Question

Pune taxi services has a fixed charge plus a variable charge based on the distance covered. For travelling 10km the total fare paid by Somu is Rs.150 and for a journey of 15km the total fare paid by Ramu is RS220. Then Tomy will pay _as the total fare for travelling a distance of 25 km.

• A. Rs. 350
• B. Rs. 380
• C. Rs. 360
• D. Rs. 400

Answer 1

The Correct Option is C

Let's denote the fixed charge as \( F \) and the variable charge per kilometer as \( V \).
Given:
1. For traveling 10 km, Somu pays Rs. 150:
\[ F + 10V = 150 \]
2. For traveling 15 km, Ramu pays Rs. 220:
\[ F + 15V = 220 \]
We have two linear equations:
\[ F + 10V = 150 \]
\[ F + 15V = 220 \]
To find \( F \) and \( V \), subtract the first equation from the second:
\[ (F + 15V) - (F + 10V) = 220 - 150 \]
\[ 5V = 70 \]
\[ V = 14 \]
Now, substitute \( V \) back into the first equation to find \( F \):
\[ F + 10(14) = 150 \]
\[ F + 140 = 150 \]
\[ F = 10 \]
Now that we have \( F \) and \( V \), we can find the total fare for Tomy who travels 25 km:
\[ F + 25V = 10 + 25(14) \]
\[ F + 25V = 10 + 350 \]
\[ F + 25V = 360 \]
Thus, Tomy will pay Rs. 360 for traveling 25 km.
Answer: C Rs. 360

Answer 2

Instead of solving for the fixed charge and rate separately, compare the two given trips directly. Going from 10 km to 15 km, the distance increases by 5 km and the fare increases from Rs. 150 to Rs. 220, an increase of Rs. 70. So the variable rate per km is:
\[\frac{70}{5}=14 \text{ Rs./km}\]

Now extend the 15 km trip (Rs. 220) to 25 km, an increase of 10 km:
\[220 + 10\times14 = 220+140 = 360\]

1. Option A (Rs. 350): Does not match 360.
2. Option B (Rs. 380): Does not match 360.
3. Option C (Rs. 360): Matches exactly.
4. Option D (Rs. 400): Does not match 360.

Since the fixed charge cancels out when comparing trips, the fare for 25 km works out to Rs. 360 without needing to find the fixed charge separately.

Hence, the correct answer is Option C: Rs. 360.