A runner's average speed reduces by 25% every hour. If he runs 16 km in the first hour and he runs for 3 hours, then what is his overall average speed?

Correct — B, 12.33 km/hr. A 25% reduction multiplies the speed by 0.75, and it is applied to the speed held in the previous hour. So the runner covers 16 km in the first hour, 16 × 0.75 = 12 km in the second, and 12 × 0.75 = 9 km in the third. That is 37 km in three hours, and average speed is total distance divided by total time: 37 ÷ 3 = 12.333…, which the paper prints as 12.33 km/hr.

• (a)12 km/hr — Implies a total of 36 km, which is what you get by subtracting a flat 4 km/hr each hour — 16, 12, 8. The reduction is a quarter of the current speed, and a quarter of 12 is 3, not 4.
• (c)10.33 km/hr — Implies 31 km in three hours. No consistent reading of a 25% hourly reduction gives that; it is a low anchor for anyone who thinks the speed collapses faster than it does.
• (d)13 km/hr — Implies 39 km. It is the round number just above the true value, which makes it tempting to anyone who computes 37 ÷ 3 and rounds in the wrong direction.

Average speed is total distance divided by total time. It is not the plain mean of the individual speeds — except in the special case where each speed is held for the same length of time, which is exactly the case here, so (16 + 12 + 9) ÷ 3 also gives 12.33. A percentage reduction repeated each period is geometric, so the absolute drop shrinks every time: 4 km/hr in the second hour and only 3 km/hr in the third.

Two readings of 'reduces by 25% every hour' compete, and the paper prices both. Taking 25% of the current speed gives 16, 12, 9 and a total of 37 km. Taking 25% of the first hour's speed as a fixed deduction gives 16, 12, 8 and a total of 36 km, which is option (a) at exactly 12 km/hr. The standard reading of a repeated percentage change is the multiplicative one, and it is the one the key follows. It is also worth noticing why the mean of the speeds is legitimate here and usually is not: the runner spends one hour at each speed, so the times are equal and the weights cancel. When distances are equal instead of times, the average speed is the harmonic mean and the arithmetic mean overstates it.

• Average speed is total distance ÷ total time, never the plain mean of speeds unless each speed is held for an equal time.
• A 25% reduction multiplies the speed by 0.75, giving 16, 12 and 9 km/hr in the three hours.
• The distances are 16, 12 and 9 km, adding to 37 km over three hours.
• 37 ÷ 3 = 12.333…, printed in the paper as 12.33 km/hr.
• Repeated percentage change is geometric, so the absolute fall shrinks each period — 4 km/hr and then 3 km/hr here.

• Subtracting a fixed amount each hour instead of a fixed percentage of the current value.
• Averaging the three speeds without checking that each was held for the same time.
• Rounding 12.333 up to 13 when the paper offers the exact two-decimal value.

Asked as a short multi-stage speed item where the wording of the reduction, not the arithmetic, is what separates the options.

• practice — not a real PYQ

  A machine's output falls by 20% every hour. If it produces 100 units in the first hour, how many does it produce in the third hour?

  • (a)60
  • (b)64
  • (c)72
  • (d)80

  Answer(b) 64 — the output goes 100, then 100 × 0.8 = 80, then 80 × 0.8 = 64.

• practice — not a real PYQ

  A man walks 6 km in the first hour and 4 km in the second hour. His average speed for the two hours is

  • (a)4.5 km/hr
  • (b)5 km/hr
  • (c)5.5 km/hr
  • (d)6 km/hr

  Answer(b) 5 km/hr — 10 km covered in 2 hours.