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Solved Examples

Question 1: Find a number such that the sum of one-fourth part and one-sixth part is 30.
Solution:
Let the number be x

The Problem states that:

$\frac{x}{4} + \frac{x}{6}$ = 30

=> $\frac{6x + 4x}{24}$ = 30

=> $\frac{10x}{24}$ = 30

=> 10x = 30 * 24

=> x = $\frac{30 * 24}{10}$

=> x = 72, is the answer.

Question 2: Find the value of m, when x = 2.

x2 + (m - 5)x + 7 = 0
Solution:
x2 + (m - 5)x + 7 = 0

To find the value of m, Put x = 2

22 + (m - 5)*2 + 7 = 0

=> 4 + 2m - 10 + 7 = 0

=> 1 + 2m = 0

=> 2m = -1

=> m = $\frac{-1}{2}$

Question 3: A father is 6 times older than his son. After 12 years, he will be twice as old as his son. Find the present age of both.

Solution:
Let the present age of the son = x years

Therefore the present age of the father = 6x

After 12 years:

Son's age = x + 12

Father's age = 6x + 12

The problem states:

6x + 12 = 2(x + 12)

=> 6x + 12 = 2x + 24

=> 6x - 2x = 24 - 12

=> 4x = 12

Divide each side by 4

=> x = 3
Hence
Son's age = 3 years

and father's age = 6 * 3 = 18 years.