Question

one third of a number exceeds its one fourth by 1. Find the number

Answer 1

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Fractions

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one third of a number exceeds its one fourth by 1. Find the number

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According to the statement ,

Let the number be x

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One third of a number exceeds its one fourth by one .

$\mapsto\:\huge\dfrac{x}{3}\:=\:\huge\dfrac{x}{4}\:+\:1$

This statement can also be written like :

The difference of one third and one fourth of a number gives us one .

Therefore ,

We have $\hookrightarrow \:\huge\dfrac{x}{3}\:-\:\huge\dfrac{x}{4}\:=\:1$

$\\\:$

$\hookrightarrow\:\huge\dfrac{4x\:-\:3x}{12}\:=\:1$

$\\\:$

$\hookrightarrow\huge\:4x\:-\:3x\:=\:1\:\times\:12$

$\\\:$

$\hookrightarrow\huge\:x\:=\:12$

So , hence the required number is 12 .

Hope it helps you dear :)

Answer 2

Solution :-

Let us assume that, the given number is x .

So,

→ (1/3) of x = (x/3)

and,

→ (1/4) of x = (x/4)

given that,

→ (1/3) of x - (1/4) of x = 1

So,

→ (x/3) - (x/4) = 1

→ (4x - 3x)/12 = 1

→ (x/12) = 1

→ x = 1 * 12

→ x = 12 (Ans.)

Hence, the required number is equal to 12 .

Verification :-

→ (1/3) * 12 - (1/4) * 12 = 1

→ 4 - 3 = 1

→ 1 = 1

Learn more :-

how many one - fourth will make a half

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