Simplification-Test 8 (Based on Algebraic formulae/Statement simplifications)

Answer: Option C

Explanation

From the above question,

${\text{(76.32)}}^{\text{2}}-{(28.82)}^{\text{2}}\text{=?}$

We can simplify this as,

$\begin{array}{l}{\text{= (76.32)}}^{\text{2}}-{(28.82)}^{\text{2}}\\ \\ \text{= (76.32 + 28.82)(76.32 - 28.82)}\\ \\ \therefore [{\text{a}}^{\text{2}}-{\text{b}}^{\text{2}}\text{=(a+ b)(a}-\text{b)}]\\ \\ \text{= (105.14)×(47.5)= 4994.15}\end{array}$

Hence, Option C is correct.

Answer: Option B

Explanation

Here,

Vijay's mother is left with Rs.600

and $$\begin{gathered} 1-\frac{5}{8}=600\Rightarrow \frac{3}{8}=600 \\ \Rightarrow 1= Rs 600 \\ Now, \frac{2}{3}=1600\Rightarrow 1=2400 \end{gathered}$$

This is 30%  of total money what Abhay had.

So, 30%=2400

$\therefore 100\%=\frac{2400}{30}\times 100= Rs 800$

Hence, Option B is correct.

Answer: Option C

Explanation

Given,

Money spent on paying electricity bill =Rs 6000

Money spent on paying water bill =Rs 750

Money spent on paying telephone bill =Rs 2500

Money spent on paying cable bill =Rs 300

Total amount = Rs 9550

This is 40% of his monthly salary.

$\therefore 100\%=\frac{9550}{40}\times 100=23875$

∴ Annual salary =23875×12=Rs. 286500

Hence, option C is correct.

Answer: Option A

Explanation

$\begin{array}{l}\text{Here, }\\ \text{we can express the given statement as follows}\\ \Rightarrow 24\%\text{\hspace{0.17em}of}\frac{4}{9}{\text{\hspace{0.17em}of\hspace{0.17em}5\hspace{0.17em}of\hspace{0.17em}(27)}}^{\text{2}}\\ \\ =\frac{24}{100}\times \frac{4}{9}\times 5\times 729[\because {27}^2=729]\\ \\ =\frac{24}{100}\times \frac{4}{9}\times 5\times 729\\ \\ =\frac{24\times 4\times 5\times 81}{100}=\frac{24\times 81}{5}\\ \\ =81\times 4.8=388.8\end{array}$

Hence, option A is correct.

Answer: Option A

Explanation

Here, 

The total amount spent

$\begin{array}{l}\text{=}(\frac{591}{3}+\frac{45}{60}\times 780)\text{paise}\\ \\ \text{= (197 + 585) paise}\\ \\ \text{= 782 paise = Rs 7.82}\end{array}$

Hence, option A is correct.