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Q:

In an election, there were two candidates only. The candidate who got 62% of the total votes polled and was elected by a majority of 192 votes. The total number of votes polled was?

Answer

Suppose total votes polled is x

$\inline \Rightarrow$ $\inline \frac{62x}{100}=\frac{38x}{100}+192$

$\inline \Rightarrow \frac{62x}{100}-\frac{38x}{100}=192$

$\inline \Rightarrow \frac{24x}{100}=192\Rightarrow x=800$

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Subject: Percentage

Q:

A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder?

Answer

Number = ( 779 x a) + 47, where "a" is the quotient

= (19 x 41 x a) + (19 x 2) + 9

= 19 x (41a + 2) + 9

= 19 x (New quotient) + 9

$\inline \fn_jvn \therefore$ Required remainder = 9

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Subject: Numbers

Q:

Simplify the following equation.

$\frac{19}{43} + \frac{1}{(2 + \frac{1}{3 + \frac{1}{1 + \frac{1}{4}}})}$

A) 43/19	B) 1
C) 38/19	D) None of these

Answer & Explanation Answer: D) None of these

Explanation:

After solving we get,

62/931.

None of the options satisfy.

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Q:

Simplify

$\frac{1 . 5^{3} + 4 . 7^{3} + 3 . 8^{3} - 3 x 1.5 x 4.7 x 3.8}{1 . 5^{2} + 4 . 7^{2} + 3 . 8^{2} - 1.5 x 4.7 - 4.7 x 3.8 - 1.5 x 3.8}$

A) 6	B) 8
C) 10	D) 12

Answer & Explanation Answer: C) 10

Explanation:

Apply $\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a^{2} + b^{2} + c^{2} - a b - b c - c a} = a + b + c$

Hence the answer is 1.5 + 4.7 + 3.8 = 10.

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Q:

Simplify and find '?'

$48 \sqrt{?} + 32 \sqrt{?} = 320$

A) 4	B) 8
C) 16	D) 32

Answer & Explanation Answer: C) 16

Explanation:

given

$48 \sqrt{?} + 32 \sqrt{?} = 320$

=> $6 \sqrt{?} + 4 \sqrt{?} = 40$

Now squaring on both sides

=> $36 x ? + 16 x ? + 48 x ? = 1600$

=> 100 x ? = 1600

=> ? = 16

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Q:

$17 \frac{4}{7} + 13 \frac{2}{12} - ? = 11 \frac{2}{3}$

A) 16	B) 17
C) 18	D) 19

Answer & Explanation Answer: D) 19

Explanation:

$17 \frac{4}{7} + 13 \frac{2}{12} - ? = 11 \frac{2}{3}$

$\frac{123}{7} + \frac{158}{12} - ? = \frac{35}{3}$

=> $? = \frac{123}{7} + \frac{158}{12} - \frac{35}{3}$

=> ? = $\frac{1476 + 1106 - 980}{84}$

=> ? = 19.07

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Q:

$142^{2} \div \sqrt{1260.25} = ?$

A) 586	B) 578
C) 568	D) 566

Answer & Explanation Answer: C) 568

Explanation:

$142 x 142 x \frac{1}{\sqrt{1260.25}}$

=> $142 x 142 x \frac{1}{35.5} = 568$

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Q:

$\frac{23 x 12 + 49 x 15}{31^{2} + 50} = ?$

A) 0.5	B) 1
C) 2	D) 3

Answer & Explanation Answer: B) 1

Explanation:

$\frac{276 + 35}{961 + 50} = \frac{1011}{1011} = 1$

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Filed Under: Simplification
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