Question

Three pipes A, B and C can fill a tank in 12 hours. All the pipes started working together and after 3 hours, C is closed. If A and B can fill the remaining part in 10 hours, then the number of hours taken by C alone to fill the tank is ______.

• A. 100 hours
• B. 110 hours
• C. 120 hours
• D. 130 hours

Hint:

Find the combined rate, subtract A and B's rate found from the remaining part, to get C's rate.

Answer 1

The Correct Option is C

Step 1: Assign a total capacity to the tank instead of using fractions.
Let the tank hold 120 units of water, a number that divides evenly by 12, matching the given time.

Step 2: Find the combined hourly rate of all three pipes.
Since all three together fill 120 units in 12 hours, their combined rate is $120/12 = 10$ units per hour.

Step 3: Find how much is filled in the first 3 hours, and what is left.
In 3 hours, all three pipes fill $3 \times 10 = 30$ units, leaving $120 - 30 = 90$ units still empty.

Step 4: Find A and B's combined rate from the remaining part.
A and B fill these 90 units in 10 hours, so their combined rate is $90/10 = 9$ units per hour.

Step 5: Subtract to get C's rate, then find C's time alone.
C's rate is $10 - 9 = 1$ unit per hour. To fill the full 120 units alone, C needs $120/1 = 120$ hours.

Final Answer:
Working in whole units instead of fractions, C alone still takes 120 hours.
\[ \boxed{120 \text{ hours}} \]