Swapna travels by car equal distances with the speeds of 10 km/h, 15 km/h and 20 km/h and takes a total of 65 min. The total distance travelled by her (in km) is:

Correct option is B

Given:
Swapna travels equal distances at three different speeds:
Speed 1 $$v_1$$​  = 10 km/h
Speed 2 $$v_2$$​  = 15 km/h
Speed 3 $$v_3$$​ = 20 km/h
Total time taken = 65 minutes =$$\frac{65}{60} \text{hours} = \frac{13}{12}\text{ hours}$$​
Let, Distance traveled at each speed = d  km
Formulas Used:
Time taken for each part of the journey:
$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$​
Solution:
 Time taken at 10 km/h:
$$t_1 = \frac{d}{10}$$​​
Time taken at 15 km/h:
$$t_2 = \frac{d}{15}$$​​
Time taken at 20 km/h:
$$t_3 = \frac{d}{20}$$​​
​$$t_1 + t_2 + t_3 = \frac{d}{10} + \frac{d}{15} + \frac{d}{20}$$​

​$$\frac{6d}{60} + \frac{4d}{60} + \frac{3d}{60} = \frac{13d}{60}$$​

Now,

​$$\frac{13d}{60} = \frac{13}{12}$$

$$d = \frac{60}{12} = 5 \text{ km}$$

$$\text{Total distance} = 3d = 3 \times 5 = 15 \text{ km}$$

Option (b) is right.