Question

A number consist of two digits. If the square of the digits in the tens place is substrate from the square of the digits in the units place, the result is 65. The sum of the original number and the number obtained by interchanging the digits is 143. Find the original number

Answer 1

Answer:

Hi there !!

Here's your answer

Let the digit in the tens place be x

the sum of digits is 13

So,

the digit in units place = 13 - x

The original Number formed will be

10(x) + 13 - x

= 10x + 13 - x

= 9x + 13 __________(i)

Given,

if the digits are reversed, the number formed exceeds the original number by 27

So,

by interchanging the digits,

we have,

digit in tens place = 13 - x

digit in units place = x

The new number is

10(13 - x) + x

= 130 - 10x + x

= 130 - 9x _________(ii)

So,

the following balanced equation will be formed

130 - 9x - 27 = 9x + 13

103 - 9x = 9x + 13

103 - 13 = 9x + 9x

90 = 18x

x = 90/18

x = 5

Therefore,

digit in tens place = x = 5

digit in units place = 13 - x = 13 - 5 = 8

Thus,

the new number is 58

__________________________________

Hope it helps !!