Question

Question↴

Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes. But if he travels to 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.

Don't Spam! ​

Answer 1

$\underline{\sf{\blue{Question}}}$

• Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes. But if he travels to 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.

$\underline{\sf{\orange{Answer}}}$

• Speed of train = 100km/h
• Speed of taxi = 80km/h

$\underline{\sf{\green{Given}}}$

• Abdul travelled 300km by train & 200km by taxi
• Time taken = 5 hours 30 minutes
• Abdul travelled 260km by train & 240km by taxi
• Time taken = 6 min longer

$\underline{\sf{\purple{To\: Calculate}}}$

• Speed of the train & taxi

$\underline{\sf{\orange{Explanation}}}$

Let the Speed of the train = x km/h

Speed of taxi = y km/h

$\underline{\sf{\green{According\: To \: Question}}}$

Case I

Distance covered by train = 300 km

Then

Time taken by train (t1) = 300/x

And

Distance covered by taxi = 200km

So

Time taken by taxi (t2) = 200/y

Now

➺ t1+t2 = 5+ (30/60)

➺ 300/x+200/y=5+(30/60)

➺ 300/x+200/y= 11/2____________(1)

Case II

Distance covered by train = 260km

Then

Time taken by train (t3)= 260/x

And

Distance covered by taxi = 240km

Then

Time taken by taxi (t4)= 240/y

➺ t3+t4= 5+(36/60)

➺ 260/x+240/y = 28/5___________(2)

Now

Let 1/x= a , 1/y= b

Then

From equation 1 and 2

➺ 300a+200b= 11/2

➺ 100(3a+2b)= 11/2

➺ 3a+2b = 11/200______________(3)

And

➺ 260a + 240b= 28/5

➺ 20(13a+12b)=28/5

➺ 13a + 12b= 28/100____________(4)

On Multiplying equation 3 by 6

➺ 6(3a+2b=11/200)

➺ 18a +12b= 66/200____________(5)

On Subtracting equation 4 from 5

18a + 12b = 66/200

13a + 12b = 28/100

- - -

_________________

5a = 66/200 - 26/100

➺ 5a = (66-56)/200

➺ 5a = 10/200

➺ a = 1/20×5

➺ a = 1/100

➺ 1/x = 1/100

➺ x = 100

From equation 3 put a= 1/100

➺ 3/100+ 2b= 11/200

➺ 2b= 11/200-3/100

➺ 2b = 5/200

➺ 2b= 1/40

➺ b= 1/80

➺1/y= 1/80

➺ y = 80

$\underline{\sf{\blue{Hence}}}$

• Speed of train = 100km/h
• Speed of taxi = 80km/h

___________________________________________

Answer 2

GIVEN :-

⇝ Abdul travelled 300 km by train and 200 km by taxi taking 5 hrs 30 mins.

⇝ But, if he travels 260 km by train and 240 km by taxi, he takes 6 min longer.

TO FIND :-

⇝ What is the speed of the train and that of the taxi.

SOLUTION :-

Let the speed of the train be x km/h

And the speed of the taxi be y km/h

$\star{ \underline{ \underline {\fbox \pink{According to the question,}}}}$

$\sf\dfrac{300}{x} + \dfrac{200}{y} = 5\dfrac{1}{2}$

$\sf\implies \dfrac{300}{x} + \dfrac{200}{y} = \dfrac{11}{2}$

.. (1)

$\sf\dfrac{260}{x} + \dfrac{240}{y}$

$\sf = (\dfrac{11}{2} + \dfrac{1}{10} )$

$\sf \implies \dfrac{260}{x}$

.. (2)

$</p><p>\sf Let \dfrac{1}{x}=\dfrac{1}{y}$

$\sf \therefore 300u + 200v = \dfrac{11}{2}$

$\sf And, 260u + 240v = \dfrac{56}{10}$

⬛ By solving the equation (3) and (4) we get,

$\sf\mapsto u = \dfrac{1}{100} \\ \sf\mapsto v = \dfrac{1}{80} \\ \sf⟹ 80 km/h.$

Hence, the speed of the train and that of taxi are 100 km/h and 80 km/h respectively.

$\star{ \underline{ \underline {\fbox \red{Hence \: verified}}}}\star$