Question
Download Solution PDFThe sum of the digits of a two-digit number is 10, when the number is reversed, the number increases by 72. Find the numbers.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
x + y = 10
(10y + x) - (10x + y) = 72
Formula Used:
Number = 10x + y
Reversed = 10y + x
Calculations:
(10y + x) - (10x + y) = 72
⇒ y - x = 8
Also, x + y = 10
⇒ y = 10 - x
Then,
⇒ (10 - x) - x = 8
⇒ 10 - 2x = 8
⇒ 2x = 2
⇒ x = 1
⇒ y = 10 - 1 = 9
Number = 10 × 1 + 9 = 19
∴ Number is 19.
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