Question

the sum of the digit of two number is 14. If the number formed by reversing the digit is less than the original number by 18. find the orginial numbers​

Answer 1

Answer:

Given :-

• The sum of the digit of two number is 14.
• The number formed by reversing the digits is less than the original number by 18.

Find Out :-

• Original number.

Solution :-

Let the first digit be x

And, the second digit be 14 - x

And the original number = 10x + 14 - x = 9x + 14

According to the question,

➛ 10(14 - x) + x = 9x + 14 - 18

➛ 140 - 10x + x = 9x - 4

➛ 140 - 9x = 9x - 4

➛ - 9x - 9x = - 4 - 140

➛ - 18x = - 144

➛ x = $\tt{\dfrac{- 144}{- 18}}$

➠ x = 8

Original number,

↦ 9x + 14

↦ 9(8) + 14

↦ 72 + 14

➦ 86

Therefore, the original number is 86.

Answer 2

Solution:

The original number is 86

Step by step Explanation:

Let the unit digit be x and ten's digit be y

Then , Two digit Number = 10y+x

Number on Reversing = 10x+y

According to the question

The sum of the digit of the two numbers is 14

$\sf\implies\:x+y=14.....(1)$

And, If the number formed by reversing the digit is less than the original number by 18 Then ,

$\sf\implies\:10x+y=10y+x-18$

$\sf\implies\:18=9y-9x$

$\sf\implies\:9(y-x)=18$

$\sf\implies\:y-x=2...(2)$

Now, Add Equation (1) & (2).Then,

$\sf\implies\:2y=16$

$\sf\implies\:y=8$

Put the value of y = 8 in equation (1) then,

$\sf\implies\:x+8=14$

$\sf\implies\:x=14-8$

$\sf\implies\:x=6$

Thus , x = 6 and y = 8

Hence , Number = 10y+x =86