Question

in a number of 2 digits unit is twice the tens digit .if 36 be added to the number the digits are reversed .what is the number ​


guys plz answer ...i need it soon

Answer 1

$\mathfrak{\huge{\underline{Solution:}}}$

$\textbf{\huge{\underline{Given:}}}$

● Unit digit is twice the tens digit

● Numbers are reversed after being added to 36

___________

Let the digit at units place be x and digit at tens place be y

$\star \sf \: Original \: No. = 10x + y$

$\star \sf \: Interchanged \: No. = 10y + x$

Given :

$\implies \: \rm \: y = 2x......eq.(i)$

$\textbf{\underline{\underline{According\:To\:Question:}}}$

$\hookrightarrow \: \sf \: 10x + y + 36 = 10y + x$

$\hookrightarrow \sf \: 10x + y - x - 10y = - 36$

$\hookrightarrow \sf 9x - 9y = - 36$

$\hookrightarrow \sf \: 9(x - y) = - 36$

Putting the value of y = 2x from eq.(i)

$\hookrightarrow \sf9(x - 2x) = - 36$

$\hookrightarrow \sf9 (- x) = - 36$

$\hookrightarrow \sf \: - 9x = - 36$

$\hookrightarrow \sf x = \cancel \dfrac{ - 36}{ - 9}$

$\hookrightarrow \sf \: x = \large\boxed{4}$

Putting the value of x = 4 in eq.(i)

$\implies \: \rm \: y = 2x$

$\implies \rm \: y = 2 \times 4$

$\implies \rm \: y = \large \boxed{8}$

Hence,The Digit at unit place = 4 and digit at tens place = 8

$\star \sf \: Original \: No. = 48$

$\star \sf \: Interchanged \: No. = 84$

Answer 2

Answer: 48

Step-by-step explanation:

Let the digit in unit's place be 'y'.

Similarly, digit in ten's place be 'x'.

So, The number formed will be: 10x + y.

Case 1:

Given that the unit's digit is twice the ten's digit.

=> y = 2x ....(1)

Case 2:

Given that, when 36 is added to the number i.e 10x + y, then the digits are reversed to 10y + x.

.°. [10x + y] + 36 = 10y + x

Substituting the given values,

9x - 9y + 36 = 0

From (1),

9x - 9 ( 2x ) = -36

9x - 18x = -36

-9x = -36

x = 4

Thus,

From (1),

y = 2x

=> y = 8

Number formed = 10x + y

= 10 × 4 + 8

= 48

Thus, the number formed is 48.