Question

The result of dividing a two digit number by the number formed by reversing the digits is 7/4. The difference
between the two digits is 2. Find the two digit number.​

Answer 1

Answer:-

Let the number be (10x + y).

Given:

Difference between the digits = 2

x - y = 2

x = 2 + y -- equation (1)

And also given that,

The result of dividing the number by the number formed by reversing the digits is 7/4.

Reversed number = 10y + x.

According to the above situation,

$\frac{10x + y}{10y + x} = \frac{7}{4}$

Substitute "x" value here.

$\frac{10(2 + y) + y}{10y + 2 + y} = \frac{7}{4} \\ \\ \frac{20 + 10y + y}{11y + 2} = \frac{7}{4} \\ \\ \frac{20 + 11y}{11y + 2} = \frac{7}{4}$

After cross multiplication we get,

$4(20 + 11y) = 7(11y + 2) \\ \\ 80 + 44y = 77y + 14 \\ \\ 80 - 14 = 77y - 44y \\ \\ 33y = 66 \\ \\ y = \frac{66}{33} \\ \\ y = 2$

Substitute "y" value in equation (1)

x = 2 + y

x = 2 + 2

x = 4

Number = 10x + y = 10(4) + 2 = 42

Hence, the number is 42.