A) 2 km
B) 2.5 km
C) 3 km
D) 3.5 km
Correct Answer: C
Solution :
Let the following speed of boy was x km/h and his normal time was t h. By given condition, \[d=\left( t+\frac{12}{60} \right)\times 2.5\] ?(i) and \[d=\left( t-\frac{15}{60} \right)\times 4\] ?(ii) On dividing Eq. (i) by Eq, (ii), we get. \[\frac{1}{1}=\frac{\left( t+\frac{1}{5} \right)\times 2.5}{\left( t-\frac{1}{5} \right)\times 4}\] \[\Rightarrow \] \[8\left( t-\frac{1}{4} \right)=5\left( t+\frac{1}{5} \right)\] \[\Rightarrow \] \[8t-2=5t+1\] \[\Rightarrow \] \[3t=3\] \[\Rightarrow \] \[t=1\,h\] On putting the value of t in Eq. (ii), we get \[d=\left( 1-\frac{15}{60} \right)\times 4\] \[=\frac{3}{4}\times 4=3\,km\]
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