In a test match in cricket, the scores of Rohit and Virat in the first

Question

In a test match in cricket, the scores of Rohit and Virat in the first innings are in the ratio of 13 : 16. In the second innings as compared to the first innings, their scores increase by the same number of runs and their scores are in the ratio of 53 : 62 in the second innings. What is the ratio of Virat’s second innings score and his first innings score?

A. 30:23
B. 31:24
C. 5:4
D. 31:25
E. 31:26

A. 30:23
B. 31:24
C. 5:4
D. 31:25
E. 31:26

Nabneet · Accepted Answer

Answer B

espere · Answer

Could you please show how you solved the equasion before the => mark?

Regor60 · Answer

Since the ratio in the 2nd inning is fully reduced it makes sense to at least check whether these are the absolute scores.

So can we reduce 62 by an amount that yields a multiple of 16 and will it also yield a multiple of 13 when subtracted from 53 ?

14 subtracted from 62 yields 48, multiple of 16 and 14 subtracted from 53 yields 39, a multiple of 13.

39/48 = 13/16, so that works!

So his ratio is then:

62/48 = 31/24

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Nabneet · Answer

I just went the long route.
cross multiply and solve the equation.

JeffTargetTestPrep · Answer

The ratio of Rohit’s score to Virat’s score in the first innings:

13x : 16x, where x is the ratio multiplier for the first innings.

The ratio of Rohit’s score to Virat’s score in the second innings:

(13x + d) : (16x + d) = 53y : 62y, where d is their identical score increase and y is the ratio multiplier for the second innings.

The numerators in the ratios represent the same actual values, so we have:

13x + d = 53y => d = 53y – 13x

The denominators in the ratios represent the same actual values, so we have:

16x + d = 62y  
16x + 53y – 13x = 62y
3x = 9y
x = 3y

So, the ratio of Virat’s second innings score to Virat’s first innings score is:

62y/(16x) = 62y/(16 ) =
62y/(48y) = 62/48 =
31/24

Answer: B

finisher009 · Answer

The key is to notice that the difference between the parts of the ratio changes.

1. Analyze the Ratios and Their Differences:
• First innings ratio (Rohit:Virat) is 13:16. The difference is 16 - 13 = 3 parts.
• Second innings ratio is 53:62. The difference is 62 - 53 = 9 parts.

2. Equalize the Differences: The difference in the second innings (9) is three times the difference in the first innings (3). This means the actual scores are based on a version of the first ratio that has been scaled up by 3.
• Scale the first ratio by 3: (13 * 3) : (16 * 3) -> 39 : 48.
• This tells us Virat’s first innings score is a multiple of 48.

3. Find the Final Ratio: Now compare Virat’s scaled first innings part (48) to his second innings part (62).
• The question asks for the ratio of Virat’s second innings score to his first innings score.
• Ratio = 62 : 48
• Simplify by dividing both by 2: 31 : 24

This matches answer B.

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