Mathematics
The sum of digits of a two digit number is 7. If the digits are reversed, the new number increased by 3 equals 4 times the original number. Find the number.
Linear Equations
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Answer
Let digit at ten's place be x and unit's digit be y.
Number = 10 × x + y = 10x + y.
Reverse number = 10 × y + x = 10y + x.
Given, sum of digits is 7
∴ x + y = 7
⇒ x = 7 - y ……(i)
According to question,
⇒ 4(10x + y) = 10y + x + 3
⇒ 40x + 4y = 10y + x + 3
⇒ 40x - x + 4y - 10y = 3
⇒ 39x - 6y = 3
⇒ 3(13x - 2y) = 3
⇒ 13x - 2y = 1 …….(ii)
Substituting value of x from (i) in (ii) we get,
⇒ 13(7 - y) - 2y = 1
⇒ 91 - 13y - 2y = 1
⇒ 91 - 15y = 1
⇒ 15y = 91 - 1
⇒ 15y = 90
⇒ y = 6.
Substituting value of y in (i) we get,
x = 7 - y = 7 - 6 = 1.
∴ Number = 10x + y = 10(1) + 6 = 16.
Hence, number = 16.
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