Complex Examples on Numbers

In this class, We discuss Complex Examples on Numbers.

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The reader should have prior knowledge of basic examples of numbers. Click Here.

Example 1:

A number consists of three digits whose sum is 10.

The middle digit equals the sum of the other two digits, and the number will be increased by 99 if the digits are reversed.

Is the number?

Solution:

Let the middle digit is x.

From the first two conditions:

1) sum of digits is 10.

2) middle digit is equal to the sum of the other two digits.

From the above two conditions, x = 5

Conditions satisfy for x = 5, and the remaining digits are 3 and 2.

The possible numbers are 253 and 352

From the third condition, the number 352, when reversed, the number is decreased by 99.

So the result is 253.

Example 2:

In a two-digit number, the digit in the units place is more than twice the digit in the tens place by 1.

If the digit in the unit and tens place are interchanged, then the difference between the newly formed and the original number is less than the original number by 1.

What is the original number?

Solution:

Let ten’s digit is x.

Units digit is 2x+1

Number = 10(x) + (2x+1) = 12x+1

[10x + (2x+1)] – [(10(2x+1) + x) – (10x + (2x+1)] = 1

(12x + 1) – (9x+9) = 1

3x = 9

x = 3

number = 37