question_answer

A student goes to school at the rate of \[2\frac{1}{2}\,\,km/h\] and reaches 6 min late. If he travels at the speed of 3 km/h, he is 10 min early. The distance (in km) between the school and his house is

A) 5                                 

B) 4

C) 3                                 

D) 1

Correct Answer: B

Solution :

Let the required distance be x km.

Difference between time \[=\frac{16}{60}\]

Then, \[\frac{x}{5}-\frac{x}{3}=\frac{16}{60}\]\[\Rightarrow \]\[\frac{2x}{5}-\frac{x}{3}=\frac{4}{15}\]

\[\Rightarrow \]   \[\frac{6x-5x}{15}=\frac{4}{15}\]

\[x=4\,km\]

Alternate Method

Here, \[{{t}_{1}}=6\,\,\min ,\]\[{{t}_{2}}=10\,\,\min ,\]

\[{{S}_{1}}=2\frac{1}{2}=\frac{5}{2}\,\,km/h\] and \[{{S}_{2}}=3\,km/h\]

Distance \[=\,\,\frac{({{t}_{1}}+{{t}_{2}}){{S}_{1}}{{S}_{2}}}{({{S}_{2}}-{{S}_{1}})\times 60}=\frac{(6+10)\times \frac{5}{2}\times 3}{\left( 3-\frac{5}{2} \right)\times 60}\]

\[=\,\,\frac{\frac{16\times 15}{2}}{\frac{1}{2}\times 60}=\frac{16\times 15}{60}=4\,km\]