Question

a two digit number and a number with digits interchanged add upto 165, again it is given that its tens place digit is less than unit place digit by 1, find sum of all factors of number.
pls gimme answer

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,

A two digit number and a number obtained by interchanging the digits adds up to 165.

$\rm :\longmapsto\:10y + x + 10x + y = 165$

$\rm :\longmapsto\:11y + 11x = 165$

$\rm :\longmapsto\:11(y + x) = 165$

$\rm :\longmapsto\:y + x= 15$

$\rm :\longmapsto\:y= 15 - x - - - (1)$

Also,

Tens place digit is 1 less than the unit place digit

$\rm :\longmapsto\:y = x - 1$

$\rm :\longmapsto\:15 - x = x - 1 \: \: \: \: \: \: \: \{ \: using \: (1) \: \}$

$\rm :\longmapsto\:2x = 16$

$\bf\implies \:x = 8$

On substituting the value of x in equation (1) we get

$\rm :\longmapsto\:y = 15 - 8$

$\bf\implies \:y = 7$

Hence,

• Number formed = 10y + x = 10 × 7 + 8 = 78

Now, factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

Hence, sum of factors of 78 = 1+2+3+6+13+26+39+78 = 168

Basic Concept Used :-

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.