Following table shows runs scored by four batsmen in both innings of a test match. Who is the fastest run scorer in the test match ? Batsman | First Inning: Runs scored | First Inning: Balls faced | Second Inning: Runs scored | Second Inning: Balls faced P | 79 | 91 | 56 | 154 Q | 05 | 12 | 50 | 85 R | 14 | 76 | 61 | 99 S | 37 | 50 | 13 | 55

Correct — option (2), Q.

Fastest scoring means the most runs per ball faced. In cricket this is the strike rate: runs per 100 balls. For the whole test match, add both innings before dividing.

Step 1 — P.
Runs 79 + 56 = 135; balls 91 + 154 = 245
135 ÷ 245 × 100 ≈ 55.1

Step 2 — Q.
Runs 05 + 50 = 55; balls 12 + 85 = 97
55 ÷ 97 × 100 ≈ 56.7

Step 3 — R.
Runs 14 + 61 = 75; balls 76 + 99 = 175
75 ÷ 175 × 100 ≈ 42.9

Step 4 — S.
Runs 37 + 13 = 50; balls 50 + 55 = 105
50 ÷ 105 × 100 ≈ 47.6

Step 5 — compare.
Q 56.7 > P 55.1 > S 47.6 > R 42.9
Fastest run scorer: Q

Q made only 55 runs, fewer than P and R, but scored them at the highest rate per ball.

The idea to remember: a rate over the whole match is total runs ÷ total balls; averaging the two innings' rates can give a different number.

Why the others are wrong

• (1)
  P — Option (1), P, made the most runs, 135, and played the fastest single innings, 79 off 91 balls, about 86.8 per 100.

  But the 154 balls of P's second innings pull the match rate down to 135 ÷ 245 × 100 ≈ 55.1, just below Q's 56.7. Averaging P's two innings rates would give about 61.6 and put P first by mistake.

• (3)
  R — Option (3), R, scored 75 runs off 175 balls, about 42.9 per 100 balls, the slowest of the four.

  R's second innings, 61 off 99, ran at about 61.6 per 100, but the first, 14 off 76, was slow, and the match rate counts both.

• (4)
  S — Option (4), S, scored 37 off 50 balls in the first innings, 74 per 100, the second-fastest single innings in the table.

  The second innings, 13 off 55, brings the match rate to 50 ÷ 105 × 100 ≈ 47.6, below both Q and P.

A rate is one quantity per unit of another: runs per ball, kilometres per hour, rupees per kilogram.

The rate over two parts is the total of the first quantity divided by the total of the second. When both parts have the same base, here the same number of balls, it equals the simple average of the two part-rates; with unequal bases it generally does not.

The combined rate is a weighted average of the part-rates, each weighted by its share of the base. P's slow 154-ball innings weighs more than his quick 91-ball innings.

Key facts

• Strike rate = runs scored ÷ balls faced × 100.
• Match strike rates: P 135/245 ≈ 55.1, Q 55/97 ≈ 56.7, R 75/175 ≈ 42.9, S 50/105 ≈ 47.6.
• A combined rate = total runs ÷ total balls, a weighted average of the innings rates.
• Batting average = runs ÷ number of times dismissed; it is a different measure from strike rate.
• Average speed over a journey = total distance ÷ total time.

Common traps

• Averaging the innings rates. P's innings rates, about 86.8 and 36.4, average about 61.6, but his match rate is 55.1.
• Picking the most runs. P made 135, but fast scoring is about runs per ball, not runs alone.
• Picking the fastest single innings. P's 79 off 91 and S's 37 off 50 were the quickest innings, but the stem asks about the whole test match.

UnlockIAS will link similar questions from RAS Pre 2018 and 2016 here once those papers are published on this site.

• practice — not a real PYQ

  A batter scored 45 runs off 50 balls in the first innings and 15 runs off 100 balls in the second innings. What is the batter's strike rate (runs per 100 balls) for the match ?

  • (a)52.5
  • (b)40
  • (c)60
  • (d)90
  Answer(2) — Total runs 60, total balls 150: 60 ÷ 150 × 100 = 40. Option (1) averages the two innings rates, 90 and 15; option (3) is the total runs, not a rate; option (4) is the first innings' rate alone.
• practice — not a real PYQ

  Four bowlers bowled two spells each. Runs conceded and overs bowled: A: 24 runs in 4 overs, then 18 runs in 2 overs B: 30 runs in 6 overs, then 12 runs in 3 overs C: 20 runs in 2 overs, then 10 runs in 5 overs D: 16 runs in 4 overs, then 35 runs in 5 overs Who conceded the fewest runs per over across both spells ?

  • (a)A
  • (b)B
  • (c)C
  • (d)D
  Answer(3) — Totals: A 42 runs in 6 overs = 7.0; B 42 in 9 ≈ 4.67; C 30 in 7 ≈ 4.29; D 51 in 9 ≈ 5.67. C is lowest.

  Averaging each bowler's two spell rates would wrongly put option (2), B (5 and 4, mean 4.5), ahead of C (10 and 2, mean 6); options (1) and (4) come out lowest under neither method.