Kaushal travelled for 12 hours 55 minutes at the speed of 24 k... | Mathematics MCQ | Examoogle

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Kaushal travelled for 12 hours 55 minutes at the speed of 24 km/h. At what speed (in km/h) should he travel to cover the same distance in 5 hours?

62 Question ID : 441009545460 Option 1 ID : 4410092137239 Option 2 ID : 4410092137238 Option 3 ID : 4410092137237 Option 4 ID : 4410092137236 Status : Answered Chosen Option : D

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsArithmetic

Option D

62 Question ID : 441009545460 Option 1 ID : 4410092137239 Option 2 ID : 4410092137238 Option 3 ID : 4410092137237 Option 4 ID : 4410092137236 Status : Answered Chosen Option : D

Quick Summary:

Use the inverse proportion property: since distance is constant, $S1 \times T1 = S2 \times T2$ . Convert minutes to fraction of an hour: $12 \frac{55}{60} = 12 \frac{11}{12} = \frac{155}{12}$ hours.

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📐MAMath SolutionDirect Formula

📋 Given

Time taken T1 = 12 hours 55 minutes, Speed S1 = 24 km/h, New Time T2 = 5 hours.

🔢 Formula Used

D=S×TD = S \times TD=S×T

⚡ Exam Hall Shortcut / Speed Trick

Use the inverse proportion property: since distance is constant, $S1 \times T1 = S2 \times T2$ . Convert minutes to fraction of an hour: $12 \frac{55}{60} = 12 \frac{11}{12} = \frac{155}{12}$ hours.

⚠️ Common Student Trap / Pitfall

Students often treat 12 hours 55 minutes as 12.55 hours instead of converting 55 minutes into $\frac{55}{60}$ hours.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Convert total time into hours

Convert 12 hours 55 minutes to hours: $T1 = 12 + \frac{55}{60} = 12 + \frac{11}{12} = \frac{144+11}{12} = \frac{155}{12}$ hours.

T1=15512 hoursT1 = \frac{155}{12} \text{ hours}T1=12155​ hours

Calculate the total distance

Since Distance $D = S1 \times T1$ , calculate $D = 24 \times \frac{155}{12}$ .

D=24×15512=2×155=310 kmD = 24 \times \frac{155}{12} = 2 \times 155 = 310 \text{ km}D=24×12155​=2×155=310 km

Calculate new speed

To cover the same distance $D = 310$ km in $T2 = 5$ hours, use $S2 = \frac{D}{T2}$ .

S2=3105=62 km/hS2 = \frac{310}{5} = 62 \text{ km/h}S2=5310​=62 km/h

✅

D is correct because calculating the total distance as 310 km and dividing by the new time of 5 hours results in 62 km/h.

Core Concepts Used

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Time, Speed and Distance Fractional conversion Inverse proportionality

💡 EXAM TIP

This inverse relationship $S \propto \frac{1}{T}$ is also fundamental in work and wages problems where work is equivalent to distance and workers are equivalent to speed.

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