A train reaches Station D by overshooting Station C by $\frac{1}{4}$ km. Station B lies exactly between stations A and D, and the total distance between Station A and Station D is $3 \frac{1}{5}$ km. Calculate the distance between Station B to Station C.

32/20 km

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27/5 km

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27/20 km

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32/5 km

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Solution

The correct option is C 27/20 km
Given:
Distance between stations C and D
= $\frac{1}{4}$ km
Distance between stations A and D
= $3 \frac{1}{5}$ km = $\frac{16}{5}$ km

Since Station B lies exactly between Station A and Station D
$\Rightarrow$ Distance between Station B to Station D = $\frac{16}{5}$ ÷ 2 = $\frac{8}{5}$ km

Distance between Station B and Station C
= Distance between Station B and Station D - Distance between Station C and Station D

= $\frac{8}{5}$ - $\frac{1}{4}$

= $\frac{32 - 5}{20}$

= $\frac{27}{20}$ km

Therefore, option (c) is the correct answer.

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