Abdul travelled 300 km by train …

Suppose, speed of the train be x km/hr and the speed of taxi be y km/h.
time taken to cover 300 km by the train = {tex}\frac { 300 } { x }{/tex}hours
time taken to cover 200 km by the taxi = {tex}\frac { 200 } { y }{/tex} hours
Total time taken = {tex}5 \frac { 30 } { 60 } \text { hours } = 5 \frac { 1 } { 2 } \text { hours } = \frac { 11 } { 2 }{/tex} hours
{tex}\therefore \frac { 300 } { x } + \frac { 200 } { y } = \frac { 11 } { 2 }{/tex}
{tex}\Rightarrow \frac { 600 } { x } + \frac { 400 } { y } = 11{/tex}
Put {tex}\frac 1x{/tex} = u and {tex}\frac 1y{/tex} = v
{tex}\Rightarrow{/tex}{tex}600u + 400v = 11{/tex}..........(i)

time taken  to cover {tex}260\ km{/tex} by the train = {tex}\frac { 260 } { x }{/tex}hours
time taken to cover {tex}240\ km{/tex} by the taxi = {tex}\frac { 240 } { y }{/tex} hours
Total time taken = {tex}5 \frac { 36 } { 60 } \text { hours } = 5 \frac { 1 } { 2 } \text { hours } = \frac { 11 } { 2 }{/tex}hours
{tex}\Rightarrow{/tex}{tex}1300u + 1200v = 28{/tex}..........(ii)
Multiplying (i) by 3 and subtracting (ii) from it, 
{tex}\Rightarrow500 u = 5 \Rightarrow u = \frac { 5 } { 500 } \Rightarrow u = \frac { 1 } { 100 }{/tex}
Substituting u = {tex}\frac{1}{100}{/tex} in (i), {tex}\Rightarrow{/tex} v = {tex}\frac{1}{80}{/tex}
{tex}\therefore u = \frac { 1 } { 100 } \Rightarrow \frac { 1 } { x } = \frac { 1 } { 100 } \Rightarrow x = 100{/tex}
{tex}v = \frac { 1 } { 80 } \Rightarrow \frac { 1 } { y } = \frac { 1 } { 80 } \Rightarrow y = 80{/tex}
{tex}\therefore{/tex} the speed of the train = {tex}100\ km/hr{/tex}
the speed of the taxi = {tex}80\ km/hr{/tex}