Time Increase Due to Reduced Speed Problem

❓ Question

A person goes to his office from his home daily at a fixed speed. But today he reduced his speed by 20% and as a result he reaches his office 16 minute late. What was the time taken to reach his office daily?

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🖼 Question Image

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✍️ Short Explanation

This is a time-speed relation problem.

👉 Distance remains constant
👉 Speed decreases by 20%
👉 Time increases accordingly.

Use:

$$\text{Time} \propto \frac1{\text{Speed}}$$

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🔷 Step 1 — Assume Original Speed and Time 💯

Let:

Original speed:

$$v$$

Original time:

$$t$$

Distance:

$$d=vt$$

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🔷 Step 2 — Reduced Speed

Speed reduced by:

$$20\%$$

New speed:

$$0.8v$$

New time:

$$\frac{d}{0.8v}$$

Substitute:

$$d=vt$$
$$\text{New time}=\frac{vt}{0.8v}$$
$$=\frac{t}{0.8}$$
$$=\frac54 t$$

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🔷 Step 3 — Increase in Time

Extra delay:

$$\frac54 t-t$$
$$=\frac14 t$$

Given delay:

$$16 \text{ minutes}$$

So:

$$\frac14 t=16$$
$$t=64 \text{ minutes}$$

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🔷 Step 4 — JEE Trap Alert 🚨

❌ Speed decrease ko direct time decrease maan lena

❌ Percentage relation ulta use kar dena

❌ Distance constant condition ignore kar dena

Remember:

$$\text{Time inversely proportional to speed}$$

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✅ Final Answer

$$\boxed{64\text{ minutes}}$$

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