Question:
Runs scored by Sachin in a charity match are 10 more than the balls faced by Lara. The number of balls faced by Sachin is 5 less than the runs scored by Lara. Together, they have scored 105 runs and Sachin faced 10 balls less than the balls faced by Lara. How many runs were scored by Sachin?
Runs scored by Sachin in a charity match are 10 more than the balls faced by Lara. The number of balls faced by Sachin is 5 less than the runs scored by Lara. Together, they have scored 105 runs and Sachin faced 10 balls less than the balls faced by Lara. How many runs were scored by Sachin?
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Assign distinct variables for each unknown and write down equations step-by-step to avoid confusion.
Updated On: Jun 12, 2026
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Translate the word problem into a system of algebraic equations and solve for the variable representing Sachin's runs.
Step 2: Detailed Explanation:
1. Let \( S_r \) = Sachin's runs, \( S_b \) = Sachin's balls, \( L_r \) = Lara's runs, \( L_b \) = Lara's balls.
2. From the problem:
- \( S_r = L_b + 10 \)
- \( S_b = L_r - 5 \)
- \( S_r + L_r = 105 \)
- \( S_b = L_b - 10 \)
3. Substituting the equations:
- From \( S_b = L_b - 10 \) and \( S_b = L_r - 5 \), we get \( L_b - 10 = L_r - 5 \), so \( L_b = L_r + 5 \).
- Substitute \( L_b \) into \( S_r = L_b + 10 \): \( S_r = (L_r + 5) + 10 = L_r + 15 \).
4. Now use \( S_r + L_r = 105 \):
- \( (L_r + 15) + L_r = 105 \)
- \( 2L_r = 90 \implies L_r = 45 \).
- \( S_r = 45 + 15 = 60 \).
Step 3: Final Answer:
Sachin scored 60 runs.
Translate the word problem into a system of algebraic equations and solve for the variable representing Sachin's runs.
Step 2: Detailed Explanation:
1. Let \( S_r \) = Sachin's runs, \( S_b \) = Sachin's balls, \( L_r \) = Lara's runs, \( L_b \) = Lara's balls.
2. From the problem:
- \( S_r = L_b + 10 \)
- \( S_b = L_r - 5 \)
- \( S_r + L_r = 105 \)
- \( S_b = L_b - 10 \)
3. Substituting the equations:
- From \( S_b = L_b - 10 \) and \( S_b = L_r - 5 \), we get \( L_b - 10 = L_r - 5 \), so \( L_b = L_r + 5 \).
- Substitute \( L_b \) into \( S_r = L_b + 10 \): \( S_r = (L_r + 5) + 10 = L_r + 15 \).
4. Now use \( S_r + L_r = 105 \):
- \( (L_r + 15) + L_r = 105 \)
- \( 2L_r = 90 \implies L_r = 45 \).
- \( S_r = 45 + 15 = 60 \).
Step 3: Final Answer:
Sachin scored 60 runs.
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