Question

A two digit number is 4 times the sum of its digits. If 18 is added to the number, the new number is obtained is that by interchanging the digits of the original number. Find the number. ​

Answer 1

Answer:

$\large\boxed{\sf{24}}$

Step-by-step explanation:

Let the digit at ones place is "x"

and, the digit at tens place is "y"

.°. The number is (10y+x)

Now, according to question,

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

=> 10y + x = 4x + 4y

=> 10y - 4y = 4x - x

=> 6y = 3x

=> x = 2y ........(1)

Now, when the digits are interchanged,

New number = (10x + y)

According to Question,

=>10y + x + 18 = 10x + y

=> 10y - y + 18 = 10x - x

=> 9y + 18 = 9x

=> y + 2 = x

=> x = y + 2 ..........(2)

Niw, from eqn (1) and (2), we get

=> 2y = y + 2

=> y = 2

Putting the value of y in eqn (2), we get

=> x = 2 + 2

=> x = 4

.°. Number = 10×2 + 4 = 20 + 4 = 24

Answer 2

$\huge\bold{\red{Solution}}$

$\mathrm{Let\:Digit\:at\:one's\:place\:be\:y}$

$\mathrm{And\:Digit\:at\:ten's\:place\:be\:x}$

So now , the two digit number becomes = 10x + y

→ATQ

10x + y = 4(x+y) ----------- eq (1)

Now, when the digits are interchanged the number becomes = 10y + x

→ATQ

(10x + y) + 18 = 10y + x -----------eq (2)

$\mathrm{\red{Solving\:equation\:1}}$

→10x + y = 4x + 4y

→10x - 4x = 4y -y

→6x = 3y

→y = $\dfrac{6x}{3}$

${\boxed{\bf{y=2x}}}$

$\mathrm{\red{Now\:solving\:equation\:2}}$

→10x + y + 18 = 10y + x

→10x + (2x) +18 = 10(2x) + x ----[ y= 2x ]

→12x + 18 = 21 x

→21x - 12x = 18

→9x = 18

→x = $\dfrac{18}{9}$

${\boxed{\bf{x=2}}}$

Now, y = 2x

$\therefore$ y = 2(2) = 4

$\bold{\green{Number-}}$ 10x + y

= 10(2) + 4

= 20 + 4

= 24

$\huge{\underline{\boxed{\mathrm{Ans. = 24}}}}$