Simplification-Test 9 (Complete Revision)

Answer: Option E

Explanation

According to the question

let Rahul's marks in mathematics = x

$$\begin{gathered} = \frac{1}{3x}-\frac{1}{2y}=30 \\ = 2x-3y=180 ---\left(1\right) \\ Also given \\ = x+4=480 ---\left(2\right) \\ By solving Equation \left(1\right) and \left(2\right), \\ we get, \\ = x = 324 and y = 156 \end{gathered}$$

Hence, Option E is correct.

Answer: Option D

Explanation

Let consider the monthly income = x

Amount spend on house rent = $\frac{2x}{5}$

Amount spend on food = $\frac{3x}{10}$

Amount spend on conveyance =$\frac{x}{8}$

After expenditure, the left amount = 2800

According to the question,

$$\begin{gathered} = x-\left(\frac{2x}{5}+\frac{3x}{10}+\frac{x}{8}\right)=2800 \\ =x-\left(\frac{\left(16x+12x+5x\right)}{40}\right)=2800 \\ =x-\frac{33x}{40}=2800 \\ =\frac{(40x-33x)}{40}= 2800 \\ =\frac{7x}{40}=2800 \\ = 7x=2800\times 40 \\ =x=2800\times \frac{40}{7} \\ =x=400\times 40 \\ =x=16000 \end{gathered}$$

Expenditure on food$=3\times \frac{16000}{10}=4800$

Expenditure on conveyance =$\frac{x}{8}=1\times \frac{16000}{8}=2000$

Expenditure on food and conveyance together

= (4800+2000) = 6800

Hence, Option D is correct.

Answer: Option B

Explanation

Let Mr. Arun is on tour for x days

Then, According to the question

Difference in expenses per day and extended tour is 

$$\begin{gathered} = \frac{360}{x}-\frac{360}{\left(x+4\right)}=3 \\ =360 \left(\frac{1}{x}-\frac{1}{\left(x+4\right)}\right)=3 \\ =\left(\frac{1}{x}-\frac{1}{\left(x+4\right)}\right)=\frac{3}{360} \\ =\left(\frac{1}{x}-\frac{1}{\left(x+4\right)}\right)=\frac{1}{120} \\ =\left(\frac{x+4-x}{x\left(x+4\right)}\right)=\frac{1}{120} \\ =\left(\frac{4}{x^2+4x}\right)=\frac{1}{120} \\ =x^2+4x=4\times 120 \\ =x^2+4x=480 \\ =x^2+4x-480=0 \\ =x^2+24x-20x-480=0 \\ =\left(x+4\right) \left(x-20\right)=0 \\ \therefore x=20 \end{gathered}$$

(We ignore the '-ve' value of 'x')

i.e, Because day's cannot be negative.

Answer: Option D

Explanation

According to the question,

Let at present, there are 'C' men, then number of women = 5c

Before the men had left,

Number of men = c+45 and 

Number of women = 5c

∴ c+45=2×5c

= 9c=45

= c = $\frac{45}{9}$=5

Hence, number of women in the beginning

= 5c+15=5×5+15

= 25+15 =40

∴ Double of the women = 40×2=80

Answer: Option A

Explanation

Given that,

$$\begin{gathered} =\frac{2}{5}=0.4, = \frac{3}{8}=0.375 \\ =\frac{4}{9}=0.44, \frac{5}{13}=0.38 \\ =\frac{6}{11}=0.54 \end{gathered}$$

$Ascending order is =\frac{3}{8}, \frac{5}{13}, \frac{2}{5}, \frac{4}{9}, \frac{6}{11}$

So, the fourth value will be $\frac{4}{9}$.

Hence, Option A is correct.