JEE Main & Advanced Mathematics Equations and Inequalities Question Bank Self Evaluation Test - Linear Inequalities

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

A) 45

B) 35

C) 25

D) None of these

Correct Answer: B

Solution :

[b] Let Ravi got x marks in third unit test.

\[\therefore \] Average marks obtained by Ravi

\[=\frac{Sum\text{ }of\text{ }marks\text{ }in\text{ }all\text{ }tests}{Number\text{ }of\text{ }tests}\]

\[=\frac{70+75+x}{3}=\frac{145+x}{3}\]

Now, it is given that he wants to obtain an average of at least 60 narks.

At least 60 marks means that the marks should be greater than or equal to 60.

\[i.e.\frac{145+x}{3}\ge 60\]

\[\Rightarrow 145+x\ge 60\times 3\]

\[\Rightarrow 145+x\ge 180\]

Now, transferring the term 145 to R.H.S.,

\[x\ge 180-145\Rightarrow x\ge 35\]

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.