Question

The middle digit of number between 100 and 1000 is zero, and the sum of the other digits is 11 . if the digits are interchanged , the numbers so formed exceeds the original number by 495. find the number.​

Answer 1

$\huge{\red{\boxed{Answer:}}}$

Let the number between the numbers 100 and 1000 be ➡ x0y

Sum of other digits (x + y) ➡ 11

Hundreds digit x = 100x

and ones digit y = y

➡ 100x + y

Interchanged digits x and y =

➡ 100y + x

Difference between them =

➡ 100x + y - (100y + x) = 495

➡ 100x + y - 100y - x = 495

➡ 100x - x - 100 + y = 495

➡ 99x - 99y = 495

➡ x - y = 495/99

➡ x - y = 5

According to question, x + y = 11

➡ x + x - y + y = 11 + 5

➡ 2x = 16

➡ x = 16/2 = 8

➡ x = 8, y = 11 - 8 = 3

Number between 100 & 1000 = 803

$\Large{\blue{\boxed{x = 8\: and\: y = 3}}}$

$\huge{\green{\boxed{Verification:}}}$

➡ x = 8, y = 3

➡ Number = x0y = 803

➡ Sum of other digits except middle digit = 11

➡ 8 + 3 = 11

Hence, x0y = 803

Extra Information -

What is place value?

The value of the place of a digit in a number is known as place value. For example - 596, the value of 5 in this number is 500, it is its place value.

What is ones digit?

The digit which is at the one's place is known as ones digit.

Take a number, 6, this number have one number. The only number, i.e. 6, is at one's place so it is ones digit, its value is only 6.

What is Tens digit?

The digit which is at the ten's place is known as tens digit.

Take a number, 36, this number have two numbers. The first number, i.e. 3, is at ten's place so it is tens digit, Its value is 30.

What is Hundreds digit?

The digit which is at the hundred's place is known as hundreds digit.

Take a number, 236, this number have three numbers. The first number, i.e. 2, is at hundred's place so it is hundreds digit, its value is 200.