Question

the number obtained by interchanging the two digits exceeds the given number by a multiple of a prime number greater than 3. which of the following could be the number ?​

Answer 1

Answer: The answer is 57!!!!!!

Step-by-step explanation:

Let x represent the “tens” digit

let y represent the “ones” digit

So the original number is 10x + y

the reversed number is 10y + x

10x + y + 18 = 10y + x This is the new number is 18 more than the original

x + y =12 This is the sum of the digits is 12

Isolate x in x + y = 12 subtract y from both sides. x = 12 - y

Substitute 12-y for every x in: 10x + y + 18 = 10y + x =>

10(12-y) + y + 18 = 10y + (12-y) Distribute the 10

120 -10y + y + 18 = 10y + 12 - y Combine like terms

138 - 9y = 9y + 12 Add 9y on both sides

138 = 18y + 12 Subtract 12 on both sides

126 = 18 y divide both sides by 18

7 = y

x = 12 - y => x = 12 - 7 => x = 5

Original Number 57, new number 75. Check 75 -57 = 18

There's an alternate method too:

Let us assume x and y are the two digits of the number

 

Therefore, two-digit number is = 10x + y and the reversed

number = 10y + x

 

Given:

 

x + y = 12

 

y = 12 – x -----------1

 

Also given:

 

10y + x - 10x – y = 18

 

9y – 9x = 18

 

y – x = 2 -------------2

 

Substitute the value of y from eqn 1 in eqn 2

 

12 – x – x = 2

 

12 – 2x = 2

 

2x = 10

 

x = 5

 

Therefore, y = 12 – x = 12 – 5 = 7

 

Therefore, the two-digit number is 10x + y = (10*5) + 7 = 57

Or Simply,

Let us start with digit 1 

first digit 1 & 2nd digit is 11 (as sum is 12) not possible 

first digit 2 & 2nd digit is 10 (as sum is 12) not possible 

first digit 3 & 2nd digit is 9 (as sum is 12) possible 

so 93 – 39 = 54 

84 – 48 = 36 

75 – 57 = 18 required difference 

so original number is 57 

Hope This Helps :)