Chapter 6.1, Problem 19P

The result of dividing a two-digit number by the number with its digits reversed is $\frac{7}{4}$.

If the sum of the digits is 12, what is the number?

To determine

To find number according to the given situation

Answer to Problem 19P

84

Explanation of Solution

Given:

Sum of the digits of the number is 12.

Division of the number by the number obtained by reversing the digits gives $\frac{7}{4}.$

Calculation:

Let,

The digit at the unit place be $x$

The digit at tens place be $y$

Hence, the required number becomes $10y+x.$

And the number obtained by reversing the digits is $10x+y.$

Now, the sum of digits is 12, which means,

$\Rightarrow x+y=12$

Division of the number by the number obtained by reversing the digits gives $\frac{7}{4}$ ,which is,

  $\begin{array}{l}\Rightarrow \frac{10y+x}{10x+y}=\frac{7}{4}\\ \Rightarrow 40y+4x=70x+7y\\ \Rightarrow 66x=33y\\ \Rightarrow 2x=y\end{array}$

Let,

$x+y=12--------(i)$

  $2x=y-------(ii)$

Now, substituting the value of $y$ from equation ( ii ) in equation ( i ),

  $\begin{array}{l}\Rightarrow x+2x=12\\ \Rightarrow 3x=12\\ \Rightarrow x=4\end{array}$

Substituting the value of $x$ in equation ( ii ),

  $\begin{array}{l}\Rightarrow y=2\times 4\\ \Rightarrow y=8\end{array}$

The required number is $=10\times 8+4=84.$

Conclusion:

Hence, the required number is 84.