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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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Q:

$\frac{7}{8} o f 448 + \frac{6}{7} o f 3374 = ?$

A) 3084	B) 3184
C) 3584	D) None of these

Answer & Explanation Answer: D) None of these

Explanation:

$\frac{7}{8} x 448 + \frac{6}{7} x 3374 = > 392 + 2892 = > 3284$

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Q:

$2660 o f \frac{1}{7} o f \frac{1}{2} o f \frac{1}{9.5} o f \frac{1}{2} = ?$

A) 1	B) 10
C) 0.1	D) 100

Answer & Explanation Answer: B) 10

Explanation:

$\frac{1}{7} x \frac{1}{2} x \frac{1}{9.5} x \frac{1}{2} x 2660 = \frac{2660}{266} = 10$

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Q:

The average of ages of threee persons is 60 years . Those ages are in the proportion of 1:2:3. what is the age of the youngest one among them?

Answer

Suppose the ages of three persons are x, 2x, 3x years respectively

$\Rightarrow \frac{x+2x+3x}{3}=60$

$\Rightarrow 6x=180$

$\Rightarrow x=30$

Hence, age of youngest person = x = 30 years.

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Subject: Problems on Ages

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