Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-1

A student goes to school at the rate of \[\frac{5}{2}km/h\] and reaches 6 min late. If he travels at the speed of \[3\text{ }km/h,\] he reaches 10 min earlier. The distance of the school is [SSC (CPO) 2014]

A) 46 km

B) 20 km

C) 10 km

D) 4 km

Correct Answer: D

Solution :

[d] Let the distance to school be D km and time taken is t.

Case I When he goes at a rate of \[\frac{5}{2}\,\,km/h.\]

He reaches 6 min late.

\[\therefore \] \[\frac{D}{\frac{5}{2}}=t+\frac{6}{60}\]\[\Rightarrow \]\[\frac{2D}{5}=t+\frac{1}{10}\]

\[\Rightarrow \] \[t=\frac{2D}{5}-\frac{1}{10}\]

Case II When he goes at a rate of 3 km/h.

He reaches 10 min earlier

\[\therefore \] \[\frac{D}{3}=t-\frac{10}{60}\]\[\Rightarrow \]\[\frac{D}{3}=t-\frac{1}{6}\]

On putting value of t from Eq. (i).

\[\frac{D}{3}=\frac{2D}{5}-\frac{1}{10}-\frac{1}{6}\]

\[\Rightarrow \] \[\frac{2D}{5}-\frac{D}{3}=\frac{1}{10}+\frac{1}{6}\]

\[\Rightarrow \] \[\frac{6D-5D}{15}=\frac{3+5}{30}\]\[\Rightarrow \]\[D=\frac{8\times 15}{30}=4km\]