Question

[CBSE 2006]
12. A number consisting of two digits is seven times the sum of its digits.
When 27 is subtracted from the number, the digits are reversed. Find
the number.​

Answer 1

Answer:

27 is the answer of these que tions

Answer 2

$\large\underline{\sf{Solution-}}$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Let-\begin{cases} &\sf{ones \: digit \: = \: x} \\ &\sf{tens \: digit \: = \: y} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:So-\begin{cases} &\sf{Number \: formed = 10y + x} \\ &\sf{Reverse \: number = 10 x+y } \end{cases}\end{gathered}\end{gathered}$

☆ According to statement

A number consisting of two digits is seven times the sum of its digits.

$\rm :\longmapsto\:10y + x = 7(x + y)$

$\rm :\longmapsto\:10y + x = 7x + 7y$

$\rm :\longmapsto\:10y - 7y = 7x - x$

$\rm :\longmapsto\:3y = 6x$

$\bf :\longmapsto\:y = 2x - - - (1)$

☆ According to statement again,

When 27 is subtracted from the number, the digits are reversed.

$\rm :\longmapsto\:10y + x - 27 = 10x + y$

$\rm :\longmapsto\:10y + x -10x - y = 27$

$\rm :\longmapsto\:9y -9x = 27$

$\rm :\longmapsto\:9(y -x)= 27$

$\rm :\longmapsto\:y -x= 3$

$\rm :\longmapsto\:2x -x= 3$

$\bf :\longmapsto\:x = 3 - - - (2)$

On substituting the value of x in equation (1), we get

$\rm :\longmapsto\:y = 2 \times 3$

$\bf :\longmapsto\:y = 6$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Hence-\begin{cases} &\sf{ones \: digit \: = \: 3} \\ &\sf{tens \: digit \: = \: 6} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:So-\begin{cases} &\sf{Number \: formed = 10y + x = 63} \\ &\sf{Reverse \: number = 10 x+y = 36 } \end{cases}\end{gathered}\end{gathered}$

Hence, The required two digit number is 63.