Question

If one fifth of a number increased by 5 is equal to 4 less than one fourth of that number, what is the number?

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Answer 1

Step-by-step explanation:

Hey)

Step-by-step explanation:

Let the number be a

$= > \: \frac{1}{4}a - 4 = \frac{1}{5} a + 5 \\ = > \: taking \: variable \: term \: on \: 1side \: and \: nos \: on \: other \: side \\ = > \frac{1}{4} a - \frac{1}{5} a = 5 + 4 \\ \frac{a}{20} = 9 \\ \\ shifting \: \: 20 \: to \: right \: hand \: side \\ \: a = 20 \times 9 \\ a = 180$

Therefore

The number is 180

Answer 2

Answer:

Number = 180

Step-by-step explanation:

$\bold{\underline{\underline {Assume\::}}}$

Let the number be x.

$\bold{\underline{\underline {Given\::}}}$

• One-fifth of a number is increased by five which is equal to four less than one-fourth of that number.

$\bold{\underline{\underline {Solution\::}}}$

One-fifth of the number. Let number is x.

So, One-fifth of number = 1/5x

As, One-fifth of the number increased by 5. So, we add 5 in it.

i.e (1/5) x + 5

Similarly,

Four less than one-fourth of that number.

i.e. (1/4) x - 4

According to question,

=> $\sf{\dfrac{x}{5}\:+\:5\:=\:\dfrac{x}{4}\:-\:4}$

=> $\sf{\dfrac{x\:+\:25}{5}\:=\:\dfrac{x\:-\:16}{4}}$

Cross-multiply them

=> $\sf{4(x\:+\:25)\:=\:5(x\:-\:16)}$

=> $\sf{4x\:+\:100\:=\:5x\:-\:80}$

=> $\sf{5x\:-\:4x\:=\:100\:+\:80}$

=> $\sf{x\:=\:180}$

•°• Number is 180.