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 the runs scored by A in ODIs are redistributed equally to B and C in the ratio 3:4, and D’s T20 runs are doubled, what will be the new difference between the total runs of the highest and lowest scorers?
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:
Redistribution of A's ODI runs
A's ODI = 231 runs redistributed to B and C in the ratio 3:4.
Total parts = 3 + 4 = 7
B gets = (3/7) × 231 = 99
C gets = (4/7) × 231 = 132
So, update B's and C’s ODI:
B new ODI = 77 + 99 = 176
C new ODI = 218 + 132 = 350
A ODI = 0 (since it’s fully redistributed)
Double D’s T20 runs
D original T20 = 95
New T20 = 95 × 2 = 190
New Total Runs:
| Player | Test | ODI | T20 | New Total |
|---|---|---|---|---|
| A | 420 | 0 | 39 | 459 |
| B | 356 | 176 | 11 | 543 |
| C | 712 | 350 | 180 | 1242 |
| D | 704 | 176 | 190 | 1070 |
Difference between the highest and lowest scorers
Highest = C = 1242
Lowest = A = 459
Difference = 1242 − 459 = 783
Thus, the correct answer is 783.
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