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?
Step-by-step Solution:
Let the runs scored by Sachin be \( R_s \) and balls faced be \( B_s \). Let the runs scored by Lara be \( R_l \) and balls faced be \( B_l \). From the problem statement, we have the following equations: 1. \( R_s = B_l + 10 \) 2. \( B_s = R_l - 5 \) 3. \( R_s + R_l = 105 \) 4. \( B_s = B_l - 10 \) From equation (4), substituting into equation (2): \[ B_l - 10 = R_l - 5 \implies R_l = B_l - 5 \] Now substitute \( R_l \) into equation (3): \[ R_s + (B_l - 5) = 105 \implies R_s + B_l = 110 \] From equation (1), we know \( B_l = R_s - 10 \). Substituting this into the new equation: \[ R_s + (R_s - 10) = 110 \] \[ 2R_s - 10 = 110 \] \[ 2R_s = 120 \implies R_s = 60 \] Sachin scored 60 runs.