Question 73

Two pipes X and Y can fill an empty tank in ‘t’ minutes. If pipe X alone takes 6 minutes more than ‘t’ to fill the tank and Y alone takes 54 minutes more than ‘t’to fill the tank, then X and Y together will fill the tank in (in minutes):

Solution

Let volume of tank = $$x$$ units

X's efficiency = $$\frac{x}{t+6}$$ units/min

Similarly, Y's efficiency = $$\frac{x}{t+54}$$ units/min

Time taken by both = $$(\frac{x}{t+6}+\frac{x}{t+54})\times t=x$$

=> $$(2t+60)t=(t+6)(t+54)$$

=> $$2t^2+60t=t^2+60t+324$$

=> $$t^2=324$$

=> $$t=\sqrt{324}=18$$

$$\therefore$$ Time taken by X and Y together = 18 minutes

=> Ans - (A)

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