NIMCET 2008 — Reasoning PYQ

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Question

NIMCET 2008 — Reasoning PYQ

NIMCET | Reasoning | 2008

A watch which gains 10 s in 5 min was set correct at 9 am when the watch indicated 20 min past 7 O’ clock, the same evening, the true time is

Choose the correct answer:

Explanation

1. Calculate the Error Rate

The watch gains 10 seconds every 5 minutes.

First, let's find the total "watch time" that passes for every 5 minutes of "true time":

True Time interval = $5 \text{ min}$
Watch Time interval = $5 \text{ min} + 10 \text{ sec}$

To make the units consistent:

5 \text{ min} + 10 \text{ sec} = 5 + \frac{10}{60} = 5 + \frac{1}{6} = \frac{31}{6} \text{ minutes}

So, $\frac{31}{6}$ minutes of the Watch Time is equal to $5$ minutes of the True Time.

2. Find the Total Watch Time Elapsed

The watch was set correct at 9 am.

The watch now shows 7:20 pm (20 min past 7) the same evening.

Time from 9 am to 12 pm = $3 \text{ hours}$
Time from 12 pm to 7:20 pm = $7 \text{ hours } 20 \text{ minutes}$
Total Watch Time = $10 \text{ hours } 20 \text{ minutes}$

Convert this total into minutes:

\text{Total Watch Minutes} = (10 \times 60) + 20 = 620 \text{ minutes}

3. Calculate the True Time Elapsed

We use the ratio derived in step 1:

\text{True Time} = \text{Watch Time} \times \left( \frac{\text{True Interval}}{\text{Watch Interval}} \right)

Substituting the values:

\text{True Time} = 620 \times \left( \frac{5}{31/6} \right)

\text{True Time} = 620 \times \left( \frac{5 \times 6}{31} \right)

\text{True Time} = 620 \times \frac{30}{31}

Now, simplify:

\text{True Time} = 20 \times 30 = 600 \text{ minutes}

4. Determine the Actual Time

Convert the 600 minutes of True Time back into hours:

\frac{600}{60} = 10 \text{ hours}

The true time is exactly 10 hours after 9 am.

$9 \text{ am} + 10 \text{ hours} = 7 \text{ pm}$

Final Answer

The true time is 7 pm.

The correct option is (a).