NIMCET 2014 — Reasoning PYQ

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Question

NIMCET 2014 — Reasoning PYQ

NIMCET | Reasoning | 2014

The sum of ages of a daughter and mother is 63 yr. Four years back, the mother's age was 4 times that of daughter's age at that time. What is the present age of the mother?

Choose the correct answer:

Explanation

Solution

Step 1: Define variables

Let the present age of the mother be $M$ and the present age of the daughter be $D$ .

Step 2: Formulate equations based on the given conditions

Condition 1: The sum of their present ages is $63 \text{ yr}$ .

$M + D = 63 \quad \text{---(Equation 1)}$
Condition 2: Four years ago, the mother was $4$ times as old as the daughter.

Four years ago, Mother's age was $(M - 4)$ and Daughter's age was $(D - 4)$ .

$(M - 4) = 4(D - 4) \quad \text{---(Equation 2)}$

Step 3: Solve the equations

From Equation 1, we can express $D$ in terms of $M$ :

D = 63 - M

Substitute this value of $D$ into Equation 2:

(M - 4) = 4((63 - M) - 4)

(M - 4) = 4(59 - M)

M - 4 = 236 - 4M

Now, bring the $M$ terms to one side:

M + 4M = 236 + 4

5M = 240

M = \frac{240}{5}

M = 48

Conclusion:

The present age of the mother is 48 years.

Correct Option: 2 ( $48 \text{ yr}$ )