Answer:
Let x be the initial speed of the bus we know that \[Speed=\frac{Dis\tan ce}{Time}\] or \[Time=\frac{Dis\tan ce}{Speed}\] Thus, we have \[3=\frac{75}{x}+\frac{90}{x+10}\] \[\Rightarrow 3=\frac{75(x+10)+90x}{x(x+10)}\] \[\Rightarrow 3(x)(x+10)=75x+750+90x\] \[\Rightarrow 3{{x}^{2}}+30x=75x+750+90x\] \[\Rightarrow 3{{x}^{2}}-135x-750=0\] \[\Rightarrow {{x}^{2}}-45x-250=0\] \[\Rightarrow {{x}^{2}}-50x+5x-250=0\] \[\Rightarrow x(x-50)+5(x-50)=0\] \[\Rightarrow (x+5)(x-50)=0\] \[\Rightarrow x=-5\] or \[x=50\] Since, speed cannot be negative So, \[x=50\] Hence, the initial speed of bus is \[50\text{ }km/hr\].
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