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?

Let the balls faced by Lara be $x$.

Runs scored by Sachin are $10$ more than balls faced by Lara.

So,

Sachin's runs $=x+10$

Sachin faced $10$ balls less than Lara.

So,

Sachin's balls $=x-10$

Also, Sachin's balls are $5$ less than Lara's runs.

So,

Lara's runs $=x-5$

Together they scored $105$ runs.

Therefore,

$(x+10)+(x-5)=105$

$2x+5=105$

$2x=100$

$x=50$

So, Sachin's runs are:

$x+10=50+10=60$