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Q.

A two - digit number is 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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a

12

b

25

c

28

d

26 

answer is A.

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Detailed Solution

It is given that,
Two - digit number is 4 times the sum of its digits and if 18 is added to the number, the digits are reversed.
Consider, the unit’s digit be y and the ten’s digit be x.
Then, the original number be 10x + y.
After reversing the digits:
New number = x + 10y
According to question,
Two-digit number is 4 times the sum of its digits so,
10x+y=4(x+y) ⇒10x-4x-4y+y=0 ⇒6x-3y=0 ⇒2x-y=0      … (1)  And if 18 is added to the number, then the digits are reversed so,
10x + y + 18 = x + 10y  
⇒10x-x+y-10y=-18 ⇒9x-9y=-18 ⇒x-y=-2      … (2)  Find the value of one variable in terms of other variables from the first equation:
From equation (1),
y=2x     … (3)
Substitute the value of y=2x in equation (2),
x-2x=-2
⇒x=1 Put the value of x=1 in equation (3) to find the value of y:
y=2x=2×1=2 Then,
Original number = 10x + y
⇒Original number = 10 × 1 + 2
⇒Original number = 10 + 2
⇒Original number = 12
So, the number is 12.
Hence, option (1) is correct.
 
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