Question

Taxi charges in a city consists of fixed charges and remaining depending upon the distance travelled in kilometers. If a person travels 70 kms, he pays ₹1,130 and for travelling 100 kms, he pays ₹1,550. Find the charges for travelling 140 kms.

• A. 2000
• B. 2260
• C. 2170
• D. 2110

Answer 1

The Correct Option is D

To solve this problem, we need to find the fixed and variable components of the taxi charges, then calculate the cost for 140 km.

Let's define: 

• F = fixed charge
• V = variable charge per kilometer

We have two equations from the problem statement:

1. For 70 km: \( F + 70V = 1130 \)
2. For 100 km: \( F + 100V = 1550 \)

To find \( F \) and \( V \), we subtract the first equation from the second:

\( (F + 100V) - (F + 70V) = 1550 - 1130 \)

\( 30V = 420 \)

\( V = 14 \)

Next, substitute \( V = 14 \) back into one of the equations to find \( F \):

\( F + 70 \times 14 = 1130 \)

\( F + 980 = 1130 \)

\( F = 150 \)

Now, we calculate the charges for 140 km:

\( Total\;Charge = F + 140V \)

\( Total\;Charge = 150 + 140 \times 14 \)

\( Total\;Charge = 150 + 1960 \)

\( Total\;Charge = 2110 \)

Therefore, the charge for traveling 140 km is ₹2,110.