Question

Ravi obtained $70$ and $75$ marks in first two unit tests. Then, the minimum marks he should get in the third test to have an average of at least $60$ marks, are

Answer 1

Let Ravi got $x$ marks in third unit test.
$\therefore $ Average marks obtained by Ravi
$=\frac{\text{Sum of marks in all tests}}{\text{Number of tests}} = \frac{70 +75 +x}{3}$
$= \frac{145 +x}{3}$
Now, it is given that he wants to obtain an average of at least $60$ marks.
At least $60$ marks means that the marks should be greater than or equal to $60$. i.e.
$ \frac{145 +x}{3} \ge60$
$\Rightarrow 145 +x \ge60 \times3$
$\Rightarrow 145 +x \ge180$
Now, transferring the term $145$ to $R.H.S$.,
$x \ge180 -145$
$\Rightarrow x \ge35$
i.e. Ravi should get greater than or equal to $35$ marks in third unit test to get an average of at least $60$ marks.
$\therefore $ Minimum marks Ravi should get $= 35$.