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?

• A. 40
• B. 50
• C. 60
• D. 120

Hint:

Assign distinct variables for each unknown and write down equations step-by-step to avoid confusion.

Answer 1

The Correct Option is C

Step 1: Name the four quantities.
Let Sachin's runs and balls be $S_r, S_b$, and Lara's runs and balls be $L_r, L_b$.
Step 2: Translate each sentence.
Sachin's runs are 10 more than Lara's balls: $S_r = L_b + 10$. Sachin's balls are 5 less than Lara's runs: $S_b = L_r - 5$. Together they scored 105: $S_r + L_r = 105$. Sachin faced 10 balls fewer than Lara: $S_b = L_b - 10$.
Step 3: Link Lara's runs and balls.
From $S_b = L_r - 5$ and $S_b = L_b - 10$, set them equal: $L_r - 5 = L_b - 10$, so $L_b = L_r + 5$.
Step 4: Express Sachin's runs in terms of Lara's runs.
Substitute into $S_r = L_b + 10$: $S_r = (L_r + 5) + 10 = L_r + 15$.
Step 5: Use the total runs.
Put this into $S_r + L_r = 105$: $(L_r + 15) + L_r = 105$, so $2L_r = 90$ and $L_r = 45$.
Step 6: Compute Sachin's runs.
Then $S_r = 45 + 15 = 60$.
\[ \boxed{60} \]