Q9 of 266 Page 4

A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

Let the one’s digit be ‘a’ and ten’s digit be ‘b’


Given, number is 3 more than 4 times the sum of its digits.


10b + a = 4(a + b) + 3


⇒ 10b + a = 4a + 4b + 3


⇒ a = 2b - 1 -----(1)


Also, if 18 is added to the number, the digits are reversed.


⇒ 10b + a + 18 = 10a + b


⇒ a – b = 2 ----- (2)


Subtracting eq2 from eq1


⇒ a – 2b – a + b = -1 – 2


⇒ b = 3


Thus, a = 6 – 1 = 5


Number is 35.


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