Finding Car Hire Charges

Video Explanation

Question

The car hire charges consist of a fixed charge plus a charge per km. For 12 km, the charge is ₹89. For 20 km, the charge is ₹145. Find the charge for 30 km.

Solution

Step 1: Let Variables

Let fixed charge = \(x\)

Let charge per km = \(y\)

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Step 2: Form Equations

For 12 km:

\[ x + 12y = 89 \quad (1) \]

For 20 km:

\[ x + 20y = 145 \quad (2) \]

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Step 3: Solve Linear Equations

Subtract (1) from (2):

\[ 8y = 56 \]

\[ y = 7 \]

Substitute into (1):

\[ x + 12(7) = 89 \]

\[ x + 84 = 89 \]

\[ x = 5 \]

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Step 4: Find Charge for 30 km

\[ \text{Total charge} = x + 30y = 5 + 30(7) \]

\[ = 5 + 210 = 215 \]

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Conclusion

\[ \text{Charge for 30 km} = ₹215 \]

Verification

12 km: \(5 + 84 = 89\) ✔

20 km: \(5 + 140 = 145\) ✔