Question

sum of two digits is 14 if we add 18 to the original number the digits interchamge their places . write the equation for these statements​

Answer 1

Answer:

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Step-by-step explanation:

let the numbers be xy

general form of the number =10x+y

sum of digits of a number =14

x+y=14………[1]

if 18 is added to the number, then digits are interchanged

10x+y+18=10y +x

9x-9y=-18

X-y=-2………[2]

the linear equations are 1) x+y=14

2) X-y=-2

adding [1],[2]

2x=12

x=6

x+y=14

y=14-x

y=14-6

y=8

there fore the number =10*6+8

=68

check:-

1)6+8=14

2)68+18=86

Answer 2

Answer:

68

Step-by-step explanation:

Let the unit digit be b and tens digit be a. Hence number be ab, which can also be written as 10a + b.

   Given, sum of digits = 14

⇒ a + b = 14   ⇒ a = 14 - b

  When 18 is added, number is 10a + b + 18 & digits are reversed so new number becomes ba or 10b + a.

⇒ 10a + b + 18 = 10b + a

⇒ 10a - a + b - 10b = - 18

⇒ 9a - 9b = - 18

⇒ a - b = - 2

⇒ 14 - b - b = - 2     { a = 14 - b }

⇒ 14 + 2 = 2b

⇒ 16 = 2b   ⇒ 8 = b

   Hence, a = 14 - 8 = 6

Required number is ab = 68