Question

Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus

NCERT Class X
Mathematics - Exemplar Problems

Chapter _PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Answer 1

I have added a attachment in that whole answer is written.

Answer 2

Speed of Rickshaw is $\bold{=10\ \mathrm{km} / \mathrm{h}}$

Speed of Bus $\bold{=40\ \mathrm{km} / \mathrm{h}}$.

Case1:

Total distance = 14km

Total time, T = 30min $=\frac{1}{2} h$

By Rickshaw                                

Distance covered = 2Km                                    

Time taken $=t_{1}$                                          

Speed $=\frac{\text {Distance}}{\text {Tim} e}=\frac{2}{t_{1}}$

By Bus  

Distance covered = 12Km

Time taken  $=\frac{1}{2}-t_{1}=\frac{1-2 t_{1}}{2 t_{1}}$

Speed $=\frac{\text {Distance}}{\text {Time}}=\frac{24 \mathrm{t}_{1}}{1-2 \mathrm{t}_{1}}$

Case 2 :

Total distance = 14km

Total time, $t_{2}=39 \min =\frac{13}{20} h$

By Rickshaw                                  

Distance covered = 4Km                                    

Time taken $=t_{2}$                                      

Speed $=\frac{\text {Distance}}{\text {Time}}=\frac{4}{t_{2}}$    

In both case, Speed is equal.

Comparing Speed of rickshaw                      

$\frac{2}{t_{1}}=\frac{4}{t_{2}} \Rightarrow t_{2}=2 t_{1}$                  

By Bus

Distance covered = 10Km                                    

Time taken $=\frac{13}{20}-t_{2}=\frac{13-20 t_{2}}{20}$

Speed $=\frac{\text {Distance}}{\text {Tim} e}=\frac{200}{13-20 t_{2}}$  

Comparing speed of bus

$\frac{24 t_{1}}{1-2 t_{1}}=\frac{200}{13-20 t_{2}}$

$3\left(13-20 t_{2}\right)=25\left(1-2 t_{1}\right)$

$39-60 t_{2}=25-50 t_{1}$

$39-25=60 t 2-50 t_{1}$

$14=60 t_{2}-50 t 1$

$120 t_{1}-50 t_{1}=14$

$70 t_{1}=14$                                                          

Substitute $t_{2}=2 t_{1}$                

$t_{1}=\frac{1}{5}$

Speed of Rickshaw is $=\frac{2}{t_{1}}=10 \mathrm{km} / \mathrm{h}$

Speed of Bus $=\frac{24}{1-2 t_{1}}=\frac{24}{1-\frac{2}{5}}=24 \times \frac{5}{3}=40 \mathrm{km} / \mathrm{h}$.