Math, asked by anshumansingh123, 10 months ago

6.
The sum of digits of a 2-digit number
is 6 If the digits of the numbers are reversed
the new number is decreased by 36 find the
number. ​

Answers

Answered by MяƖиνιѕιвʟє
18

Given :-

  • The sum of digits of a 2-digit number is 6 If the digits of the numbers are reversed the new number is decreased by 36

To find :-

  • Original number

Solution :-

Let the ones digit be y then tens digit be x

  • Original number = (10x + y)

According to the first condition

  • Sum of digits of a 2-digit number is 6

→ x + y = 6 -----(i)

According to the second condition

  • The digits of the numbers are reversed
  • the new number is decreased by 36

  • Reversed number = (10y + x)

→ 10x + y = 10y + x - 36

→ 10x + y - 10y - x = - 36

→ 9x - 9y = - 36

→ 9(x - y) = - 36

→ x - y = - 4 -------(ii)

Add both the equations

→ (x + y) + (x - y) = - 4 + 6

→ x + y + x - y = 2

→ 2x = 2

→ x = 2/2 = 1

Put the value of x in equation (ii)

→ x - y = - 4

→ 1 - y = - 4

→ y = 1 + 4 = 5

Therefore ,

  • Tens digit = x = 1

  • Ones digit = y = 5

Hence,

  • Original number = 10x + y = 15

  • Reversed number = 10y + x = 51
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