Question

the sum of the digit ofa two digit number is 8 .if the digit are reversed the number is increased by 54. find the number

Answer 1

Hey !!!

This is your answer.

Given :
Sum of two digits = 8.
If the digits are reversed then the it is 54 more than the original one.

A two digit number is of the form....

10a + b.

Let tens place digit be a and unit place digit be b.

Sum of two digits = 8.
So. a+b = 8 .. ......(i).

Original number .= 10a + b
As the new number 54 more than original...
therefore..
10b+a - (10 a + b) = 54
10b + a - 10a - b = 54.
9b - 9a = 54
b - a = 6 ..... ........(ii)

Adding equation (i) and (ii). we get....

b + a = 8
b - a = 6
---------------
2b = 14

b = 7.

Putting b = 7 in equation (I).
we get a = 1.
So... the original number = 10a + b
= 10 × 1 + 7
= 17.

Hence the original number is 17.

Hope it helps