Question

the sum of digit of a 2 digit number is 7.if the digit are reversed the new number increases by 3 less then 4 times the original number. find the original number​

Answer 1

$\huge\sf\pink{Answer}$

☞ The original number is 16

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$\huge\sf\blue{Given}$

✭ Sum of the digits of a two digit number is 7

✭ If the digits are reversed the new number increases by 3 less than 4 times the original Number

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

◈ The Original Number?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Let}}$

• The number be 10x+y
• When reversed it becomes 10y+x

☯ $\underline{\boldsymbol{As \ Per \ the \ Question}}$

➳ $\sf x+y = 7$

➳ $\sf x = 7-y\:\:\: -eq(1)$

Also,

➝ $\sf 10y+x-3 = 4(10x+y)$

➝ $\sf 10y+x-3 = 40x+4y$

➝ $\sf 10y+x-3-40x-4y = 0$

➝ $\sf 10y-4y+x-40x-3 = 0$

➝ $\sf 6y-39x-3=0$

➝ $\sf 39x-6y-3 = 0$

✪ Divide the whole Equation by 3

➝ $\sf \dfrac{39x+6y-3}{3}$

➝ $\sf 13x-2y=1 \:\:\: -eq(2)$

Substituting the Value of eq(1) in eq(2)

➢ $\sf 13(7-y)-2y = 1$

➢ $\sf 91-13y-2y = 1$

➢ $\sf -15y = -90$

➢ $\sf y = \dfrac{-90}{-15}$

➢ $\sf \red{y = 6}$

Substituting the value of y in eq(1)

➠ $\sf x=7-6$

➠ $\sf \orange{x=1}$

$\sf \therefore The \ Number \ is \ 16$

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