Three taps A, B, C fill up a tank independent | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The rates of filling for taps $A, B, C$ are $\frac{1}{10}, \frac{1}{20}, \frac{1}{30}$ of the tank per hour,respectively.Let the pairs be $(A, B),

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(A) The rates of filling for taps $A, B, C$ are $\frac{1}{10}, \frac{1}{20}, \frac{1}{30}$ of the tank per hour,respectively.Let the pairs be $(A, B), (B, C), (C, A)$. The combined rates are:$(A+B) = \frac{1}{10} + \frac{1}{20} = \frac{3}{20} = 0.15$$(B+C) = \frac{1}{20} + \frac{1}{30} = \frac{5}{60} = \frac{1}{12} \approx 0.0833$$(C+A) = \frac{1}{30} + \frac{1}{10} = \frac{4}{30} = \frac{2}{15} \approx 0.1333$To minimize time,we use the fastest pairs as much as possible. The rates in descending order are $(A+B) > (C+A) > (B+C)$.In $3 \, h$,using each pair once,the tank filled is $\frac{3}{20} + \frac{2}{15} + \frac{1}{12} = \frac{9+8+5}{60} = \frac{22}{60} = \frac{11}{30}$.Remaining part is $1 - \frac{11}{30} = \frac{19}{30}$.To fill the remaining $\frac{19}{30}$ as fast as possible,we use the fastest pair $(A+B)$ with rate $\frac{3}{20}$.Time required = $\frac{19/30}{3/20} = \frac{19}{30} 	imes \frac{20}{3} = \frac{38}{9} \approx 4.22 \, h$.Total time = $3 + 4.22 = 7.22 \, h$. Since we must use each pair for at least one hour,and the question implies integer hours,we check the options. Given the options,$8 \, h$ is the smallest integer satisfying the condition.

Three taps $A, B, C$ fill up a tank independently in $10 \, h$,$20 \, h$,and $30 \, h$,respectively. Initially,the tank is empty. Exactly one pair of taps is open during each hour,and every pair of taps is open for at least one hour. What is the minimum number of hours required to fill the tank?

Similar Questions

$A$ point charge $+Q$ is positioned at the centre of the base of a square pyramid as shown. The flux through one of the four identical upper faces of the pyramid is

The value of electric potential at any point due to an electric dipole is

Which of the following is a level of biological organization?

The random variable $X$ takes the values $1, 2, 3, \ldots, m$. If $P(X=n) = \frac{1}{m}$ for each $n$,then the variance of $X$ is

If the gravitational acceleration at the surface of the Earth is $g$,then the increase in potential energy in lifting an object of mass $m$ to a height equal to half of the radius of the Earth from the surface will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module