Three pipes A, B, and C can fill a tank together in 2 hours. Pipes B and C take 3 hours to fill the tank, while pipes A and C take 4 hours to fill the tank. Which of the following statements are correct ?
(A) Pipe A alone takes 6 hours to fill the tank.
(B) Pipe B alone takes 5 hours to fill the tank.
(C) Pipe B alone takes 4 hours to fill the tank.
(D) Pipe C alone takes 12 hours to fill the tank.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (C) and (D) only
Let a, b and c be the parts of the tank filled in one hour by pipes A, B and C. Then
\( \displaystyle a+b+c=\frac{1}{2} \)
\( \displaystyle b+c=\frac{1}{3} \)
\( \displaystyle a+c=\frac{1}{4} \)
Subtracting:
\( \displaystyle a=\frac{1}{2}-\frac{1}{3}=\frac{1}{6} \)
\( \displaystyle b=\frac{1}{2}-\frac{1}{4}=\frac{1}{4} \)
\( \displaystyle c=\frac{1}{3}-\frac{1}{4}=\frac{1}{12} \)
So pipe A alone takes 6 hours, pipe B alone 4 hours and pipe C alone 12 hours.
Checking the statements
(A) Pipe A alone takes 6 hours to fill the tank. — Correct. \( a=\frac{1}{6} \), so 6 hours.
(B) Pipe B alone takes 5 hours to fill the tank. — Incorrect. \( b=\frac{1}{4} \), so B takes 4 hours, not 5.
(C) Pipe B alone takes 4 hours to fill the tank. — Correct. \( b=\frac{1}{4} \), so 4 hours.
(D) Pipe C alone takes 12 hours to fill the tank. — Correct. \( c=\frac{1}{12} \), so 12 hours.