Question

In a two - digit number, the unit's digit is 3 more than the tens digit. The
number formed by interchanging the digits and the original number are in the ratio 7:4 Find the number

please answer this question with a proper solution ​

Answer 1

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.

Solution :-

• Let digit at ten's place be 'x'.

So,

• Digit at ones place be ' x + 3 '.

Thus,

• Number formed is = 10x + x + 3 = 11x + 3

And

Reverse Number = 10×(x + 3) + x×1 = 10x + 30 + x = 11x + 30

Now,

According to statement,

$\rm :\longmapsto\:\dfrac{Number \: formed}{Reverse \: Number} = \dfrac{4}{7}$

$\rm :\longmapsto\:\dfrac{11x + 3}{11x + 30} = \dfrac{4}{7}$

$\rm :\longmapsto\:77x + 21 = 44x + 120$

$\rm :\longmapsto\:77x - 44x = 120 - 21$

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

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

Thus,

• Number formed = 11x + 3 = 11 × 3 + 3 = 33 + 3 = 36.