A tap can fill an oil tank in 14 hours. After half the tank is filled, 7 more similar taps are opened. What is the total time taken to fill the oil tank completely?

Correct — D.
One tap fills the whole tank in 14 hours.

Phase 1, one tap fills half: 14 ÷ 2 = 7 hours
Phase 2, taps running: 1 + 7 = 8 taps
Eight taps fill the other half 8 times as fast: 7 ÷ 8 = 7⁄8 hour
Convert: 7⁄8 × 60 = 52.5 min = 52 min 30 sec

Total = 7 hr + 52 min 30 sec = 7 hr 52 min 30 sec → option (d)

Why the others are wrong

• (a)
  6 hr 55 min — 6 hr 55 min is less than the 7 hours the single tap needs for the first half alone, so no total can be this small.
• (b)
  6 hr 52 min 20 sec — 6 hr 52 min 20 sec is also under 7 hours, the time the first half takes before the extra taps even open.
• (c)
  7 hr — 7 hr covers only the first half. It leaves out the 52 min 30 sec that eight taps need for the remaining half.

Split the job where the rate changes. Before that point one tap works. After it, eight identical taps work together.

Identical taps add their rates. One tap fills 1⁄14 of the tank per hour, so eight fill 8⁄14 = 4⁄7 per hour.

Half a tank at 4⁄7 per hour takes (1⁄2) ÷ (4⁄7) = 7⁄8 hour, the same as 7 ÷ 8.

Key facts

• A tap that fills a tank in T hours fills 1⁄T of it per hour
• n identical taps together fill the tank in T ⁄ n hours
• 7⁄8 hour = 52.5 minutes = 52 min 30 sec
• When the rate changes partway, time each phase separately and add

Common traps

• Counting 7 taps in the second phase instead of 1 + 7 = 8
• Reporting one phase (7 hr, or 52 min 30 sec) when the question asks for the total time

No directly related past PYQ was found.