Question

1 poin
2) A two digit number T is added to
the number formed by reversing its
digits. The sum obtained is 99. The
tens digit of T was twice its units digit.
Find its tens digit.​

Answer 1

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

Given that

• Tens digit of T was twice its unit digit.

Let assume that

• Digit at unit place = x

So,

• Digit at tens place = 2x

Thus,

• Two digit number, T = 10 × 2x + x = 20x + x = 21x

And

• Reverse Number = 10 × x + 2x × 1 = 10x + 2x = 12x

According to statement,

Sum of two digit number and reverse number = 99

$\rm :\longmapsto\:21x + 12x = 99$

$\rm :\longmapsto\:33x = 99$

$\rm :\implies\:x = 3$

So,

• Digit at unit place = 3

and

• Digit at tens place = 2x = 2 × 3 = 6

Basic Concept Used :-

Writing System 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.