NIMCET 2008 — Reasoning PYQ

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Question

NIMCET 2008 — Reasoning PYQ

NIMCET | Reasoning | 2008

A person travels on a cycle from home to church on a straight road with wind against him. He took 4 h to reach there. On the way back to the home, he took 3 h to reach as wind was in the same direction. If there is no wind, how much times does he take to travel from home to church?

Choose the correct answer:

Explanation

1. Define Variables:

Let $x$ be the speed of the cyclist in still air.
Let $w$ be the speed of the wind.
Let $d$ be the distance between home and church.

2. Establish Equations:

Against the wind (Upwind): Speed $= x - w$ . Time $= 4\text{ h}$ .

$d = 4(x - w) \implies \frac{d}{4} = x - w$
With the wind (Downwind): Speed $= x + w$ . Time $= 3\text{ h}$ .

$d = 3(x + w) \implies \frac{d}{3} = x + w$

3. Solve for $x$ (Speed in still air):

Add the two equations to eliminate $w$ :

(x - w) + (x + w) = \frac{d}{4} + \frac{d}{3}

2x = \frac{3d + 4d}{12}

2x = \frac{7d}{12} \implies x = \frac{7d}{24}

4. Calculate Time without wind ( $T$ ):

Time taken when there is no wind is $T = \frac{d}{x}$ .

T = \frac{d}{\frac{7d}{24}} = \frac{24}{7}\text{ hours}

5. Convert to Hours, Minutes, and Seconds:

$T = 3 \frac{3}{7}\text{ hours} = \mathbf{3\text{ h}}$
$\frac{3}{7} \times 60 \text{ min} = \frac{180}{7} \approx 25.71\text{ min} = \mathbf{25\text{ min}}$
Remainder: $\frac{180}{7} - 25 = \frac{180 - 175}{7} = \frac{5}{7}\text{ min}$
$\frac{5}{7} \times 60 \text{ s} = \frac{300}{7} \approx \mathbf{42.8\text{ s}}$

Rounding to the nearest second gives 3 h 25 min 43 s (closest to option d).

Final Answer:

The time taken without wind is 3 h 25 min 42 s.

Correct Option: (d)