Question

The taxi charge in a city consists of a fixed charge together with the charge for the distance covered. For a distance of 8 km, the charge paid is 111 and for a journey of 12 km, the charge paid is 159.

What are the fixed charges and charges per km?

How much does a person have to pay

for travelling a distance of 5 km?​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

• Fixed charges be Rs x

• Charge per km be Rs y.

According to first condition

↝ For a journey of 8 km, the charge paid is Rs 111.

That is

↝ Fixed charge = Rs x

↝ Charge to cover 8 km = Rs 8y

Therefore,

$\rm :\longmapsto\:x + 8y = 111 - - - (1)$

According to second condition,

↝ For a journey of 12 km, the charge paid is Rs 159.

That is

↝ Fixed charge = Rs x

↝ Charge to cover 12 km = Rs 18y

Therefore,

$\rm :\longmapsto\:x + 12y = 159 - - - (2)$

↝ On Subtracting equation (1) from equation (2), we get

$\rm :\longmapsto\:4y = 48$

$\bf\implies \:y = 12$

↝ On Substituting the value of y in equation (1), we get

$\rm :\longmapsto\:x + 12 \times 8 = 111$

$\rm :\longmapsto\:x + 96 = 111$

$\rm :\longmapsto\:x = 111 - 96$

$\bf\implies \:x = 15$

Hence,

• Fixed charge = Rs 15

• Charge per km = Rs 12

Now,

↝ Charge to be paid to travel 5 km

$\rm \: \: = \: x + 5y$

$\rm \: \: = \: 15 + 5 \times 12$

$\rm \: \: = \: 15 + 60$

$\rm \: \: = \: 75$

So,

• Charge paid to travel 5 km = Rs 75.