Question 18.

Ankita walks from A to C through B, and runs back through the same route at a speed that is 40% more than her walking speed. She takes exactly 3 hours 30 minutes to walk from B to C as well as to run from B to A. The total time, in minutes, she would take to walk from A to B and run from B to C, is

A
B
C
D
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Text Explanation
Let the walking speed of Ankita be $5x$, implying that her running speed (which is $40\%$ more than her walking speed), is $1.4\times 5x = 7x$.
Thus, the ratio of her walking and running speeds is $5:7$. Therefore, the ratio of the time taken by Ankita to cover a fixed distance walking and running would by $7:5$.
She takes 3 hours 30 minutes, or $3.5$ hours to walk from B to C. Since Ankita is running from B to C in the second scenario, her time will reduce inversely to the ratio of her speed. The time taken by her to run from B to C would be $\dfrac{3.5}{7}\times 5 = 2.5$ hours.
She takes 3 hours 30 minutes, or $3.5$ hours to run from A to B. Since Ankita is walking from A to B in the second scenario, her time will increase inversely to the ratio of her speed. The time taken by her to walk from A to B would be $\dfrac{3.5}{5}\times 7 = 4.9$ hours.
Therefore, the total time it takes for Ankita in the second scenario is $4.9+2.5 = 7.4$ hours. This gives $7.4*60 = 444$ minutes.
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