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CAT 2025Slot 3QAQues & Sol

ArithmeticMedium

Question

Ankita walks from A to C through B, and runs back through the same route at a speed that is 40% more than her walking speed. She takes exactly 3 hours 30 minutes to walk from B to C as well as to run from B to A. The total time, in minutes, she would take to walk from A to B and run from B to C, is

Solution

1. Concept Used

  • Topic: Time, Speed and Distance — Inverse Proportionality of Time and Speed
  • Formula: $$\text{Time} = \frac{\text{Distance}}{\text{Speed}}, \quad \frac{T_1}{T_2} = \frac{S_2}{S_1}$$

2. Calculation

Let the walking speed of Ankita be $5x$. Since her running speed is $40%$ more than her walking speed, the running speed is:

$\text{Running Speed} = 1.4 \times 5x = 7x$

So the ratio of walking speed to running speed is:

$\text{Walking : Running} = 5x : 7x = 5 : 7$

Since time is inversely proportional to speed for a fixed distance, the ratio of time taken walking to time taken running over the same distance is:

$\text{Time (Walking) : Time (Running)} = 7 : 5$

Given Information:

  • Time to walk from B to C = 3 hours 30 minutes = $3.5$ hours
  • Time to run from B to A = 3 hours 30 minutes = $3.5$ hours

Step 1 — Find time to run from B to C:

Ankita walks B to C in $3.5$ hours. To find the time she takes to run the same B to C distance, we use the ratio $7:5$:

$$T_{\text{run, B to C}} = \frac{3.5}{7} \times 5 = 2.5 \text{ hours}$$

Step 2 — Find time to walk from A to B:

Ankita runs from B to A (same as A to B) in $3.5$ hours. To find the time she takes to walk the same A to B distance, we use the ratio $7:5$:

$$T_{\text{walk, A to B}} = \frac{3.5}{5} \times 7 = 4.9 \text{ hours}$$

Step 3 — Calculate total time for walking A to B and running B to C:

$$T_{\text{total}} = 4.9 + 2.5 = 7.4 \text{ hours}$$

Converting to minutes:

$$T_{\text{total}} = 7.4 \times 60 = 444 \text{ minutes}$$

3. Solution

Answer = 444 ✅

The total time Ankita takes to walk from A to B and run from B to C is 444 minutes.