Answer is (b)

Suppose initialy price per kg of rice is 100 then their expenditure is 4000.

Now their expenditure is only increased by only 10% i.e – 4400.

Increased price of rice = 125.

So new consumption = \(\displaystyle \frac{{4400}}{{125}}=35.2\)

Answer is (c)

Boys = 4x and girls = 7x

Ratio =\(\displaystyle 4x\times \frac{{125}}{{100}}:7x\times \frac{{115}}{{100}}=100:161\)

Alterative method,

Let x be the constant ratio.

Boys : Girls = 4 : 7

Boys : Girls = 4x : 7x

The number of boys is increased by 25%.

25% of 4x = 0.25 x 4x = x

Number of boys now = 4x + x = 5x

The number of girls is increased by 15%.

15% of 7x = 0.15 x 7x = 1.05x

Number of girls now = 7x + 1.05x = 8.05x

New Ratio

Boys : Girls = 5x : 8.05x

Boys : Girls = 100(5x) : 100(8.05x)

Boys : Girls =500x : 805x

Boys : Girls =100x : 161x

Boys : Girls =100 : 161

Answer is (c)

According to question,

\(\displaystyle A\times \frac{{80}}{{100}}=B\times \frac{{50}}{{100}}\)

Therefore, B = \(\displaystyle B=\frac{{A\times 80}}{{100}}1.6A\)

B = 160% of A

x = 160

Answer is (d)

15% of (A + B)= 25% of (A – B)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{15}}{{100}}(A+B)=\frac{{25}}{{100}}(A-B)\)

\(\displaystyle \Rightarrow \)15 (A + B) = 25 (A – B)

\(\displaystyle \Rightarrow \)15 A + 15 B = 25A – 25 B

\(\displaystyle \Rightarrow \)10 A = 40 B

\(\displaystyle \Rightarrow \)A = 4 B

Now, let x% of B is equal to A

Therefore, \(\displaystyle \frac{X}{{100}}\times B=A\to \frac{X}{{100}}\times B=4B\)

x = 400%

Answer is (d)

Since 18% of the students neither play football nor cricket. It means 82% of the students either play football or cricket or both.

Using set theory

\(\displaystyle n(A\cup B)=n(A)+n(B)-n(A\cap B)\)

\(\displaystyle \Rightarrow \)82 = 40 + 50 –\(\displaystyle n(A\cap B)\)

\(\displaystyle \Rightarrow \)\(\displaystyle n(A\cap B)\) =90-82=8

Therefore, 8% students play both games.

Answer is (b)

1 hour 45 minutes = \(\displaystyle 1\frac{3}{4}\) hours= \(\displaystyle \frac{7}{4}\) hours

1 day = 24 hours

Required percent

=\(\displaystyle \frac{{\frac{7}{4}}}{{24}}\times 100\)

=\(\displaystyle \frac{7}{{4\times 24}}\times 100=7.292\%\)

Answer is (a)

\(\displaystyle a\times \frac{{12}}{{100}}=b\times \frac{{80}}{{100}}\)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{b}{a}=\frac{{120}}{{80}}=\frac{3}{2}\)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{b+a}}{{b-a}}=\frac{{\frac{b}{a}+1}}{{\frac{b}{a}-1}}=\frac{{\frac{3}{2}+1}}{{\frac{3}{2}-1}}=\frac{{\frac{5}{2}}}{{\frac{1}{2}}}=5\)

Answer is (a)

\(\displaystyle (A+B)\times \frac{{20}}{{100}}=B\times \frac{{50}}{{100}}\)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{A+B}}{5}=\frac{B}{2}\)

\(\displaystyle \Rightarrow \)2A + 2B = 5B

\(\displaystyle \Rightarrow \)2A = 3B

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{2A}}{B}=3\)

\(\displaystyle \frac{{2A-B}}{{2A+B}}=\frac{{2\frac{A}{B}-1}}{{2\frac{A}{B}+1}}=\frac{{3-1}}{{3+1}}\)

\(\displaystyle \frac{2}{4}=\frac{1}{2}=\frac{{3B-B}}{{3B+B}}=\frac{{2B}}{{4B}}=\frac{1}{2}\)

Answer is (b)

Males = \(\displaystyle 25000\times \frac{4}{5}=20000\)

Females = 5000

Educated males = \(\displaystyle 20000\times \frac{{95}}{{100}}=19000\)

Educated females \(\displaystyle \frac{{5000\times 60}}{{100}}=3000\)

Total educated persons=22000

Therefore, required percent = \(\displaystyle \frac{{22000}}{{25000}}\times 100=88\%\)

Answer is (d)

Let the third number be x,

According to the question;

First number = \(\displaystyle \frac{{20}}{{100}}\times x=\frac{x}{5}\)

Second number = \(\displaystyle \frac{{50}}{{100}}\times x=\frac{x}{2}\)

Therefore, required percentage = \(\displaystyle \frac{{\frac{x}{5}\times 100}}{{\frac{x}{2}}}=\frac{x}{5}\times \frac{2}{x}\times 100=40\%\)