Question

The sum of two digits of a two digit number is 15. If9 is added to it, the digits are
reversed. Find the number.​

Answer 1

Given :-

• The sum of two digits of a two digit number is 15. If 9 is added to it, the digits are reversed.

To find :-

• Required number

Solution :-

Let the tens digit be x then ones digit be y

Original number = 10x + y

• First condition

The sum of two digits of a two digit number is 15

x + y = 15 ----(i)

• Second condition

If 9 is added to it, the digits are reversed.

Reversed number = 10y + x

Now

→ 10x + y + 9 = 10y + x

→ 10x - x + y - 10y = - 9

→ 9x - 9y = - 9

→ 9(x - y) = - 9

→ x - y = - 1

Add both the equations

→ x + y + x - y = 15 - 1

→ 2x = 14

→ x = 14/2

→ x = 7

Putting the value of x in equation (ii)

→ x - y = - 1

→ 7 - y = - 1

→ y = 7 + 1

→ y = 8

Hence,

• Tens digit = x = 7

• Ones digit = y = 8

Therefore,

• Original number = 10x + y = 78

• Reversed number = 10y + x = 87

Answer 2

Given

• The sum of two digits of a two digit number is 15.

We Find

• Required Number in Question

Let's Take be x

• Original number = 10x + y [ First Equation ]

• So, Reversed number also = 10y + x

We know

Sum of two digits is = 15

• so, x + y = 15 [ Second Equation ]

Now ,

= 10x + y + 9 = 10y + x

= 9x - 9y = -9

= 9 (x + y) = -9

= x - y = -1

According to the question

(We Adding both equation)

= x + y + x - y = 15 - 1

= 2x = 14

= x = 14/2

= x = 7

Now , we putting values

x - y = -1

= 7 - y = -1

= y = 7 + 1

= y = 8

So, We that's clear

• X = 7
• Y = 8

So, Therefore

Original number is = 10x + y = 78

Reversed Number is = 10y + x = 87

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