Question

Four fifths of a number is10 more than two thirds of the number

Answer 1

Answer :-

The number is 75.

Solution :-

Let the number be x

Four - fifth of a number = 4/5 * x = 4x/5

Two - third of a number = 2/3 * x = 2x/3

10 more than two - third of the number = 2x/3 + 10

Given that

Four - fifth of a number = 10 more than two - third of the number

⇒ 4x/5 = 2x/3 + 10

Transpose 2x/3 to LHS

⇒ 4x/5 - 2x/3 = 10

Taking LCM

⇒ 4x(3)/5(3) - 2x(5)/3(5) = 10

⇒ 12x/15 - 10x/15 = 10

⇒ (12x - 10x)/15 = 10

⇒ 2x/15 = 10

Transpose 2/15 to RHS

⇒ x = 10 * 15/2

⇒ x = 5 * 15

⇒ x = 75

Therefore the number is 75.

Verification :-

4x/5 = 2x/3 + 10

Substitute x = 75 in the above equation.

⇒ 4(75)/5 = 2(75)/3 + 10

⇒ 4(15) = 2(25) + 10

⇒ 60 = 50 + 10

⇒ 60 = 60

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Number is 75

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

$\text{\underline{\underline{\purple{Given :}}}}$

$\tt{\dfrac{4}{5}}$ of a number is = 10 more than $\tt{\dfrac{2}{3}}$ of the same Number

$\text{\underline{\underline{\purple{To Find :}}}}$

The Number

$\text{\underline{\underline{\purple{Solution :}}}}$

Consider the Number as x

★ $\boxed{\tt{\frac{4}{5} \: of \: x = \frac{2}{3} \: of \: x+ 10}}$

$\tt{\longrightarrow} \: \dfrac{4}{5} \times x = \left(\dfrac{2}{3}\ \times x \right)+ 10$

$\tt{\longrightarrow} \: \dfrac{4x}{5}= \dfrac{2x}{3}+ 10$

$\tt{\longrightarrow} \: \dfrac{4x}{5} - \dfrac{2x}{3}=10$

LCM of 5 and 3 is = 15

$\tt{\longrightarrow} \: \dfrac{12x - 10x}{15} =10$

$\tt{\longrightarrow} \: \dfrac{2x}{15} =10$

$\tt{\longrightarrow} \: 2x = 10 \times 15$

$\tt{\longrightarrow} \: 2x = 150$

$\tt{\longrightarrow} \: x = \dfrac{150}{2}$

$\tt{\longrightarrow} \: x = 75$

$\therefore$ The Number is 75.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

As We got the number, we can verify it by substituting the value of x. If both the sides (LHS & RHS) are equal, that means the answer is Correct.

$\tt{\longrightarrow} \: \dfrac{4}{5} \times 75= \left(\dfrac{2}{3}\ \times75 \right)+ 10$

$\tt{\longrightarrow} \: 15 \times 4 = (2 \times 25)+ 10$

$\tt{\longrightarrow} \:60 = 50 + 10$

$\tt{\longrightarrow} \:60 = 60$

$\therefore$ The Number is 75.