Question

The digit in ten’s place of a two digit number is greater than the digit in unit’s

place by 1. The sum of the number and the number obtained by interchanging the

digits is 121. Find the number.

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Answer 1

Hey Meheksoni !

Answer:

65

Step-by-step explanation:

Given :

Two Digit Number

Ten's Digit = 1 + Unit's Digit

Original Number + Reversed Number = 121

Procedure :

Let the Original Number be ab.

ab = 10a + b

Hence the reversed number = ba

ba = 10b + a

a = 1 + b

ab + ba = 121

⇒ (10a + b) + (10b + a) = 121

⇒ 11a + 11b = 121

⇒ a + b = 11 --------------- Eq₁

a = 1 + b

⇒ a - b = 1 ------------------Eq₂

From Eq₁ and Eq₂,

a = 6

b = 5

Hence the number is ab.

∴ The Original number is 65.

Thanks !