Question

the number exceeds 60 percent of itself to make 40. the number is​

Answer 1

Question :

The number exceeds 60 percent of itself to make 40. Find the number.

Solution :

$\underline{\bold{To\:Find :}}$

• The number .

Let the number be x.

Atq,

$\implies x+ 60\% \: of \: x = 40 \\ \implies x + \frac{60}{100} \times x = 40 \\ \implies x + \frac{3x}{5} = 40 \\ \implies \frac{5x +3x}{5} = 40 \\ \implies \frac{8x}{5} = 40 \\ \implies 8x = 5 \times 40 \\ \implies x = \frac{5 \times 40}{8} \\ \implies x = 5 \times 5 \\ \implies x =25$

$\boxed{\green{\therefore{The \:number\: is\:25. }}}$

$\underline{\bold{Verification :}}$

$\implies x + 60 \% \: of \:x = 40 \\ \implies 25 + 60\% \:o f \: 25 = 40 \\ \implies 25 + \frac{60}{100} \times 25 = 40 \\ \implies 25 + 15 = 40 \\ \implies 40 = 40 \\ \implies \: LHS= RHS$

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Answer 2

Answer:

Let, the number be : x

Condition Given:

The number exceeds 60% of itself to make 40.

Main Aim:

To find the value of x/the number.

According to the Question:

$\bf{x + 60\% \times x = 40}$

(Equation Formation in this step)

$\bf{ = > x + \frac{60}{100} x = 40}$

(In this step, we have converted 60% to its fractional form)

$\bf{ = > x + \frac{6}{10} x = 40}$

(Cancellation of zeroes)

$\bf{ = > x + \frac{3}{5}x = 40}$

(In this step, we have cancelled 6/10 to 3/5 as taking common 2)

$\bf{ = > x + \frac{3x}{5} = 40}$

(Multiplication of nominator)

$\bf{ = > \frac{5x + 3x}{5} = 40}$

(Preparation for addition)

$\bf{ = > \frac{8x}{5} = 40}$

(Added)

$\bf{ = > 8x = 40 \times 5}$

(Taken /5 from Left Hand Side to Right Hand Side and converted into ×5)

$\bf {= > 8x = 200}$

(Multiplied 40 and 5)

$\bf {= > x = \frac{200}{8}}$

(Preparation of division, 8 is placed to RHS)

$\bf\green{ = > x = 25}$

(Value of x is found)

REQUIRED ANSWER:-

Therefore, the number is :

$\huge\boxed{25}$