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 rupees 105 and for a journey of 15 km the charge paid is rs155 what are the fixed charges and the charge per kilometre how much does a person have to pay for travelling a distance of 25 km?​

Answer 1

$\bf{\underline{\huge{\boxed{\sf{\green{Answer:}}}}}}$

$\bf{\underline{\underline{\rm{\red{Given:}}}}}$

• In a city, for a distance of 10 km the charge paid is rupees 105
• For a journey of 15 km the charge paid is ₹ 155

$\bf{\underline{\underline{\rm{\red{To\:find:}}}}}$

• The fixed charges
• The charge per kilometre
• Pay for travelling a distance of 25 km

$\bf{\underline{\underline{\rm{\red{Solution:}}}}}$

Let x be the fixed charge

Let y be the charge paid per kilometre.

$\bf{\underline{\underline{\rm{\pink{As\:per\:first\:condition:}}}}}$

• For a distance of 10 km the charge paid is rupees 105

Representing the condition mathematically,

=> x + 10y = 105 ----> 1

$\bf{\underline{\underline{\rm{\pink{As\:per\:second\:condition:}}}}}$

• For a journey of 15 km the charge paid is ₹ 155

Representing the condition mathematically,

=> x + 15y = 155 ----> 2

Multiplying equation 1 by 15,

=> 15 × x + 15 × 10y = 15 × 105

=> 15x + 150y = 1575 ----> 3

Multiplying equation 2 by 10,

=> 10 × x + 10 × 15y = 10 × 155

=> 10x + 150y = 1550 ----> 4

Solve equation 3 and equation 4 simultaneously by elimination method.

Subtract equation 4 from equation 3,

...+ 15x + 150y = + 1575

- (+ 10x + 150y = + 1550 )

---------------------------------------------

=> 5x = 25

=> x = $\bf\frac{\cancel{25}}{\cancel{5}}$

=> x = 5

Substitute x = 5 in equation 3,

=> 15x + 150y = 1575

=> 15 (5) + 150y = 1575

=> 75 + 150y = 1575

=> 150y = 1575 - 75

=> 150y = 1500

=> y = $\bf\frac{\cancel{1500}}{\cancel{150}}$

=> y = 10

For a journey of 25 km :-

=> x + 25y

Substitute the appropriate values of x and y,

=> 5 + 25 ( 10)

=> 5 + 250

=> 255

$\bf{\underline{\large{\boxed{\sf{\purple{Fixed\:charge\:=\:x\:=\:\:5}}}}}}$

$\bf{\underline{\large{\boxed{\sf{\purple{Charge\:paid\:per\:kilometre\:=\:y\:=\:10}}}}}}$

$\bf{\underline{\large{\boxed{\sf{\purple{For\:a\:journey\:of\:25\:kilometre\:a\:person\:had\:to\:pay\:\:255}}}}}}$

Answer 2

x + 10y = 105 (1)

x + 15y = 155 (2)

----------------------------

After subtracting,

5y = 50

y = 50/5 = 10

Substitute y = 10 in equation 1,

x + 10(10) = 105

x + 100 =105

x = 105 - 100

x = 5

For 25 km,

x + 25y = 5 + 25(10)

= 5 + 250

= 255