Raj picks up a three digit number and subtracts it from the same numbe

1.	Raj picks up a three digit number and subtracts it from the same number after reversing order of the digits. If the difference is divided by 9, then the remainder is ____________.1. 22. 03. 14. 3
Answer» Correct Answer - Option 2 : 0 Concept: The difference of any three-digit number by its reversing number is always an exact product of 9 So, it is divisible by 9. Calculation: Let 100x + 10y + z be the number its reverse is 100z + 10y + x Difference of the number will be ⇒ (100z + 10y + x) − (100x + 10y + z) ⇒ (100 − 1)z + (10 − 10)y + (1 − 100)x ⇒ 99z − 99x = 99(z − x) So the difference of any three-digit number with its reverse number is divisible by 9 then the remainder is 0 ∴ Remainder is 0

Raj picks up a three digit number and subtracts it from the same number after reversing order of the digits. If the difference is divided by 9, then the remainder is ____________.1. 22. 03. 14. 3

Answer» Correct Answer - Option 2 : 0

Concept:

The difference of any three-digit number by its reversing number is always an exact product of 9 So, it is divisible by 9.

Calculation:

Let 100x + 10y + z be the number its reverse is 100z + 10y + x

Difference of the number will be

⇒ (100z + 10y + x) − (100x + 10y + z)

⇒ (100 − 1)z + (10 − 10)y + (1 − 100)x

⇒ 99z − 99x = 99(z − x)

So the difference of any three-digit number with its reverse number is divisible by 9 then the remainder is 0

∴ Remainder is 0

Discussion

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