Question

7 times a two digit number is equal to 4 times the number obtained by reversing the digits.If the difference b/w the digits is 3.Find the number.

Class 10 CBSE
Pair of linear equations in two variables.​

Answer 1

Answer :-

The number is 36.

Solution :-

Let the number be x at the 10th place and y be once place

so the number will be 10x + y

According to the first condition →

$\longrightarrow7 \times (10x + y) = 4 \times (10y + x) \\ \\ \longrightarrow70x + 7y = 40y + 4x \\ \\ \longrightarrow70x - 4x + 7y - 40y = 0 \\ \\ \longrightarrow66x - 33y = 0 \\ \\ \longrightarrow33(2x - y) = 0 \\ \\ \longrightarrow2x - y = 0 \\ \\ \longrightarrow \: y = 2x - - - - - (i)$

Now, according to the second condition →

$\longrightarrow \: y - x = 3$

Putting the value of y from equation (i) →

$\longrightarrow2x - x = 3 \\ \\\longrightarrow x = 3$

Put the value of x into equation (i) →

$\longrightarrow \: y = 2x \\ \\ \longrightarrow \: y = 2 \times 3 \\ \\ \longrightarrow \: y = 6$

So, the number is →

$\longrightarrow10x + y \\ \\ \longrightarrow \: 10 \times 3 + 6 \\ \\ \longrightarrow \: 30 + 6 \\ \\ \longrightarrow \: 36$