a) 66 km/hr
b) 72 km/hr
c) 76 km/hr
d) 81 km/hr
Answer: d
Explanation:
$$\eqalign{
& 4.5\,{\text{km/hr}} = \left( {4.5 \times \frac{5}{{18}}} \right)\,{\text{m/sec}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{5}{4}\,{\text{m/sec}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1.25\,{\text{m/sec,}}\,{\text{and}} \cr
& 5.4\,km/hr = \left( {5.4 \times \frac{5}{{18}}} \right)\,{\text{m/sec}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{3}{2}\,{\text{m/sec}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1.5\,{\text{m/sec}} \cr
& {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{train}}\,{\text{be}}\,x\,{\text{m/sec}} \cr
& {\text{Then}},\,\left( {x – 1.25} \right) \times 8.4 = \left( {x – 1.5} \right) \times 8.5 \cr
& 8.4x – 10.5 = 8.5x – 12.75 \cr
& 0.1x = 2.25 \cr
& x = 22.5 \cr
& {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{train}} \cr
& = \left( {22.5 \times \frac{{18}}{5}} \right)\,{\text{km/hr}} \cr
& = 81\,{\text{km/hr}} \cr} $$
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