A two-digit number is four times the sum of its digits. If 27 is added

Question

A two-digit number is four times the sum of its digits. If 27 is added to the number, its digits are reversed. Find the number.

A 63
B 36
C 91
D 19
E 25

chetan2u · Answer

A two-digit number is four times the sum of its digits, Clearly the number is EVEN. Only B possible.

Let the number be ab, so 10a+b=4(a+b).......6a=3b....b=2a.
The number could be 12, 24, 36, .....

If 27 is added to the number, its digits are reversed.
27+10a+b=10b+a......27=9b-9a=9(b-a)=9(2a-a)=9a....a=3 and b=2a=6
number ab = 36

B

Aditi0825 · Answer

If the number is 4 times the sum of its digit, the number must be even. So the answer must be B as we have only one even number in the solution.
Let z be two digit number, x and y be unit and tens digit respectively.
So, z = 4(x+y)
 -> z = 2*2(x+y)
Any number multiplied by 2 becomes even number

ramlala · Answer

Lets say number is xy

condition 1
10x + y = 4 (x + y)
6x = 3y
y = 2x

Condition 2
10x + y + 27 = 10y + x
9y - 9x = 27
y - x = 3
2x - x = 3
x = 3
y = 2x = 6

Number is 36

Ans B

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • A two-digit number is four times the sum of its digits
• If 27 is added to the number, its digits are reversed

To find  
We need to determine
 • The value of the number

Approach and Working out  
As the number is 4 times of its sum of the digits, it implies the number is a multiple of 4
 • A multiple of 4 implies the number is always even
• Only one option is even – 36. Hence, the number is 36.

Thus, option B is the correct answer.

Correct Answer: Option B

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A two-digit number is four times the sum of its digits. If 27 is added

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