Question

A two digit number is 3 more than 4 times the sum of its digits. When 18 is added the digits of this number gets reversed. Find the number.​

Answer 1

$\huge\boxed{Answer}$

दो अंकों की संख्या के लिए ,

माना इकाई का अंक = x

तथा दहाई का अंक = y

अतः संख्या = 10y + x

प्रश्नानुसार -

10y + x = 4(x + y) + 3

10y + x = 4x + 4y + 3

6y - 3x = 3

2y - x = 1

x = 2y - 1 -------(1)

अब , 10y + x + 18 = 10x + y

9x - 9y = 18

x - y = 2

x = y + 2 -----(2)

समी.(1) एवं समी.(2) से -

2y - 1 = y + 2

y = 3

Then , x = 5

अतः संख्या = 10(3) + 5

= 30 + 5

= 35

Answer 2

Let the ten's digit and the one's digit be x and y respectively.

Therefore the original two digit number would be 10x+y.

Given

A two-digit number is 3 more than 4 times the sum of its digits

$\implies 10x+y=4(x+y)+3\\\implies 10x+y=4x+4y+3\\\implies 10x-4x+y-4y=3\\\implies 6x-3y=3\\\implies 2x-y=1--(1)$

When 18 is added the digits of this number gets reversed.

$\implies 10x+y+18=10y+x\\\implies 10x-x+y-10y=-18\\\implies 9x-9y=-18\\\implies x-y=-2--(2)$

Solving (1) and (2), we get,

$2x-y=1\\\underline{x-y=-2}\\\underline{\underline{x=3}}$

Substituting the value of x in the second equation, we get,

$\implies 3-y=-2\\\implies -y=-2-3\\\implies -y=-5\\\implies y = 5$

Number required

$= 10x + y \\ = 10(3) + 5 \\= 30 + 5 \\=35$

$\boxed{\boxed{\bold{Therefore, \ the \ number \ is \ 35}}}}}}}}}}$