NIMCET 2011 — Reasoning PYQ

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Question

NIMCET 2011 — Reasoning PYQ

NIMCET | Reasoning | 2011

A clock is set right at 8 a.m. The clock gains 10 minutes in 24 Hrs. What will be the right time when the clock indicates 1 p.m. on the following day ?

Choose the correct answer:

Explanation

Solution

1. Calculate the total time elapsed on the faulty clock:

From $8$ a.m. today to $8$ a.m. tomorrow = $24$ hours
From $8$ a.m. tomorrow to $1$ p.m. tomorrow = $5$ hours
Total time on faulty clock = $24 + 5 = 29$ hours

2. Establish the ratio between True Time and Faulty Time:

The clock gains $10$ minutes in $24$ hours.

$24$ hours of correct time = $24$ hours $10$ minutes of faulty time.
$24$ hours $10$ minutes = $24 + \frac{10}{60} = 24 + \frac{1}{6} = \frac{145}{6}$ hours.

So, $\frac{145}{6}$ hours of faulty clock = $24$ hours of correct clock.

3. Calculate the correct time for 29 faulty hours:

\text{Correct time} = 29 \times \left( \frac{24}{\frac{145}{6}} \right)

\text{Correct time} = 29 \times \frac{24 \times 6}{145}

\text{Correct time} = 29 \times \frac{144}{145}

\text{Correct time} = \frac{144}{5} \text{ hours}

\text{Correct time} = 28.8 \text{ hours}

4. Convert 28.8 hours into hours and minutes:

$28$ hours $+ 0.8 \times 60$ minutes
$28$ hours $48$ minutes

5. Determine the final time:

$8$ a.m. $+ 24$ hours = $8$ a.m. next day.
$8$ a.m. $+ 4$ hours $48$ minutes = $12.48$ p.m.

Correct Option: (b) $12.48$ p.m.