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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 Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per kilometer?

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Fixed charge is Rs.

51

and charge per kilometer is Rs.

10

Fixed charge is Rs.

10

. and charge per kilometer is Rs.

5

Fixed charge is Rs.

15

and charge per kilometer is Rs.

5

Fixed charge is Rs.

50

. and charge per kilometer is Rs

20

answer is A.

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Detailed Solution

Given a taxi with fixed charge along with charge for distance covered.
Let fixed charge be Rs x and charge per km be Rs y.

\Rightarrow x + 10 y = 105

……..(1)

\Rightarrow x + 15 y = 155

………..(2)
Now from equation (2),

\Rightarrow 15 y = 155 - x

\Rightarrow y = \frac{155 - x}{15}

………….(3)
Substituting

y = \frac{155 - x}{15}

in equation (1),

\Rightarrow x + \frac{10 (155 - x)}{15} = 105

\Rightarrow 15 x + 1550 - 10 x = 1575

\Rightarrow 5 x = 1575 - 1550

\Rightarrow 5 x = 25

\Rightarrow x = 5

Substituting

x = 5

in equation (2),

\Rightarrow 5 + 15 y = 155

\Rightarrow 15 y = 155 - 5

\Rightarrow 15 y = 150

\Rightarrow y = 10

Hence,

x = Rs . 5

and

y = Rs . 10

.
Therefore, option (1) is correct.

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