NIMCET 2012 — Reasoning PYQ

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Question

NIMCET 2012 — Reasoning PYQ

NIMCET | Reasoning | 2012

The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit’s place is 3 more than the digit in ten’s place, then the number is

Choose the correct answer:

Explanation

1. Formulate the Equations

Let the digit at the ten's place be $x$ and the digit at the unit's place be $y$ .

The two-digit number can be expressed as: $10x + y$ .

According to the first condition (Ratio is $4:1$ ):

\frac{10x + y}{x + y} = \frac{4}{1}

10x + y = 4(x + y)

10x + y = 4x + 4y

6x = 3y

2x = y \quad \text{---(Eq. 1)}

According to the second condition (Unit's digit is $3$ more than ten's digit):

y = x + 3 \quad \text{---(Eq. 2)}

2. Solve for $x$ and $y$

Substitute the value of $y$ from Eq. 1 into Eq. 2:

2x = x + 3

x = 3

Now, find $y$ using Eq. 1:

y = 2(3) = 6

3. Determine the Number

The digits are $x = 3$ and $y = 6$ .

Therefore, the number is $10(3) + 6 = 36$ .

Correct Option: (c)