Number System-Test 1

Answer: Option C

Explanation

let the two digit number be 10x+y

and the number obtained by interchanging the position of the digits be 10y+x

According to the question,

(10x+y)−(10y+x)= 9

⇒ 9x−9y=9

⇒ 9(x−y)=9

⇒ (x−y)=1---Eq1

and it is given that x+y=15---Eq2

Upon adding Eq 1 and Eq 2 we get,

(x-y=1)+(x+y=15)⇒2x=16

x=8

Inserting the value of x in the eq (2) we get y=7

So, the original number is 87. Hence option C is correct

Answer: Option A

Explanation

In the above question, a two digit number is supposed as 10y+x or 10x+y and solved as follows

And, y=x²

Let the two digit positive number be 10x+y

According to the question,  10x+y-(10y+x)=54

⇒ 9x-9y=54

⇒ x-y=6

As per the question y=x², So

⇒ x-x²=6

⇒ x-x²-6=0

⇒ x²-3x-2x-6=0

⇒ x(x-3)-2(x-3)=0

⇒ (x-2)(x-3)=0

⇒ x=2 or x=3

∴ y=x²  or y=4, 9

Number is either 24 or 39.

According to the question difference between the original number and the number obtained by interchanging the digits is 54

Here, 24 is not possible (42-24=18)

And 39 is the original number (93-39=54)

40% of the original number is

$39\times \frac{40}{100}=3.9\times 4=15.6$

Hence, Option A is correct.

Answer: Option B

Explanation

Let the original number be 10x+y

Number obtained upon interchanging the digits is x+10y

According to the question, difference been the original number and the number after interchanging is 63

So, (10x+y)-(x+10y)=63

⇒ 9(x-y)=63

⇒ x-y =7---Eq1

It is given that x+y=11---Eq2

Upon adding adding Eq1 and Eq2 we get 

⇒ 2x=18

Therefore x=9 and y=2

∴ so the original number is [(10x9)+2]=92

Hence option B is correct.

Answer: Option B

Explanation

Let the three digit number be 100x+10y+z

According to the question z=2y and z=1.5×x

x+y+z=13

$$\begin{gathered} \therefore \frac{z}{1.5}+\frac{z}{2}+z=13 \\ \Rightarrow 2z+1.5z+3z=39 \\ \Rightarrow 6.5z = 39 \\ \Rightarrow z=\frac{39}{6.5} \end{gathered}$$

Now z=6, y=3, x=4

So the original three digit number is

(100x4)+(10x3)+(6x1)

400+30+6=436

Hence option B is correct.

Answer: Option C

Explanation

Let the number be 10x+y

and   x+y=12---Eq1

⇒ x-y=6---Eq2

By adding Eq1 and Eq2 we get,

⇒ 2x=18

⇒ x=9

Substituting the value of x in Eq1 we get, y=3

So, original two digit number is (10×9)+3=93

Hence, option C is correct.