Average Test-7 (Complete Revision)

Answer: Option A

Explanation

Here, new mean  $\overline{{\mathrm{x}}_2}$

$$\begin{gathered} =\frac{{\mathrm{x}}_1+ {\mathrm{x}}_2+....+{\mathrm{x}}_{\mathrm{n}}}{\mathrm{n}}+\frac{1+2+3+...+\mathrm{n}}{\mathrm{n}} \\ =\overline{{\mathrm{x}}_1}+\frac{\mathrm{n}\left(\mathrm{n}+1\right)}{2\mathrm{n}} \\ =\overline{{\mathrm{x}}_1}+\frac{\mathrm{n}+1}{2} \\ =\overline{{\mathrm{x}}_2}-\overline{x_1}=\overline{ {\mathrm{x}}_1}+\frac{\mathrm{n}+1}{2}-\overline{{\mathrm{x}}_1} \\ =\frac{\mathrm{n}+1}{2} \end{gathered}$$

Hence, Option A is correct

Answer: Option B

Explanation

According to the question,

The number of points the team scored was 

= 8×84-92+85

= 672-92+85= 665

Hence, Option B is correct.

Answer: Option D

Explanation

According to the question,

Required fraction

$$\begin{gathered} = \frac{1}{4}+\frac{1}{6}-3\times \frac{1}{12} \\ = \frac{1}{4}+\frac{1}{6}-\frac{1}{4} \\ =\frac{1}{12} \end{gathered}$$

Hence, Option D is correct.

Answer: Option A

Explanation

Given,

Total age of five members = 5×24

=120 yr

8 yr ago, total age of the family = 120-40

= 80 yr

∴ Average = $\frac{80}{4}$= 20 yr

Hence, Option A is correct.

Answer: Option C

Explanation

According to the question,

A=30 km/h, B=15 km/h, C=10 km/h

we know the formula,

Average speed= $\frac{3\mathrm{ABC}}{\text{AB+BC+CD}}$

∴ Required average speed

$$\begin{gathered} = \frac{3\times 30\times 15\times 10}{30\times 15+15\times 10+10\times 30} \\ =\frac{13500}{900} \end{gathered}$$

 = 15 km/h

Hence, Option C is correct.