Question

Khilona earned scores of $97,73$ and $88$ respectively in her first three examinations. If she scored $80$ in the fourth examination, then her average score will be

• A. Increased by $1$
• B. Increased by $1.5$
• C. Decreased by $1$
• D. Decreased by $1.5$

Answer 1

The correct option is D

Decreased by $1.5$

Step 1: Find the average marks before fourth examination

$\mathrm{Average}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{Marks}\mathrm{Obtained}\mathrm{in}\mathrm{all}\mathrm{Examinations}}{\mathrm{Number}\mathrm{of}\mathrm{Examinations}}$

Average marks before fourth examination $=$ Average in first three examinations

$\Rightarrow$Average marks before fourth examination $=$ $\frac{97+73+88}{3}=\frac{258}{3}$

$\Rightarrow$Average marks before fourth examination $=$ $86$ marks

Step 2: Find the average marks after fourth examination

Average marks after fourth examination $=$$\frac{97+73+88+80}{4}=\frac{338}{4}$

$\Rightarrow$Average marks after fourth examination$=$ $84.5$ marks

Step 3: Find the difference between average marks before and after fourth examination

Difference in average marks before and after fourth examination$=86-84.5=1.5$

Thus, if Khilona scored $80$ in the fourth examination, then her average score will be decreased by $1.5$

Therefore, option D is the correct answer.