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3. A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the
number, its digits are reversed. Find the number.
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Answers
Answer: The number is 24
Step-by-step explanation:
Let the digits be, x and y
therefore, the number will be 10*y + x (as y comes in the tens digit)
CASE : 1 According to the Question,
= 10*y + x = 4 (x+y)
= 10y + x = 4x + 4y
= 10y - 4y = 4x - x
= 6y = 3x -------------- (1)
CASE: 2 According to the question,
= (10y + x)+ 18 = 10x + y ( the digits interchange)
= 10y - y + 18 = 10x - x
= 9y + 18 = 9x
= 9y - 9x = -18 ----------------------(2)
From eq. 1
x = 6y/3 -----------------------(3)
Substituiting the value of x in eq. 2
= 9y - 9 * 6y/3 = -18
= 9y - 18y = -18
= -9y = -18
= y = -18/-9
= y = 2 (minus cancels)
Substitute the value of y in eq. 3
= x = 6 * 2/3
= x = 12/3 => 4
= x = 4
There fore x = 4 and y = 2
Therefore, according to the equation ,
10y + x
= 10*2 + 4
= 24.
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