Match List-I with List-II.
| List-I | List-II | ||
| (A) | Hours taken by two pipes that fill a tank in 4 hours and 12 hours, opened together | (I) | 3 |
| (B) | Hours taken to fill a tank when a pipe that fills it in 6 hours and an outlet that empties it in 10 hours are both open | (II) | 4 |
| (C) | Hours taken by three pipes that fill a tank in 10, 15 and 30 hours, opened together | (III) | 5 |
| (D) | Hours taken by an outlet that empties a full tank in 8 hours to empty the tank when it is half full | (IV) | 15 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(I), (B)-(IV), (C)-(III), (D)-(II)
In each case, the parts of the tank per hour are added for filling pipes and subtracted for outlets.
(A) Hours taken by two pipes that fill a tank in 4 hours and 12 hours, opened together
This matches (I) 3.
\( \displaystyle \frac{1}{4} + \frac{1}{12} = \frac{3 + 1}{12} = \frac{1}{3} \)
(B) Hours taken to fill a tank when a pipe that fills it in 6 hours and an outlet that empties it in 10 hours are both open
This matches (IV) 15.
\( \displaystyle \frac{1}{6} - \frac{1}{10} = \frac{5 - 3}{30} = \frac{1}{15} \)
(C) Hours taken by three pipes that fill a tank in 10, 15 and 30 hours, opened together
This matches (III) 5.
\( \displaystyle \frac{1}{10} + \frac{1}{15} + \frac{1}{30} = \frac{3 + 2 + 1}{30} = \frac{1}{5} \)
(D) Hours taken by an outlet that empties a full tank in 8 hours to empty the tank when it is half full
This matches (II) 4. Half the water takes half the time:
\( \displaystyle \frac{1}{2} \div \frac{1}{8} = 4 \)