The average runs of a cricket player of 10 innings were 40. How many runs must she make in her next inning so as to increase her average of runs by 3?

73

Average of 10 innings = $\frac{Total\; score\; in\; 10\; innings}{10}$

⇒ $\frac{Total\; score\; in\; 10\; innings}{10}$ = 40

⇒ Total score in 10 innings = 40 x 10 = 400

Let the score in 11th inning be $x$,

New average = 40 + 3 = 43

⇒ $\frac{Score\; of\; 10\; innings\; +\; x}{11}$ = 43

⇒ 400 + $x$ = 43 x 11

⇒      $x$      = 473 - 400  = 73

The runs that the player must make in the next inning is 73.