Number System-Test 3

Answer: Option E

Explanation

According to the question

Let the number be x and y

Given ratio 3:4

Given Condition 8(3a²)=4a²+504

⇒ 72a²=16a²+504

⇒72a²-16a²=504

⇒ 56a²=504

⇒a²=9

⇒a=3

∴ x= 3a= 3×3 =9

  y=4a=4×3=12

⇒x=9, y=12

Hence, Option E is correct.

Answer: Option B

Explanation

Let the fraction be $\frac{x}{y}$

According to the question

Given x+y=11

= x=11-y ---Eq(1)

$$\begin{gathered} = \frac{x+1}{y-2}=\frac{3}{2} ---Eq\left(2\right) \\ Substitute \text{'}x\text{'} in Eq\left(2\right) we get, \\ =\frac{{\displaystyle (11-y)+1}}{{\displaystyle y-2}}=\frac{{\displaystyle 3}}{{\displaystyle 2}} \\ =\frac{{\displaystyle (11-y)+1}}{{\displaystyle y-2}}=\frac{{\displaystyle 3}}{{\displaystyle 2}} \\ =\frac{{\displaystyle 12-y}}{{\displaystyle y-2}}=\frac{{\displaystyle 3}}{{\displaystyle 2}} \end{gathered}$$

= 2(12-y)=3(y-2)

= 24-2y=3y-6

= -2y-3y=-6-24

= -5y= -30

= y=6

Substitute 'y' in Eq(1) we get,

= x=11-(6)

= x=5

∴ (x,y)=(5,6)

Hence, Option B is correct.

Answer: Option C

Explanation

Let the first number be 'x' and the second number be 'y'

According to the question 

Sum of twice the first number and thrice the second number is 141 = 2x+3y=141  ---Eq(1) 

Sum of thrice the first number and twiice the second number is 174 = 3x+2y=174 ---Eq(2)

From Eq(1) 

$$\begin{gathered} = 2x+3y=241 \\ = x=58-\frac{2}{3}y ---eq\left(3\right) \\ = 2\left(58-\frac{2}{3}y\right)+3y=141 \\ = y=15 \\ Substitue \text{'}y\text{'} value in Eq\left(3\right) we get, \\ = x=58-\frac{2}{3}\times \left(15\right) \\ =x=48 \\ \therefore (x,y)=(48,15) \end{gathered}$$

The largest number is x=48

Hence, Option C is ccorrect.

Answer: Option B

Explanation

Let the Ten's digit be 'x' and unit's digit be 'y'

The two-digit number = 10x+y (where, x>y)

According to the question

⇒ x+y=14 ---Eq(1)

⇒ x-y=2 ---Eq(2)

Solving Eq(1) and Eq(2) 

⇒ x-y=2

=x= 2+y

substitute 'x' in Eq(1) we get

⇒ y=6

substitute 'y' in Eq(2) we get

⇒ x=2+6=8

⇒ x=8, y=6

∴ Required product =8×6=48

Hence, Option B is correct.

Answer: Option A

Explanation

Let the middle digit be 'x'

Then, 2x=10 or x=5

So, the number is either 253 or 325

Since, the number increases on reversing the digits. So, the hundreds digit is smaller than units digit

∴ Required number be 253.

Hence, Option A is correct.