Question

the sum of the digits of the two digit number is 14. if 18 is subtracted from the number digits are reversed.find the number.

Answer 1

Answer:

The original number is 64

Step-by-step explanation:

Let the digits in tens place be = x

Let the digit in ones place be = y

According to question,

x + y = 14 ---- eq. 1

The format of a regular two digit number is 10x + y

For example, a number such as 36 can be written as 10 x 3 + 6

So, the original number is 10x + y

If the digits are reversed, the number becomes 10y + x

According to question,

10x + y - 18 = 10y + x

9x - 9y = 18

Simplifying this equation gives

9(x - y) = 18

x - y = 2 ---- eq. 2

Adding eq. 1 and eq. 2

We get

x + y + x - y = 14 - 2

2x = 12

x = 6

Substituting x in eq. 2

6 - y = 2

y = 4

Therefore, the original number = 10x + y

= 10 x 6 + 4

= 64

Answer 2

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{let:}}}}$

• $\sf{The\: ones\: digit=x}$
• $\sf{The\: ten's\: digit=y}$
• $\sf{The\: Number=10y+x}$

$\small{\underline{\orange{\rm{To\: Find:}}}}$

• $\sf{The\: Number=?}$

$\large{\underline{\red{\rm{Given,\:in\:1st\:case:}}}}$

• $\sf{the\:sum\:of\:2\: digits=14}$

$\rm{\implies x+y=14}$

$\rm\purple{\implies x+y=14------(i)}$

$\large{\underline{\red{\rm{Given,\:in\:2nd\:case:}}}}$

• $\sf{If\:18\:is\: subtracted\: from\:the\: Number\: digits\:are\: reversed}$

$\rm{\implies 10y+x-18=10x+y}$

$\rm{\implies 10x-x+y-10y=-18}$

$\rm{\implies 9x-9y=-18}$

• $\sf{Dividing\:by\:9\:on\: both\: sides}$

$\rm{\implies x-y=-2}$

$\rm\purple{\implies x-y=-2-----(ii)}$

• $\sf{Now,\: solving\: equation}$

$\rm{\implies x+y=14}$

$\rm{\implies x-y=-2}$

• $\sf{by\: solving\:we\:get}$

$\rm{\implies 2x=12}$

$\rm\green{\implies x=6}$

• $\sf{putting\:the\: value\:of\:x=6\:in\:eq\:1}$

$\rm{\implies x+y=14}$

$\rm{\implies 6+y=14}$

$\rm{\implies y=14-6}$

$\rm\green{\implies y=8}$

Hence,

$\rm\orange{\implies The\: Number=10y+x=10*8+6=86}$

$\rm\orange{\implies The\: reversed\:Number=10x+y=10*6+8=68}$