A person cycles from hostel to college at a speed of 20 kmph and reaches 13.5 minutes late.

A person cycles from hostel to college at a speed of 20 kmph and reaches 13.5 minutes late. If he cycles at a speed of 24 kmph and reaches early by 13.5 minutes, find the distance between hostel and college. (In km)

एक व्यक्ति हॉस्टल से कॉलेज तक 20 किमी प्रति घंटे की गति से साइकिल चलाता है और 13.5 मिनट देरी से पहुंचता है। यदि वह 24 किमी प्रति घंटे की गति से साइकिल चलाता है और 13.5 मिनट जल्दी पहुंचता है, तो हॉस्टल और कॉलेज के बीच की दूरी ज्ञात कीजिए। (किमी में)

a) 52
b) 54
c) 48
d) 50

Ans : b) 54

UP Police SI Paper – Mathematics

Solution:

We can solve this problem using the time-distance formula and a simple trick:

Formula used:

Distance = $\frac{S_1 \times S_2}{S_2 - S_1} \times \text{Time Difference (in hours)}$

Where:

S1=20S_1 = 20S1=20 kmph (slower speed)
S2=24S_2 = 24S2=24 kmph (faster speed)
The total time difference is 13.5+13.5=27 minutes, = 27/60 hrs

Step-by-step solution:

Apply the formula:

Distance = $\frac {20 \times 24}{24 - 20} \times \frac {27}{60}$
= $\frac {480}{4}\times\frac {27}{60}$ = 54 Km

Thus, the distance between the hostel and the college is 54 km.