​A man rides his bicycle for 10 km at an average speed of 12 km/h and further travels 12 km at an average speed of 10 km/h. What is his approximate average speed for the entire trip?​

Correct option is A

Given:

Distance traveled in the first part: 10 km

Speed in the first part: 12 km/h

Distance traveled in the second part: 12 km

Speed in the second part: 10 km/h

Formula Used:

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

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

Solution:

me taken for the first part:

Time1 = $$\frac{\text{Distance 1} }{\text{Speed 1}}$$​ = $$\frac{10 km }{12 km/h}$$​ = $$\frac{5 }{6}$$​ hours

Time2 = $$\frac{\text{Distance 2} }{\text{Speed 2}}$$​ =$$\frac{12 \, \text{km}}{10 \, \text{km/h}} = \frac{6}{5} \, \text{hours}$$​​

Total Distance  = 10 km + 12 km = 22 km

Total Time = $$\frac{5 }{6}$$​ hours + $$\frac{6}{5}$$​ hours = $$\frac{(25 + 36) }{ 30}$$​ hours = $$\frac{61}{30}$$​ hours​​

Average Speed = $$\frac{22 \text{ km}}{\frac{61}{30} \text{ hours}}$$​​

Average Speed = $$22 \times \left(\frac{30}{61}\right) \text{ km/h}$$​​

Average Speed ≈ 10.9 km/h

Therefore, the approximate average speed for the entire trip is 10.9 km/h.

Option (a) is right answer.