A bike running at a speed of 50 km/h reaches its destination 10 minutes late. If it runs at 60 km/h it is late by 5 minutes. How many minutes should the bike take, travelling at usual speed to complete the journey on the same route to reach on time?

Correct option is C

​Given:​

At 50 km/hr, the bike is 10 minutes late.

At 60 km/hr, the bike is 5 minutes late.

Formula Used:

$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$​

Solution: ​

Let, 

D as the distance to be covered

T as the time the bike should take to reach on time

​At 50 km/hr:

Time taken = $$T + \frac{10}{60} \, \text{hours} \quad (\text{10 minutes} = \frac{10}{60} \, \text{hours})$$​​

​$$\text{Distance} = \text{Speed} \times \text{Time} = 50 \times \left( T + \frac{1}{6} \right)$$​​

At 60 km/hr:

​$$\text{Time taken} = T + \frac{5}{60} \, \text{hours}$$

$$\text{Distance} = \text{Speed} \times \text{Time} = 60 \times \left( T + \frac{1}{12} \right)$$​​​

Since the distance is the same in both cases:

​$$50 \left( T + \frac{1}{6} \right) = 60 \left( T + \frac{1}{12} \right)$$​​

​$$50T + \frac{25}{3} = 60T + 5$$​​

​$$10T = \frac{10}{3}$$​​

​$$T = \frac{1}{3} \, \text{hours}$$​​

Converting to minutes:

​$$T = \frac{1}{3} \times 60 = 20 \, \text{minutes}$$​​

Therefore, the bike should take 20 minutes to complete the journey on time.