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11 Sep 2025, 02:13
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Difficulty:
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67% (02:32) correct
33%
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wrong
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The ratio of runs scored by Dhoni and Virat in the first match is 9:7, and in the next match is 11:8. If the total runs scored by Virat in these two matches is 190, which is 65 less than the runs scored by Dhoni, how many runs did Virat score in the first match?
A. 56
B. 90
C. 70
D. 84
E. 105
Screenshot 2025-09-11 2.39.37 PM.png [ 59.76 KiB | Viewed 623 times ]
A. 56
B. 90
C. 70
D. 84
E. 105
Attachment:
Screenshot 2025-09-11 2.39.37 PM.png [ 59.76 KiB | Viewed 623 times ]
11 Sep 2025, 04:06
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Naseeb007
\(\frac{D1 }{ V1} = \frac{9k}{7k}\)
\(\frac{D2 }{ V2} = \frac{11a}{8a}\)
Virat's score in both matches => \(7k + 8a = 190\) ...........(i)
It is 65 less than Dhoni's total score => \(7k + 8a = (Dhoni's total score) - 65\)
=> \(7k + 8a = (9k + 11a) - 65\) ................(since Dhoni's score in both matches is 9k + 11a)
=> \(2k + 3a = 65\) ................... (ii)
Solving (i) and (ii)
\(a = 15\), and \(k = 10\)
Virat's score in first match \(= 7k = 70\)
Answer C.
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11 Sep 2025, 07:51
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Here we can use divisibility since the number of runs will be an integer
Virat's runs scored in the first match must be divisible by 7 and his runs scored in the second match that must be divisible by 8 (given the ratios provided)
B. 90 is impossible since not divisible by 7
Of the other options we can work out from the total 190 how many would be scored in the second match:
A. 56 --> 190 - 56 = 134 not divisible by 8
C. 70 --> 190 - 70 = 120 is divisible by 8
D. 84 --> 190 - 84 = 106 not divisible by 8
E. 105 --> 190 - 105 - 85 not divisible by 8
Only possible answer is C
Virat's runs scored in the first match must be divisible by 7 and his runs scored in the second match that must be divisible by 8 (given the ratios provided)
B. 90 is impossible since not divisible by 7
Of the other options we can work out from the total 190 how many would be scored in the second match:
A. 56 --> 190 - 56 = 134 not divisible by 8
C. 70 --> 190 - 70 = 120 is divisible by 8
D. 84 --> 190 - 84 = 106 not divisible by 8
E. 105 --> 190 - 105 - 85 not divisible by 8
Only possible answer is C
