Question

one fourth of a number is 30 less than the number itself.The value of the number is

Answer 1

Let the number be x
1/4 x=30
So x=30*4
=>x=120

Answer 2

The number is 40

Given :

One fourth of a number is 30 less than the number itself.

To find :

The number

Solution :

Step 1 of 2 :

Form the equation

Let the required number = x

Now it is given that one fourth of a number is 30 less than the number itself.

By the given condition

$\displaystyle \sf{ \frac{x}{4} = x - 30 }$

Step 2 of 2 :

Find the number

$\displaystyle \sf{ \frac{x}{4} = x - 30 }$

$\displaystyle \sf{ \implies x - \frac{x}{4} = 30 }$

$\displaystyle \sf{ \implies \frac{4x - x}{4} = 30 }$

$\displaystyle \sf{ \implies \frac{3 x}{4} = 30 }$

$\displaystyle \sf{ \implies x = 30 \times \frac{4}{3} }$

$\displaystyle \sf{ \implies x = 40}$

Hence the required number = 40

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