Question

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Answer 1

Answer:

Explanation:

Given :-

For a distance of 10 km, the charge paid is Rs 105.

For a distance of 15 km, the charge paid is Rs 155.          

Solution :-

Let the fixed charge for taxi = Rs x                  

And variable cost per km = Rs y                  

Total cost = fixed charge + variable charge                  

According to the Question,             

⇒ x + 10y = 105 … (i)                  

⇒ x = 105 - 10y                         

⇒ x + 15y = 155                  

Putting the value of x we get                  

⇒ 105 - 10y + 15y = 155                  

⇒ 5y = 155 - 105                  

⇒ 5y = 50                  

Dividing by 5, we get                  

⇒ y = 50/5 = 10                  

Putting this value in equation (i) we get                  

⇒ x = 105 - 10 × 10                  

⇒ x = 5                  

Cost for traveling a distance of 25 km                  

= x + 25y                  

= 5 + 25 × 10                  

= 5 + 250                  

= Rs. 255              

Hence, A person has to pay Rs 255 for 25 Km.

Answer 2

Question -

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Solution -

Let Fixed Charge be Rs. x And Charge per km be y.

⟹ x + 10y = 105 ......(i)

⟹ x + 15y = 155.......(ii)

From Equation 2-

⟹ 15y = 155 - x

$⟹y= \frac{155 - x}{15}$.....(iii)

After Substituting -

$⟹ x + \frac{10(155-x)}{15}=105$

⟹ 15x + 1550 - 10x = 1575

⟹ 5x = 1575 - 1550

⟹ 5x = 25

⟹ x = 5

Substituting x in eq2

⟹ 5 + 15y = 155

⟹15y = 155 - 5

⟹15y = 150

⟹ y = 10

Hence ,

x = 5

y = 10

Fixed Charge Rs. 55 and Charge per km is Rs. 1010

For 25 kilometres person have to pay = 5 + 10 × 25 = 255 Rs.