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 105 and for a journey of 15 km, the charge paid is 155. How much does a person have to pay for traveling a distance of 25 km?​

Answer 1

Let fixed charges of taxi be ₹ x.

And Running charges of taxi = ₹ y

According to the question,

Expenses of travelling 10 km = ₹ 105 [ Given ]

⇒ x + 10y = 105 .........( 1 )

Expenses of travelling 15 km = ₹ 155 [ Given ]

⇒ x + 15y = 155 ...........( 2 )

⇒ x = 155 - 15y .............( 3 )

Now,

Putting x = 155 - 15y in equation ( 1 ),we get

x + 10y = 105

⇒ 155 - 15y + 10y = 105

⇒ 155 - 5y = 105

⇒ - 5y = 105 - 155

⇒ -5y = -50

⇒ y = 10

And,

Putting the value of y = 10 in equation ( 2 ),we get

x + 15y = 155

⇒ x + 15 × 10 = 155

⇒ x + 150 = 155

⇒ x = 5

Hence,fixed charges of taxi is ₹ 5 and running charges per km is ₹ 10.

★ A person have to pay for traveling a distance of 25 km = 5 + 25 × 10

= 5 + 250

= ₹255

Answer 2

$\bf{\underline{\underline \blue{Solution:-}}}$

$\sf\underline{\red{\:\:\: AnswEr:-\:\:\:}}$

• A person have to pay Rs 255 for 25 Km.

$\sf\underline{\red{\:\:\: Given:-\:\:\:}}$

• 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 105 and for a journey of 15 km, the charge paid is 155.

$\sf\underline{\red{\:\:\: Need\:To\: Find:-\:\:\:}}$

• How much does a person have to pay for traveling a distance of 25 km?

$\bf{\underline{\underline \blue{Explanation:-}}}$

Let the fixed charge for taxi = Rs x

And variable cost per km = Rs y

$\bigstar \: \boxed{ \sf \: Total \:Cost = fixed\: charge + variable \:charge }$

$\sf\underline{\green{\:\:\: Given\:That:-\:\:\:}}$

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

$\dashrightarrow \sf {x + 10y = 105}$.... (i)

$\dashrightarrow \sf {x = 105 - 10y}$

$\sf\underline{\green{\:\:\: Given\:That:-\:\:\:}}$

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

$\dashrightarrow \sf {x + 15y = 155}$

$\sf\underline{\red{\:\:\: Putting\:the\: value \:of \:x:-\:\:\:}}$

$\dashrightarrow \sf {105 - 10y + 15y = 155}$

$\dashrightarrow \sf {5y = 155 - 105}$

$\dashrightarrow \sf {5y = 50}$

$\sf\underline{\red{\:\:\: Now, Diving\:by\: 5:-\:\:\:}}$

$\dashrightarrow \sf {y = \dfrac{\cancel{50}}{\cancel{5}}\:}$

$\dashrightarrow \sf {y = 10}$

$\sf\underline{\red{\:\:\: Putting\:the\: values\:in\: equation\:(i):-\:\:\:}}$

$\dashrightarrow \sf {x = 105 - 10 \times 10}$

$\dashrightarrow \sf {x = 5}$

❥︎People have to pay for traveling a distance of 25 km.

$\dashrightarrow \sf {x + 25y}$

$\dashrightarrow \sf {5 + 25 \times 10}$

$\dashrightarrow \sf {5 + 250}$

$\dashrightarrow \sf { 255}$

$\sf\underline{\green{\:\:\: ThereFore:-\:\:\:}}$

• A person have to pay Rs 255 for 25 Km.

$\rule{200}{2}$