# Equations 1/1

The basic rules of forming equations as follow.
1. 'a' exceeds 'b' by 100 ⇒ a – b = 100
2. 'a' is twice that of 'b'  ⇒ $$\dfrac{a}{b} = 2$$ or $a = 2b$
3.  'a' is 25% less than 'b' ⇒ $$a = \left( {100 - 25} \right)\% b$$ or $$a = 75\% \left( b \right)$$
4.  'a' is 20% more than 'b' ⇒ $$a = 120\% \left( b \right)$$
5. $${a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)$$
6. $${\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}$$
7. $${\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}$$
8. $${\left( {a + b} \right)^2} = {\left( {a - b} \right)^2} + 4ab$$

## Exercise

1. $\displaystyle\frac{4}{5}$ of a number exceeds its $\displaystyle\frac{2}{3}$ by 8. The number is
a. 30
b. 60
c. 90
d. None of these

2. If 1 is added to the denominator of fraction, the fraction becomes $\displaystyle\frac{1}{2}$. If 1 is added to the numerator, the fraction becomes 1. The fraction is
a. $\displaystyle\frac{4}{7}$
b. $\displaystyle\frac{5}{9}{\rm{ }}$
c. $\displaystyle\frac{2}{3}$
d. $\displaystyle\frac{{10}}{{11}}$

3. The sum of two numbers is twice their difference. If one of the numbers is 10, the other number is
a. ${\rm{3}}\displaystyle\frac{1}{3}$
b. 30
c. ${\rm{ - 3}}\displaystyle\frac{1}{3}$
d. a or b

4. The sum of squares of two numbers is 80 and the square of their difference is 36. The product of the two numbers is.
a. 22
b. 44
c. 58
d. 116

5. 11 times a number gives 132. The number is
a. 11
b. 12
c. 13.2
d. None

6. If 1/5th of a number decreased by 5 is 5, then the number is
a. 25
b. 50
c. 60
d. 75

7. The difference of two numbers is 2 and the difference of their squares is 12. The sum of the number is
a. 6
b. 8
c. 10
d. 22

8. The sum of two numbers is 29 and the difference of their squares is 145. The difference between the number is
a. 13
b. 5
c. 8
d. 11