Mathematics
The sum of the digits of a two digit number is 12. If the number is decreased by 18, its digits get reversed. The number is
48
84
57
75
Answer
Let the digit at ten's place be x and digit at one's place be y.
Given, sum of digits = 12.
x + y = 12 …….(i)
Number = 10 × x + y = 10x + y
On reversing digits, number = 10 × y + x = 10y + x.
⇒ 10x + y - 18 = 10y + x
⇒ 10x - x + y - 10y - 18 = 0
⇒ 9x - 9y = 18
⇒ 9(x - y) = 18
⇒ x - y = 2 …….(ii)
Adding (i) and (ii) we get,
⇒ x + y + (x - y) = 12 + 2
⇒ 2x = 14
⇒ x = 7.
Substituting value of x in (i) we get,
⇒ 7 + y = 12
⇒ y = 5.
Number = 10 × x + y = 10 × 7 + 5 = 75.
Hence, Option 4 is the correct option.
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