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Sum of the digits of a 2-digit number is 7. If number obtained by interchanging the digits is 9 more than the original number, then what is the sum of the squares of the digits of the number?

Sum of the digits of a 2-digit number is 7. If number obtained by interchanging the digits is 9 more than the original number, then what is the sum of the squares of the digits of the number? Correct Answer 25

Given:

Sum of two digit = 7

Concept:

Two digit number is in the form of 10x + y

where y and x are unit's and ten's digit respectively.

Calculation:

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

x + y = 7

⇒ x = 7 - y      ---- (1)

Original number = 10x + y

Interchange digit number = 10y + x

According to question:

10y + x = 10x + y + 9

⇒ 10y + x - 10x - y = 9

⇒ -9x + 9y = 9

⇒ -x + y = 1

-(7 - y) + y = 1 (from 1)

⇒ -7 + y + y = 1

⇒ 2y = 1 + 7

⇒ 2y = 8

⇒ y = 4

x = 7 - 4

⇒ x = 3

(3)2 + (4)2

⇒ 9 + 16

⇒ 25

∴  The sum of the squares of the digits of the number is 25.

 

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