A two-digit number is 3 more than 4 times the sum of its dig1ts. IF 18 1s
added to the number, the digits are reversed. Find the number.
Answers
Step-by-step explanation:
ANSWER
Let the digit in ones place be x and tens place be y.
Original number is 10y+x.
Number formed by reversing the digits is 10x+y
Given 10y+x=4(x+y)+3
⇒10y+x−4x−4y=3
⇒6y−3x=3
⇒2y−x=1.............(1)
Also given that when 18 is added to the number the digits gets interchanged.
Therefore, (10y+x)+18=10x+y
⇒9x−9y=18
⇒x−y=2.............(2)
Add (1) and (2), we get
2y−y−x+x=1+2
y=3
Put y=3 in x−y=2, we get
x−3=2
i.e. x=5
Hence, the number is (10y+x)=10(3)+5=35.
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Asked on December 20, 2019 by
Faizul Directionar
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.
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ANSWER
Let the digit in ones place be x and tens place be y.
Original number is 10y+x.
Number formed by reversing the digits is 10x+y
Given 10y+x=4(x+y)+3
⇒10y+x−4x−4y=3
⇒6y−3x=3
⇒2y−x=1.............(1)
Also given that when 18 is added to the number the digits gets interchanged.
Therefore, (10y+x)+18=10x+y
⇒9x−9y=18
⇒x−y=2.............(2)
Add (1) and (2), we get
2y−y−x+x=1+2
y=3
Put y=3 in x−y=2, we get
x−3=2
i.e. x=5
Hence, the number is (10y+x)=10(3)+5=35.