Question
Download Solution PDFComprehension
Directions: Study the following information carefully and answer the questions.
Following information shows the data regarding number of runs scored by A, B, C and D in Test, ODI and T20 matches.
The runs scored by C in T20 matches are 40 more than one-third of the runs scored by A in Test matches. The average of the total runs scored by A is 230, and the runs scored by him in ODIs are 55% of the runs scored in Test matches. In ODIs, D scored 42 runs fewer than C, while B scored exactly one-third of the runs scored by A, and the total sum of runs scored by B, C, and D in ODIs is 471. In Test matches, D scored 4 times the runs he scored in ODIs, while C scored 8 more runs than D in the same format. In T20 matches, C and D scored 180 and 95 runs respectively. The runs scored by C in Test matches are twice the runs scored by B in the same format. The runs scored by B in T20 matches are one-seventh of the runs scored by him in ODIs.
If a player is randomly selected from the top two highest total run-scorers, what is the probability that their Test runs exceed 700?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGeneral Solution:
Let the runs scored by A in Test matches = x
Then:
ODIs = 55% of x = 0.55x
T20s = Total of A’s average = 230 × 3 = 690
So, A's T20 runs = 690 − (x + 0.55x) = 690 − 1.55x
C's T20 runs = 40 more than one-third of A’s Test runs:
C's T20 = (1/3) × x + 40
We're told:
C and D scored 180 and 95 runs respectively in T20
So:
C's T20 = 180 = (1/3)x + 40
⇒ (1/3)x = 140 ⇒ x = 420
Now that we know x = 420, substitute values for A:
A's Test = 420
A's ODI = 0.55 × 420 = 231
A's T20 = 690 − (420 + 231) = 39
ODI data:
C's ODI = c
D's ODI = c − 42
B's ODI = (1/3) × A ODI = (1/3) × 231 = 77
Total ODI by B, C, D = 471
⇒ 77 + c + (c − 42) = 471
⇒ 2c + 35 = 471 ⇒ 2c = 436 ⇒ c = 218
So:
C's ODI = 218
D's ODI = 176
B's ODI = 77
Test Match Data:
D's Test = 4 × D ODI = 4 × 176 = 704
C's Test = D's Test + 8 = 712
Also:
C's Test = 2 × B's Test ⇒ B's Test = 712 / 2 = 356
T20 Data:
C's T20 = 180 (already given)
D's T20 = 95
B's T20 = (1/7) × B ODI = (1/7) × 77 = 11
| Player | Test | ODI | T20 |
|---|---|---|---|
| A | 420 | 231 | 39 |
| B | 356 | 77 | 11 |
| C | 712 | 218 | 180 |
| D | 704 | 176 | 95 |
Calculations:
Identify top 2 highest total run-scorers from total runs:
C: 1110
D: 975
Among these two, who satisfies:
Test runs > 700 and ODI runs ≥ 200
C:
Test = 712 (> 700)
ODI = 218 (≥ 200)
C qualifies
D:
Test = 704 (> 700)
ODI = 176 (< 200)
D does not qualify
Probability:
Only 1 player (C) out of 2 satisfies both conditions.
So, Required probability = 1/2
Thus, the correct answer is 1/2.
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