Simplification-Test 7 (Based on Simplification of Percentages)

Answer: Option B

Explanation

Here, 

$\begin{array}{l}\Rightarrow \text{36\% of 420}-\text{56\% of 350 =?}-\text{94}\\ \\ \Rightarrow \frac{36}{100}\times 420-\frac{56}{100}\times 350=?-94\\ \\ \Rightarrow \text{151.20}-\text{196+ 94 =?}\\ \\ \Rightarrow \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}? =15120+ 94-196}\\ \\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=2452}-\text{196= 49.2}\end{array}$

Hence, Option B is correct.

Answer: Option C

Explanation

Here,

⇒ 14% of 250× ?% of 150=840

It can also be simplified as,

$\begin{array}{l}\Rightarrow \frac{14}{100}\times 250\times x\%of150=840\\ \\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}[ taking x at the place of ?]}\\ \\ \Rightarrow \frac{14}{100}\times 250\times \frac{x}{100}\times 150=840\\ \\ \Rightarrow \frac{3500}{100}\times \frac{x}{100}\times 150=840\\ \\ \Rightarrow x=\frac{840\times 100}{150\times 35}=\frac{24\times 100}{100}=16\end{array}$

Hence, Option C is correct.

Answer: Option E

Explanation

$\begin{array}{l}\text{Here,\hspace{0.17em}}\\ \Rightarrow \text{\hspace{0.17em}350\% of ?}÷\text{50 + 248 = 591}\\ \\ \text{It can also be written as}\\ \\ \Rightarrow \frac{350}{100}\times ?÷50+248=591\\ \\ \text{By putting x at the place of ?}\\ \\ \Rightarrow \text{\hspace{0.17em}\hspace{0.17em}3.5}\times x÷\text{50 + 248 = 591}\\ \\ \Rightarrow \frac{3.5x}{50}+248=591\\ \\ \Rightarrow \frac{3.5x}{50}=591-248=343\\ \\ \Rightarrow \text{3.5}x\text{ = 343}\times \text{50}\\ \\ \Rightarrow \text{x=}\frac{343\times 50}{3.5}=98\times 50=4900\end{array}$

Hence, Option E is correct.

Answer: Option A

Explanation

$\begin{array}{l}\text{Here,}\\ \Rightarrow \frac{1}{2}\text{\hspace{0.17em}of\hspace{0.17em}3842+15\% of ? = 2449}\\ \\ \Rightarrow \frac{1}{2}\times 3842+\frac{15}{100}\times x=2449\\ \\ \Rightarrow \text{1921+}\frac{15}{100}\times x=2449 [\text{put ?}=x]\\ \\ \Rightarrow \frac{15x}{100}=2449-1921\\ \\ \Rightarrow \frac{15x}{100}=528\\ \\ \Rightarrow x=\frac{528\times 100}{15}\\ \\ \Rightarrow x=\frac{528\times 100}{15}=35.2\times 100=3520\end{array}$

Hence, Option A is correct.

Answer: Option D

Explanation

$$\begin{gathered} \begin{array}{l}\text{ Here, }\\ \Rightarrow x\text{\% of 500 = y\% of 300}\\ \\ \text{It can also be written as}\\ \\ \Rightarrow \frac{x}{35}\times 500=\frac{y}{100}\times 300\Rightarrow 5x=3y\\ \\ \Rightarrow \text{ 5}x-3y\text{\hspace{0.17em}=0 \hspace{0.17em}\hspace{0.17em}\_\_\_(i)}\\ \\ \Rightarrow x=\frac{3}{5}y\\ \\ \text{Again, x\% of y\% of 200 = 60}\\ \\ \Rightarrow \frac{x}{100}\times \frac{y}{100}\times 200=60\\ \\ \Rightarrow xy=\frac{60\times 100}{2}\\ \\ \Rightarrow xy=3000\\ \\ \text{Putting \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}x\frac{3}{5}y \Rightarrow \frac{3}{5}y\times y=3000\end{array} \\ \Rightarrow y^2=1000\times 5 \\ \Rightarrow y =50\sqrt{2} \\ and \Rightarrow x=\frac{3}{5}\times 50\sqrt{2}=30\sqrt{2} \end{gathered}$$

Hence, Option D is correct.