Question

7 times a 2 digit number is equal to 4 times the number obtained by reversing the digits. The difference between the digits is 1. Find the number​

Answer 1

Step-by-step explanation:

Assume that the ten's digit number be x and one's digit number be y.

Seven times a two digit number is equal to four times the number obtained by reversing the digits.

• Original Number = 10x + y
• Reversed Number = 10y + x

As per given condition,

→ 7(10x + y) = 4(10y + x)

→ 70x + 7y = 40y + 4x

→ 70x - 4x = 40y - 7y

→ 66x = 33y

→ 2x = y

→ x = y/2

Also the difference between the digits is 1.

→ y - x = 1

→ y - y/2 = 1

→ 2y - y = 2

→ y = 2

Substitute value of y in x

→ x = 2/2

→ x = 1

Hence, the number is 12.

Answer 2

Solution :

Let the ten's place digit be r & one's place digit be m respectively;

$\boxed{\bf{Original\:number=10r+m}}\\\boxed{\bf{Reversed\:number=10m+r}}$

A/q

$\longrightarrow\sf{r-m=1}\\\\\longrightarrow\sf{r=1+m....................(1)}$

&

$\longrightarrow\sf{7(original\:number) = 4(reversed\:mumber)}\\\\\longrightarrow\sf{7(10r+m) = 4(10m+r)}\\\\\longrightarrow\sf{70r + 7m =40m + 4r}\\\\\longrightarrow\sf{70r -4r =40m-7m}\\\\\longrightarrow\sf{66r =33m}\\\\\longrightarrow\sf{66(1+m) =33m\:\:[from(1)]}\\\\\longrightarrow\sf{66 + 66m =33m}\\\\\longrightarrow\sf{33m-66m=-66}\\\\\longrightarrow\sf{-33m=-66}\\\\\longrightarrow\sf{m=\cancel{-66/-33}}\\\\\longrightarrow\bf{m=2}$

Putting the value of m in equation (1),we get;

$\longrightarrow\sf{r=1+2}\\\\\longrightarrow\bf{r=3}$

Thus;

The number is 10r + m = 10(3) + 2 = 30 + 2 = 32 .