Answer is (d)

Let the original fraction is \(\displaystyle \frac{a}{b}\)

Numerator is increased by 600%,

\(\displaystyle a\to a+\frac{{600}}{{100}}\times a=7a\)

Denominator is increased by 200%,

\(\displaystyle b\to b+\frac{{200}}{{100}}\times b=3b\)

According to the question \(\displaystyle \frac{{7a}}{{3b}}=\frac{{14}}{5}\)

Therefore, \(\displaystyle \frac{a}{b}=\frac{{14\times 3}}{{5\times 7}}=\frac{{42}}{{35}}\)

or  \(\displaystyle \frac{a}{b}=\frac{6}{5}\)

Answer is (e)

Let fraction be  \(\displaystyle \frac{x}{y}\)

According to the question \(\displaystyle \frac{{x\times 120\%}}{{y\times 125\%}}=\frac{3}{5}\)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{x}{y}=\frac{3}{5}\times \frac{{125}}{{120}}=\frac{5}{8}\)

Answer is (b)

Rohan’s marks = 75

Sonia’s marks = 65

Rohit’s marks = 65 + 45 = 110

Raman’s marks = 110 – 25 = 85

Ravi got marks = 85 + 34 = 119

Total maximum marks = 119 + 50 + 169

Percentage of Ravi’s marks= \(\displaystyle \frac{{119}}{{169}}\times 100\%=70.4\%=70\%\)

Answer is (b)

Let total monthly income of Mr. Alok be ₹ x.

According to question,

Therefore, \(\displaystyle x\times \frac{{50}}{{100}}\times \frac{{15}}{{100}}=900\)

x = ₹ 12000

Hence, monthly income of Mr. Alok = ₹12000

Answer is (b)

Let the total number of original inhabitants be x. Then,

(100 – 25)% of (100 –10)% of x = 4050

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{75}}{{100}}\times \frac{{90}}{{100}}\times x=4050\)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{27}}{{40}}x=4050\)

\(\displaystyle \Rightarrow \)\(\displaystyle x=\frac{{4050\times 40}}{{27}}=6000\)

Number of original inhabitants = 6000.

Answer is (a)

During both the transaction there are profits. So our calculating figures would be 120, 125 and 100. A’s cost is certainly less than C’s selling price

Therefore, Required price = \(\displaystyle 225\times \frac{{100}}{{120}}\times \frac{{100}}{{125}}=150\)

Answer is (a)

N  = R + 30% of R = 1.3 R

R = V – 20% of V = 80% of V = 0.8 V

Therefore, N = 1.3 × 0.8V = 1.04 V

Now, N – V = 1.04 V – V = 0.04 V = ₹800 (given)

Therefore, V = ₹ 20000

Hence, R = 0.8 × 20000 = ₹16000

Answer is (a)

Saving percentage = (100 – 55) % = 45%

If the income of Barath be ₹ x, then,

\(\displaystyle \frac{{45\times x}}{{100}}=27000\)

\(\displaystyle \Rightarrow \)x = \(\displaystyle x=\frac{{27000\times 100}}{{45}}=60000\)

Answer is (a)

% change in rate = \(\displaystyle \frac{{27-24}}{{24}}\times 100=\frac{{100}}{8}\%\)

For fixed expenditure, % change in consumption

=\(\displaystyle \frac{{\%changeinrate}}{{100+\%changeinrate}}\times 100\)

=\(\displaystyle \frac{{100/8}}{{100[1+\frac{1}{8}]}}\times 100=\frac{{100}}{9}\%=11\frac{1}{9}\%\)

Answer is (b)

First number = x

Second number = y

Therefore, \(\displaystyle x\times \frac{{50}}{{100}}=y\times \frac{3}{4}\)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{x}{2}=y\times \frac{3}{4}\)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{x}{y}=\frac{3}{4}\times 2=\frac{3}{2}\)