Question

8. The sum of the digits of a two-digit number is 10. The number formed by reversing the digits is 18 less
than the original number. Find the original number.​

Answer 1

Let unit place digit be x. Then tenth place digit will be (10-x)

The number is (10-x) 10+x = 100-9x......(1)

Reversing the digit, formed number is 10x + (10-x) = 9x + 10.........(2)

9x + 10 + 18 = 100 - 9x......(2)

Solving equation.(2) We get x = 4, then number is 100 - 9 (4) = 64

Answer 2

Answer:

Original Number = 64.

Given:

Sum of digits of original number = 10

Reversed number is 18 less than the original number.

To Find:

Original Number

Solution:

Let the ten's digit of the number be x and one's digit be y respectively.

Original Number = 10x + y

ATQ,

x + y = 10 .....(1)

Reversed Number = 10y + x

ATQ,

10y + x = 10x + y - 18

10y - y + x - 10x = -18

-9x + 9y = -18

-1(9x - 9y) = -1(18)

Dividing both sides by -1, we get:

9x - 9y = 18

Dividing both sides by 9, we get:

x - y = 2 .....(2)

Adding equation (1) and (2) , we get:

x + y + x - y = 10 + 2

2x = 12

x = 6

Substituting the value of x in equation (1) , we get:

6 + y = 10

y = 4

Substituting the value of x and y in original number, we get:

Original Number = 10 * 6 + 4

Original Number = 64

Proof:

Given,

Reversed Number = Original Number - 18

10y + x = (10x + y) - 18

10 * 4 + 6 = (10 * 6 + 4)

46 = 64 - 18

46 = 46

LHS = RHS

Hence Proved

Therefore, the answer is 64.