Question

A two digit number is such that the sum of its digits is 4.if 18 is added to the number,its digits are reversed.find the number

Answer 1

$\huge\sf\pink{Answer}$

☞ Number = 24

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ A two digit number is 4 times the Sum of its digits

✭ If 18 is added to the number the digits are reversed

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$\huge\sf\gray{To \:Find}$

◈ The original number?

$\rule{110}1$

$\huge\sf\purple{Steps}$

Number = 10x + y

Case 1

$\underline{\textsf{As Per The Question}}$

$\sf{\twoheadrightarrow 10x + y = 4(x + y) }$

$\sf{\twoheadrightarrow 10x + y = 4x + 4y }$

$\sf{\twoheadrightarrow 10x - 4x = 4y - y }$

$\sf{\twoheadrightarrow 6x = 3y }$

Dividing 3 on Both sides,

$\sf{\twoheadrightarrow 2x = y\qquad -eq(1) }$

Case 2

≫ Number obtained on reversing the digits = 10y + x

$\bullet\underline{\textsf{As Per the Question}}$

$\sf{\twoheadrightarrow 10x + y + 18 = 10y + x}$

$\sf{\twoheadrightarrow 10x + y - (10y + x) = -18}$

$\sf{\twoheadrightarrow 10x + y -10y -x = -18}$

$\sf{\twoheadrightarrow 9x - 9y = -18}$

Divide by '9' on both sides

$\sf{\twoheadrightarrow x - y = -2...2) }$

Put the value of y from eq(1) in eq(2)

$\sf{\twoheadrightarrow x - 2x = -2 }$

$\sf{\twoheadrightarrow - x = - 2 }$

$\sf{\red{\twoheadrightarrow x = 2 }}$

Put the value of x in eq(2)

$\sf{\dashrightarrow 2 - y = -2 }$

$\sf{\dashrightarrow - y = -2-2}$

$\sf{\dashrightarrow - y = - 4 }$

$\sf\orange{\dashrightarrow y = 4 }$

➳ Number = 10x + y

➳ Number = 10(2) + 4

➳ Number = 20 + 4

➳ $\sf\green{Number = 24}$

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