Anil started his journey in the morning. Till 10 a.m., he covered$$\frac 12$$​ of his journey, and on the same day till 1 a.m. be covered $$\frac 45$$​ of his journey. At what time did he start his journey?

Correct option is C

Given:
Anil covered $$\frac 12$$​of his journey till 10 a.m.
He covered $$\frac 45$$​ of his journey till 1 p.m. (not a.m., since journey continues same day).
Solution:
Journey covered between 10 a.m. and 1 p.m. = $$\frac{4}{5} - \frac{1}{2} = \frac{8 - 5}{10} = \frac{3}{10}$$​ of journey.
Time taken for $$\frac{3}{10}$$​ journey = 3 hours.
Time for whole journey =$$\left( 1 \div \tfrac{3}{10} \right) \times 3 = \left( \tfrac{10}{3} \right) \times 3$$ = 10 hours.
He had completed $$\frac 12$$​ journey by 10 a.m. => Time for $$\frac 12$$​ journey = $$\frac {10}2$$​ = 5 hours.
So, he started at 10 a.m. – 5 hours = 5 a.m.