Question

The sum of the digits of a two-digit number is 7. The number formed by reversing the digits is 45 more than the original number find the original number.

Answer 1

Let the number be 10x+y
also given that x+y = 7
so, x = 7-y ---(1)

also, 10y + x = 10x+y +45
9y = 45 +9x
y = 5+x ----(2)

putting the value of (1) in (2)

so, y = 5+ ( 7-y)
=> y = 5 + 7 - y
=> y +y = 12
=> 2y = 12
=> y = 6

so, x = 7-y = 7-6
=> x = 1
Hence for original number we must put value of x and y that is 1 and 6 respectively... Therefore 10x+y=10×1+6=16

so, the number is 16.

Hope that helps you!!! ☺️☺️☺️

Answer 2

Answer:

→ The original number is 16 .

Step-by-step explanation:

Let the unit's digit of the original number be x .

And, the ten's digit of the original number be y .

Now, A/Q,

→ Sum of the two digits number is 7 .

∵ x + y = 7 ............(1) .

Original number = 10x + y .

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

A/Q,

→ The number obtained on reversing the digit is 45 more than the original number .

∵ 10x + y + 45 = 10y + x  .

⇒ 10x - x + y - 10y = - 45 .

⇒ 9x - 9y = - 45 .

⇒ 9( x - y ) = - 45 .

⇒ x - y = - 45/9 .

∵ x - y = -5 ...........(2) .

On substracting equation (1) and (2), we get

x + y = 7 .

x - y = -5 .

-  +     +

________

⇒ 2y = 12 .

⇒ y = 12/2 .

∴ y = 6.

On putting the value of 'y' in equation (1),  we get

∵ x + y = 7 .

⇒ x + 6 = 7 .

⇒ x = 7 - 6 .

∴ x = 1 .

Therefore , the original number = 10x + y .

= 10 × 1 + 6 .

= 10 + 6 .

= 16 .

Hence, the original number is 16 .

THANKS

#BeBrainly .