Question

write (1+2i) (1+3i) (2+i)^-1 in the form a+ ib​

Answer 1

$\displaystyle\Huge \bf\red{\underline{\underline{ANSWER}}} </p><p>$

Let the speed of the train be x km/hr and the speed of the bus is y km/hr.

So according to question and using

$\huge \boxed{\sf{Time = \frac{Distance}{speed}}} </p><p>$

Total distance =300 km

Mansi travels 60 km by train and 300−60=240 by bus in 4 minute,

$\bf\frac{60}{x} + \frac{240}{y} = \red4</p><p>$

and 100 km by train, 300−100=200 by bus, and takes 10 minutes more,

$\bf {\frac{100}{x} + \frac{200}{y} = 4 + \frac{1}{6} = \frac{24 + 1 }{6} = \purple{\frac{25}{6}}}</p><p>$

Now, let

$\bf\color{blue}{\frac{1}{x} = a}$

and.

$\bf \color{blue}{ \frac{1}{y} = b }$

$\bfthen 60a+240b=4.............(1)$

$\bf100a+200b=25/6----(2)$

multiply (1) by 5 and (2) by 6 we get

$\bf300a+1200b=20..........(3)$

$\bf600a+1200b=25...........(4)$

Subtracting (3) and (4) we get

$\bf \green{−300a=−5}$

$\bf{a = \frac{1}{60}}$

Putting the value of a in (1) we get

$\bf{60 \times \frac{1}{60} + 240b = 4}$

$</p><p> \bf240b = 3 \\ \\ \bf b = \frac{1}{80}$

Now ,

$\bf\frac{1}{x} = a \\ \\ \bf \red{a = 60 km/h \: \blue \bigstar}$

$\bf\frac{1}{y} = b \\ \\ \bf \red {b = 80 km/h \: \pink \bigstar}$

Hence, the speed of the train is 60 km/hr and the speed of the bus is 80 km/hr.