## A number consists of two digits whose sum is 9. If 27 is subtracted from the original number, its digits are interchanged. Then the original

Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the original number, its digits are interchanged. Then the original number is

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5 days 2021-09-14T17:26:32+00:00 2 Answers 0 views 0

1. ## Given:–

A number consists of 2 digits whose sum is 9 .

If 27 is subtracted from the original number , its digits are interchanged .

## Requiredtofind:–

• Original number ?

## Solution:–

Given data :

A number consists of 2 digits whose sum is 9 .

If 27 is subtracted from the original number , its digits are interchanged .

we need to find the original number .

So,

Let the unit digit be x

Ten’s digit be y

Number formed =

=> 10 ( y ) + 1 ( x )

=> 10y + x

On reversing the digits ;

Unit digit = y

Ten’s digit = x

Number formed =

=> 10 ( x ) + 1 ( y )

=> 10x + y

But,

It ia mentioned that ;

The sum of the two digits of the number is 9

So,

This implies ;

y + x = 9

y = 9 – x

consider this as equation – 1

According to problem ;

If 27 is subtracted from the original number , its digits are interchanged .

This implies ;

10y + x – 27 = 10x + y

10y – y + x – 10x = 27

9y – 9x = 27

Substitute the value of y from equation – 1

9 ( 9 – x ) – 9x = 27

81 – 9x – 9x = 27

– 18x = 27 – 81

– 18x = – 54

– ( minus ) gets cancelled on both sides

18x = 54

x = 54/18

x = 3

Substitute the value of x in equation – 1

y + x = 9

y + 3 = 9

y = 9 – 3

y = 6

### Verification:–

Case – 1

Let’s consider 63 as the original number

According to the condition ;

If 27 is subtracted from the original number , its digits are interchanged

So,

This implies ;

63 – 27 = 36

36 = 36

LHS = RHS

Case 2

Let’s consider 63 as the original number

According to the condition ;

If 27 is subtracted from the original number , its digits are interchanged

So,

This implies ;

36 – 27 = 36

9 = 36

LHS ≠ RHS

### Original number = 63

2. Answer:What the question basically means is that a 2 digit number has its sum of digits 9 and the difference between it and its reverse is 27.

Since there are only 4 pairs of 2 digit numbers with sum of its digits as 9 and whose reverse is also a 2 digit number, we can list them.

18, 81

27, 72

36, 63

45, 54

We see the difference between 36 and 63 is 27, so those are our two numbers.

The other way to solve it is using simultaneous equations, where two generic equations are formed in x and y where x and y are the two digits.

Here sum is sum of the two digits and difference is the difference between the number and its reverse.

x + y = sum … (1)

10 * x + y = 10 * y + x + difference

9 * x – 9 * y = difference

9 * (x – y) = difference

x – y = difference / 9 … (2)

Putting values we get

x + y = 9 … (1)

x – y = 27 / 9 = 3 … (2)

Solving (1) and (2)

we get x = 6 and y = 3

Therefore the numbers are 63 and 36.

pls mark brainliest