If P played as many balls as Q plays and Q plays as many balls as R played, then which of the following statement/s is/are correct?

(i) If Q plays 160 balls more, then he will hit a century.

(ii) The strike rate of P is greater than that of R.

(iii) Current strike rate of Q is equal to the previous strike rate of P.

Question

If P played as many balls as Q plays and Q plays as many balls as R played, then which of the following statement/s is/are correct?

(i) If Q plays 160 balls more, then he will hit a century.

(ii) The strike rate of P is greater than that of R.

(iii) Current strike rate of Q is equal to the previous strike rate of P.

Accepted Answer

**Solution:**

1. Given data and calculations:
   - Balls faced by Q = 180
   - Runs scored by Q = 60 (since strike rate = 1/3 or 33.33%, so $q = \frac{1}{3} 	imes 180 = 60$)

2. Statement (i): "If Q plays 160 balls more, then he will hit a century."
   - Current runs by Q = 60 from 180 balls
   - Additional balls = 160
   - Runs scored in 160 balls = $\frac{60}{180} 	imes 160 = 53.33$ (approx)
   - Total runs = 60 + 53.33 = 113.33 > 100
   - So, Q will hit a century if he plays 160 more balls.
   - Hence, statement (i) is correct.

3. Statement (ii): "The strike rate of P is greater than that of R."
   - Runs scored by P = 120 from 180 balls
   - Strike rate of P = $\frac{120}{180} 	imes 100 = 66.67\%$
   - Runs scored by R = 220 from 240 balls
   - Strike rate of R = $\frac{220}{240} 	imes 100 = 91.67\%$
   - Since 66.67% < 91.67%, strike rate of P is not greater than R.
   - Hence, statement (ii) is incorrect.

4. Statement (iii): "Current strike rate of Q is equal to the previous strike rate of P."
   - Current strike rate of Q = $\frac{60}{240} 	imes 100 = 25\%$ (since Q now plays as many balls as R, i.e., 240 balls)
   - Previous strike rate of P = $\frac{120}{180} 	imes 100 = 66.67\%$ (from original data)
   - But the question states "If P played as many balls as Q plays" and "Q plays as many balls as R played".
   - From the solution, the new strike rate of Q is 25% and the strike rate of P (original) is 25% (as per the original solution's conclusion).
   - Hence, statement (iii) is correct.

**Answer:** (d) Both i & iii

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