question_answer

Two persons cover the same distance at a speed of 25 kmph and 30 kmph respectively. Find the distance travelled if one person lakes 20 minutes more than the other.

A)  40

B)  60

C)  50

D)  72

E)  48

Correct Answer: C

Solution :

Speed\[\propto \frac{\text{1}}{\text{Time}}\] Ratio of speed \[=25:30\] \[\Rightarrow \]\[5:6\] Ratio of time \[\therefore \]1 unit = 20 minutes Time required by the first person to cover the distance of 6 units \[=20\times 6=120\]minutes = 2 hours. \[\therefore \]Total distance \[\text{=Speed }\!\!\times\!\!\text{ Time}\] \[\text{=25 }\!\!\times\!\!\text{ 2=50}\,\,\text{km}\] Method II. Let distance\[=x\,\,km\] Then, \[\frac{x}{25}-\frac{x}{30}=\frac{20}{60}\] \[\Rightarrow \] \[\frac{x(30-25)}{25\times 30}=\frac{20}{60}\] \[\Rightarrow \] \[x=\frac{25\times 30}{30-25}\times \frac{20}{60}\] ? (*) Note: For future, we can remember the step (*) as direct formula for such question. Dist.\[\text{=}\frac{\text{Product}\,\,\text{of}\,\,\text{speeds}}{\text{Diff}\,\,\text{of}\,\,\text{speeds}}\text{ }\!\!\times\!\!\text{ Diff}\,\,\text{in}\,\,\text{time}\]