Question

Prof. Mandal walks to the market and comes back in an auto. It takes him 90 minutes to make the round trip. If he takes an auto both ways, it takes him 30 minutes. On a Sunday, he decides to walk both ways. How long would it take him?

• A. 100 minutes
• B. 120 minutes
• C. 140 minutes
• D. 150 minutes
• E. None of the above

Hint:

Convert round-trip descriptions into sums of one-way times.
When two scenarios share the same distance, equate times via \(\texttime=\frac\textdistance\textspeed\). Solve for one component (e.g., \(\fracda\)) from the easier equation and back-substitute.

Answer 1

The Correct Option is D

Step 1: Let the one-way distance be \(d\), walking speed be \(w\), and auto speed be \(a\). Then one-way times are \(d/w\) and \(d/a\). From the data, \[ \frac{d}{w}+\frac{d}{a}=90,\qquad \frac{2d}{a}=30 \ ⇒\ \frac{d}{a}=15. \] Step 2: Substitute \(\frac{d}{a}=15\) into the first equation: \[ \frac{d}{w}=90-15=75. \] Walking both ways takes \[ \frac{2d}{w}=2\times 75=150\text{ minutes}. \]