Question

20) The sum of the digits of a two-digit number is 5. On adding 27 to the number.
its digits are reversed. Find the original number.
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Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

• Digit at ones place = x

• Digit at tens place = y

So,

• Number formed = 10y + x

• Reverse number = 10x + y

According to statement,

The sum of the digits of two digit number is 5.

$\rm :\longmapsto\:x + y = 5 - - - (1)$

Also, given that

A two digit number when increased by 27, the digits interchange their place.

$\rm :\longmapsto\:10y + x + 27 = 10x + y$

$\rm :\longmapsto\:10x + y - 10y - x = 27$

$\rm :\longmapsto\:9x - 9y = 27$

$\rm :\longmapsto\:x - y = 3 - - - (2)$

On adding equation (1) and (2), we get

$\rm :\longmapsto\:2x = 8$

$\bf\implies \:x = 4$

On substituting x = 4 in equation (1) we get

$\rm :\longmapsto\:4 + y = 5$

$\rm :\longmapsto\: y = 5 - 4$

$\bf\implies \:y = 1$

Hence,

• Number formed = 10y + x = 10 × 1 + 4 = 10 + 4 = 14

Concept Used :-

There are 4 methods to solve this type of pair of linear equations.

1. Method of Substitution

2. Method of Eliminations

3. Method of Cross Multiplication

4. Graphical Method

We prefer here Method of Eliminations :-

To solve systems using elimination, follow this procedure:

The Elimination Method

Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient.

Step 2: Subtract the second equation from the first to eliminate one variable

Step 3: Solve this new equation for other variable.

Step 4: Substitute the value of variable thus evaluated into either Equation 1 or Equation 2 and get the value other variable.

Additional Information :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.