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Answer the following two questions based on the information given.

Autorickshaws in a city use a meter to calculate the fare based on the distance traveled. Up to the first 1 km, Rs. 10 is charged, and thereafter for every additional 1 km, Rs. 4.50 is charged.

1. Which of these could be the general rule to calculate the fare for [tex]\(x\)[/tex] km traveled?
A. [tex]\(4.5(x-1) + 10\)[/tex]
B. [tex]\(10(x-1) + 4.5\)[/tex]
C. [tex]\(4.5x + 10\)[/tex]
D. [tex]\(10x + 4.5\)[/tex]

2. If a person travels 5 km, how much will the fare be according to the general rule chosen above?



Answer :

GinnyAnswer
To determine the correct formula for calculating the fare for [tex]\( x \)[/tex] kilometers traveled by an auto-rickshaw, we can break down the problem step by step.

1. Initial Cost for the First Kilometer:
- The fare for the first [tex]\( 1 \)[/tex] kilometer (km) is fixed at Rs. [tex]\( 10 \)[/tex].

2. Cost for Additional Distance:
- For every kilometer beyond the first kilometer, the fare is Rs. [tex]\( 4.50 \)[/tex] per kilometer.

Based on these rules, let's consider each answer choice and check if it aligns with the given fare structure:

A. [tex]\( 4.5(x-1) + 10 \)[/tex]:

This formula suggests:
- After the first kilometer, only the additional kilometers are charged at the rate of Rs. [tex]\( 4.50 \)[/tex] per km.
- So, for [tex]\( x \)[/tex] kilometers, if [tex]\( x \leq 1 \)[/tex], the fare is Rs. [tex]\( 10 \)[/tex].
- If [tex]\( x > 1 \)[/tex], the fare would be Rs. [tex]\( 10 \)[/tex] (first km) [tex]\( + 4.5(x-1) \)[/tex] (remaining kilometers).

This seems correct because it correctly adds the base charge and charges the remaining distance separately.

B. [tex]\( 10(x-1) + 4.5 \)[/tex]:

This formula suggests:
- For [tex]\( x - 1 \)[/tex] kilometers, the fare is Rs. [tex]\( 10 \)[/tex] per kilometer.
- Adding Rs. [tex]\( 4.5 \)[/tex] as a flat fee.

This formula incorrectly applies the Rs. [tex]\( 10 \)[/tex] rate to the kilometers beyond the first km, and the additional Rs. [tex]\( 4.5 \)[/tex] doesn't fit the given structure.

C. [tex]\( 4.5x + 10 \)[/tex]:

This formula suggests:
- Rs. [tex]\( 4.5 \)[/tex] per km for [tex]\( x \)[/tex] kilometers.
- Adding Rs. [tex]\( 10 \)[/tex] as an additional flat fee.

This formula does not correctly account for the specific rate for the first km being different from the subsequent kilometers.

D. [tex]\( 10x + 4.5 \)[/tex]:

This formula suggests:
- A flat rate of Rs. [tex]\( 10 \)[/tex] per kilometer for [tex]\( x \)[/tex] kilometers.
- Adding Rs. [tex]\( 4.5 \)[/tex] as an additional fee.

This formula also does not correctly account for the different rates for the first kilometer and the subsequent kilometers.

Conclusion:

The correct general rule to calculate the fare for [tex]\( x \)[/tex] kilometers traveled is:

A. [tex]\( 4.5(x-1) + 10 \)[/tex]

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