In an innings of a cricket match, three players A, B and C scored a total of 361 runs. If the ratio of the number of runs scored by A to that scored by B and also number of runs scored by B to that scored by C be 3 : 2, the number of runs scored by A was

### Concept & Combining Identical Ratios Similar to standard ratio combination, when $A:B$ and $B:C$ are given the exact same proportion, we scale them to match the common term (B) to create a unified $A:B:C$ ratio to distribute the total. $$ \text{Combined Ratio: } (A \times B_{new}) : (B \times B_{new}) : (C \times C_{new}) $$ ### Step-by-Step Solution 1. **Identify the individual ratios:** $A : B = 3 : 2$ $B : C = 3 : 2$ 2. **Equate the common term (B):** The values for B in the two ratios are 2 and 3. Their LCM is 6. Scale the first ratio by multiplying by 3: $A : B = (3 \times 3) : (2 \times 3) = 9 : 6$ Scale the second ratio by multiplying by 2: $B : C = (3 \times 2) : (2 \times 2) = 6 : 4$ 3. **Form the combined ratio:** $A : B : C = 9 : 6 : 4$ 4. **Calculate A's runs:** Total ratio parts = $9 + 6 + 4 = 19$. Total runs scored = 361. A's runs = $\frac{9}{19} \times 361$ $361 \div 19 = 19$ (Note: $19^2 = 361$) A's runs = $9 \times 19 = 171$ ### Exam Strategy & Shortcut Recognize that 361 is the square of 19 ($19 \times 19$). When you see the sum of the ratio parts is 19 ($9+6+4$), the math instantly simplifies. The multiplier is exactly 19. A's share is just $9 \times 19 = 171$. Knowing squares up to 25 gives you a massive speed advantage in aptitude tests. ### Common Pitfall A common misinterpretation of the phrasing "and also" is assuming all three scored in a $3:2:1$ or similar sequence, rather than treating them as two separate $3:2$ overlapping relationships. ### Final Answer Therefore, the correct answer is **171**.