Question

The sum of a two digit number and the numerator formed by interchaning the digit is 110.If 10 is subtracted from the first number, the new number is 4 more than 5 times the sums of the digits of the first number. Find the first number​

Answer 1

Refer to the attachment↑↑↑

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Answer 2

$\huge\sf{\underline{\underline{Answer}}}$

• Let the Ones Digit be x 
• Tens Digit be y.

▪Number which will be = (10y + x)

▪Number which will be Formed by Interchange = (10x+ y)

⇒ (10y + x) + (10x + y) = 110

⇒ 11y + 11x = 110

⇒ 11(y + x) = 110

Dividing the terms by 11

⇒ y + x = 10 ⠀⠀⠀⠀⠀⠀⠀⠀⠀

⇒ x = 10 - y ⠀⠀⠀⠀⠀⠀⠀⠀⠀

⇒ 10 = 4 + 5 × [Sum of digists]

⇒ (10y + x) - 10 = 4 + 5 × (y + x)

⇒ 10y + x - 10 = 4 + (5 × 10)

⇒ 10y + x - 10 = 4 + 50

⇒ 10y + x = 54 + 10

putting the value of x from equation number 1

⇒ 10y + 10 - y = 54 + 10

⇒ 10y - y = 54 + 10 - 10

⇒ 9y = 54

Dividing the terms by 9

⇒ y = 6

Now, we Putt the Value of y in equation 2

⇒ x = 10 - y

⇒ x = 10 - 6

⇒ x = 4

Therefore

(10y + x)

10(6) + 4

60 + 4

64

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