Number System-Test 1

Answer: Option D

Explanation

Let the number be 10x+y

According to the question, the two digit number is three times the sum of its digits

10x+y=3(x+y)

⇒ 10x-3x+y-3y=0

⇒ 7x-2y=0---Eq1

and when 45 is added to original number, the digits are reversed

10x+y+45=10y+x

⇒ 9x-9y=-45

⇒ 9y-9x=45

⇒ y-x=5---Eq2

If we multiply Eq2 by '2' we get,

 -2x+2y=5×2---Eq3

By adding Eq1 and Eq3 we get

⇒ 5x=10

⇒ x=2

Substituting the value of x we get y=7

∴ Number is (10×2)+7=27

Hence option D is correct.

Answer: Option D

Explanation

Let the original number be 10x+y and y=2x

The number obtained by interchanging the position of the digits =10y+x

⇒ 10x+y+27=10y+x

⇒ 9x-9y=-27

⇒ y-x=3 or 2x-x=3

⇒ y=3×2=6

∴ x=3,y=6

So, 50% of this number is 18.

Answer: Option D

Explanation

Let the obtained number be 10x+y

The number obtained by interchanging the position of the digits =10y+x

Again, difference = 9x-9y

Now, 9x-9y=27

x-y=3

But, here all the given options fulfill this condition.

Hence, we cannot determine an exact answer.

Answer: Option C

Explanation

Let the number in unit's place be x

Then digit at tens place will be 4x

∴  10×4x++x  ---Eq(1)

According to the question 

It given that x+4x=10

⇒ 5x=10

⇒x=2

subtitute 'x'in Eq(1) we get 

⇒10×4×2+2

⇒ 82

Hence Option C is correct.

Answer: Option A

Explanation

Let the two digit number be 10x+y and the number by interchanging the position of the digits =10y+x

Now, 10x+y-(10y+x)=36

⇒ 9x-9y=36

⇒ x-y=4

Hence, Option A is correct.