Question

The sum of digits of a two-digit numbers is 15.The number obtained by interchanging its digits exceeds the given number by 9.Find the original number.

Answer 1

HEYA!
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Let the digit at ones place be X

Let the digit at tens place be Y

According to question,

X + Y = 15 ---------------------------------------------------(1)

Number formed : X + 10 Y

Reversed number = 10X + Y

According to question,

X + 10 Y + 9 = 10 X + Y ---------------------------------------------------(2)

= X - 10 X + 10 Y - Y +9 = 0

= -9X + 9 Y + 9 = 0

Taking 9 common

-9 ( X - Y -1 ) = 0

X - Y = 1 ---------------------------------------------------(3)


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✳Solving eq . ( 1) and (3) by elimination method,

X + Y = 15

X - Y = 1

+. +. +

2X = 16

X = 8.

Putting X = 8 in (3)

8-Y = 1

-Y = -7

Y= 7.


Hence the number formed = X + 10Y

= 8 + 70

= 78.

Reversed number = 10X + Y
80 + 7 = 87.

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Answer 2

Answer:

Step-by-step explanation:

Given :-

Sum of digits of a two-digit numbers is 15.The number obtained by interchanging its digits exceeds the given number by 9.

To Find :-

The Original Number

Solution :-

Let the tens digit number be x

And the units digits number be y

Original number = (10x + y)  

According to the Question

1st Equation

x + y = 15 ……..(i)  

2nd Equation

Number obtained on reversing its digits = (10y + x)  

⇒ (10y + x) = (10x + y) + 9  

⇒ 10y + x – 10x – y = 9  

⇒ 9y – 9x = 9  

⇒ y – x = 1 …….(ii)  

On adding (i) and (ii)

⇒ 2y = 16  

⇒ y = 8  

Putting all the values in Eq (i)

⇒ x + y = 15

⇒ x + 8 = 15  

⇒ x = (15 – 8)

⇒ x = 7  

Number = (10x + y)

= 10 × 7 + 8

= 70 + 8

= 78  

Hence, the original number is 78.