Question

Sum of the two digits number is 9. When we interchange the digits the new number is 27 greater than the earlier number. Find the number.​

Answer 1

Answer:

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Step-by-step explanation:

Let x and y be the tens and units digits of the number, respectively. Then the relevant equations are x + y = 9 and 10 x + y +27 = 10 y + x. The solution for this system of equations is x = 3 and y = 6. Hence, the two-digit number is 36.

Answer 2

$\huge\underline\mathrm{SOLUTION:-}$

Given:

• The sum of the two digits is 9.

On interchanging the digits, the resulting new number is greater than the original number by 27.

Let us assume the digit of units place be x.

• Then the digit of tens place will be 9 - x.
• Thus the two-digit number is 10(9 - x) + x

Let us reverse the digit

• The number becomes 10x + (9 - x).

$\bf \underline \pink {As\:per\:the\:given\:condition:}$

10x + (9 - x) = 10(9 - x) + x + 27

= 9x + 9 = 90 - 10x + x + 27

= 9x + 9 = 117 - 9x

$\bf \underline \pink {On\:rearranging \:the\:terms,\:we\:get:}$

➠ 18x = 108

➠ x = 6

• So the digit in units place is 6.

Digit in tens place is 9 - x = 9 - 6 = 3

• Hence the number is 36.

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