Question

Scooter charges consist of fixed charges and remaining depending upon
the distance travelled in kilometers. If a person travels 12 km, he pays
45 and for travelling 20 km, he pays 73. Express the above statements
in the form of simultaneous equations and hence, find the fixed charges
and the rate per km?
[CBSE 2000 C] ​

Answer 1

Answer:

Let x be the fixed charge and y be the charge dependent on distance per km

So,

After travelling 10km total charge was 65

x+ 10y =65.......................1)

After travelling 16km total charge was 95

x+16y = 95........................2)

Substracting equation 1) by 2)

-6y= -30

y=5

Substituting y=5 in equation 1)

x+ 50 =65

x=15

So,

Fixed charge is 15 rupees and charge dependent on distance is 5 rupees

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Answer 2

$\Large{\underline{\underline{\mathfrak{AnSwEr \: :}}}}$

Let the fixed charge of the scooter be Rs. a.

And, Let the charge per kilometre be Rs. b.

According to Question

$\sf{\dashrightarrow a + 12b = 45.......(1)} \\ \\ \sf{\dashrightarrow a + 20b = 73......(2)} \\ \\ \bf{From \: Equation \: (1).} \\ \\ \sf{\dashrightarrow a = 45 - 12b} \\ \\ \bf{Put \: Value \: of \: a \: in \: Equation \: (2).} \\ \\ \sf{\dashrightarrow 45 - 12b + 20b = 73} \\ \\ \sf{\dashrightarrow 8b = 73 - 45} \\ \\ \sf{\dashrightarrow 8b = 28} \\ \\ \sf{\dashrightarrow b = \dfrac{28}{8}} \\ \\ \sf{\dashrightarrow b = 3.5}$

$\rule{200}{2}$

$\bf{Now, \: Put \: value \: of \: b \: in \: equation \: (1).} \\ \\ \sf{\dashrightarrow a + 12(3.5) = 45} \\ \\ \sf{\dashrightarrow a + 42 = 45} \\ \\ \sf{\dashrightarrow a = 45 - 42} \\ \\ \sf{\dashrightarrow a = 3}$

Hence, monthly fixed charges is Rs. 3 and charge per kilometer is Rs. 3.5