Examples on Numbers 2

In this class, We discuss Examples on Numbers 2

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

Example 1:

Of two numbers, four times the smaller one is less than three times, and the larger one by 5.

The sum of the numbers is larger than six times their difference by 6.

Find the two numbers.

Solution:

Let the numbers be x and y

x>y

3x – 4y = 5 from the first point in the question.

(x + y) – 6(x-y) = 6

-5x + 7y = 6

Solving the equations we get x = 59 and y = 43

Example 2:

The ratio between a two-digit number and the sum of the digits of the number is 4: 1.

If the digit in the ones place is three more than the digit in the ten’s place.

Find the number.

Solution:

First, we discuss decimal number system basics then we move to the solution.

In the decimal number system units, the place is given 10^0

Ten’s place is given 10^1

The number 45 is written (4 * 10^1) + (5 * 10^0)

From the question, we assume the digit in the ten’s place is considered x.

The digit in the unit’s place is x+3.

The two-digit number is (x * 10^1) + ((x+3) * 10^0)

= 10x + x + 3

= 11x + 3

Sum of two digits = x + x+3

= 2x+3

(11x+3)/(2x+3) = 4/1

solving the equation, we get x = 3

The required number is 11x+ 3 = 36