Question

a two digit number is 7 times the sum of its two digits. the number that is formed by reversing its digit is 18 less than the original number. what is the number?​

Answer 1

Answer:42

Step-by-step explanation:

let the two-digit number be 10x+y

given,the number is 7 times the sum of its digits

⇒10x+y=7(x+y)

10x+y=7x+7y

3x=6y

x=2y

the number formed by reversing the digits is 18 less than original number

⇒10x+y-(10y+x)=18

   10x+y-10y-x=18

   9x-9y=18

  9(x-y)=18

  (x-y)=18/9=2

⇒x-y=2

x=2y

⇒2y-y=2

y=2

x=4

∴the number is 42

Answer 2

Answer:

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Step-by-step explanation:

given that,

A two digit number is 7 times the sum of its digits,

let the digits be x and y,

so,

number = 10y + x,

According to the question,

10y + x = 7(x +y),

10y + x = 7x + 7y,

10y - 7y + x - 7x = 0,

3y - 6x = 0,

3(y - 2x) = 0,

y - 2x = 0,

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

also,

given that,

The number formed by reversing the digits is 18 less than original number:

so,

number formed by reversing the digits = 10x + y,

so,

10x + y = 10y + x - 18,

10x - x + y - 10y = -18,

9x - 9y = -18,

9(x - y) = -18,

x - y = -18/9,

x - y = -2 .....(2),

putting the value of y on (2),

x - y = -2,

x - 2x = -2,

-x = -2,

x = 2,

from (1),

y = 2x,

y = 2(2),

y = 4,

x = 2,

number,

= 10y + x,

= 10(4) + 2,

= 40 + 2,

= 42,

so,

the original number = 42.

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VERIFICATION

1.) two digit number is 7 times the sum of its digits,

two digit number = 42,

digits = 4 and 2,

42 = 7(4 + 2),

42 = 7×6,

42 = 42.

__________

2.) The number formed by reversing the digits is 18 less than original number .

reversed number = 24,

original number = 42,

42 = 24 + 18,

42 = 42.

___________

Hope it helps you.✔✔✔

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