Question

The highest score of a cricket player in an innings was $3/11^{th}$ of the total score and the next highest was $3/10^{th}$ of the remaining. If the difference between the two scores was 24 runs, what was the total score?

• A. 390
• B. 410
• C. 420
• D. 440

Hint:

Always express fractions with a common denominator (55 here) to easily subtract them.

Answer 1

The Correct Option is D

Step 1: Concept
Let the total score be $x$.

Step 2: Analysis
Highest score = $(3/11)x$.
Remaining score = $x - (3/11)x = (8/11)x$.
Next highest = $(3/10) \times (8/11)x = (24/110)x = (12/55)x$.

Step 3: Reasoning
Difference: $(3/11)x - (12/55)x = 24$.
Multiply $(3/11)$ by $5/5$ to get $(15/55)x$.
$(15/55)x - (12/55)x = 24 \Rightarrow (3/55)x = 24$
$x = (24 \times 55) / 3 = 8 \times 55 = 440$.

Step 4: Conclusion
The total score was 440. Note: While the text mentioned 410, the official key (2240) and math confirm 440. Final Answer: (D)