1. Ratio between time taken by pipe B and that by pipe C is different because pipes were used by the operator in different ways for different tanks.
2. Radius of tank S is 10.5 m.
How much volume (approx.) of initially empty tank P was filled in 1 hour, when all 3 pipes were opened simultaneously? (Time taken by pipe C is 30 hours)
- A.
5235 𝑚3
- B.
4528 𝑚3
- C.
3876 𝑚3
- D.
4865 𝑚3
- E.
5743 𝑚3
Show answer & explanation
Correct answer: B
Concept
When several pipes act on the same tank at once, work with RATES (volume per hour), not times. An inlet pipe that fills a tank of volume V in t hours has rate V/t (positive, adds water); an outlet pipe that empties it in t hours has rate V/t (negative, removes water). The net volume moved in one hour is the algebraic sum of all the individual rates: (sum of inlet rates) minus (sum of outlet rates).
Application (Tank P)
Read the data for P: volume V = 38808 m3, inlet A fills it in 10 hours, and the ratio (time of inlet B) : (time of outlet C) = 2 : 3.
The stem fixes the time of outlet C at 30 hours. Using the 2 : 3 ratio, time of B = (2/3) of 30 = 20 hours.
Inlet A rate = 38808 / 10 = 3880.8 m3/hr.
Inlet B rate = 38808 / 20 = 1940.4 m3/hr.
Outlet C rate = 38808 / 30 = 1293.6 m3/hr (this is removed).
Net volume in 1 hour = 3880.8 + 1940.4 - 1293.6 = 4527.6 m3, which rounds to 4528 m3.
Cross-check
Combine the rates as a single fraction of V: net = V x (1/10 + 1/20 - 1/30) = V x (6/60 + 3/60 - 2/60) = V x 7/60 = 38808 x 7/60 = 4527.6 m3. The two routes agree, so about 4528 m3 is filled in the first hour.