Arithmetic aptitude :: Problems on Numbers :: General Questions

• Problems on Numbers - General Questions
• Problems on Numbers - Important Formulas and Facts

Basic Formulae:
1). $(a+b)(a-b)=(a^{2}-b^{2})$.
2). $(a+b)^{2}=(a^{2}+b^{2}+2ab)$.
3). $(a-b)^{2}=(a^2+b^{2}-2ab)$.
4). $(a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2(ab+bc+ca)$.
5). $(a^{3}+b^{3})=(a+b)(a^{2}-ab+b^{2})$.
6). $(a^{3}-b^{3})= (a-b)(a^{2}+ab+b^{2})$.
7). $(a^{3}+b^{3}+c^{3}-3abc)=(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ac)$.
8). When $a+b+c = 0$, then $a^{3}+b^{3}+c^{3}=3abc$.

The difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is :

Answer:

Explanation:

Let the number be $x$.
Then, $x-12=20%$ of $x$
$\Leftrightarrow \frac{4x}{5}=12$
$\Leftrightarrow x = \left(\frac{12 \times 5}{4}\right)=15$.

Find the number which when multiplied by 15 is increased by 196.

Answer:

Explanation:

Let the number be $x$.
Then, $15x-x = 196$
$\Leftrightarrow 14x = 196$
$\Leftrightarrow x = 14$.

A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number ?

Answer:

Explanation:

Let the number be $x$.
Then, $3(2x+9)=75$
$\Leftrightarrow 2x+9 = 25$
$\Leftrightarrow 2x = 16 \Leftrightarrow x = 8$.

If one-third of one-fourth of a number is 15, then three-tenth of that number is :

Answer:

Explanation:

Let the number be $x$.
Then, $\frac{1}{3}$ of $\frac{1}{4}$ of $x=15$
$\Leftrightarrow x = 15 \times 12=180$.
So, required number $=\left(\frac{3}{10} \times 180\right)=54$.

The difference between a number and its three-fifth is 50. What is the number ?

Answer:

Explanation:

Let the number be $x$.
Then, $x-\frac{3}{5}x=50$
$\Leftrightarrow \frac{2}{5}x=50$
$\Leftrightarrow x =\left(\frac{50 \times 5}{2}\right)=125$.

• Problems on Numbers - General Questions