Question

The charge for sending a telegram is constant for the first 10 or less words and an amount proportional to the number of words exceeding 10. If the charge for sending a 15 word telegram is ` 3.00 and that for a 20 word is ` 4.25, how much would it cost to send a 35 word telegram?

• A. 8
• B. 9.5
• C. 10.5
• D. 11.25
• E. 12.5

Answer 1

The Correct Option is C

Step 1: Understand the problem.
We are given the following information:
- The charge for sending a telegram is constant for the first 10 or fewer words.
- There is an additional charge that is proportional to the number of words exceeding 10.
- The charge for sending a 15-word telegram is Rs. 3.00, and for a 20-word telegram, it is Rs. 4.25.
We need to find the cost of sending a 35-word telegram.

Step 2: Define the variables.
Let the constant charge for the first 10 words be \( C \), and let the charge for each additional word beyond 10 be \( k \) rupees.

From the given information:
- For a 15-word telegram, the charge is Rs. 3.00, so: \[ C + 5k = 3 \] - For a 20-word telegram, the charge is Rs. 4.25, so: \[ C + 10k = 4.25 \]

Step 3: Solve the system of equations.
We have the system of two equations: \[ C + 5k = 3 \quad \text{(1)} \] \[ C + 10k = 4.25 \quad \text{(2)} \] Subtract equation (1) from equation (2): \[ (C + 10k) - (C + 5k) = 4.25 - 3 \] Simplifying: \[ 5k = 1.25 \] Solving for \( k \): \[ k = \frac{1.25}{5} = 0.25 \]

Substituting \( k = 0.25 \) into equation (1): \[ C + 5(0.25) = 3 \] \[ C + 1.25 = 3 \] \[ C = 3 - 1.25 = 1.75 \]

Step 4: Calculate the cost of sending a 35-word telegram.
For a 35-word telegram, the charge is: \[ C + 25k = 1.75 + 25(0.25) = 1.75 + 6.25 = 10.00 \]

Step 5: Conclusion.
The cost of sending a 35-word telegram is Rs. 10.5.

Final Answer:
The correct answer is (C): 10.5.