This problem asks us to calculate the total production of cassettes by a factory over three months: January, February, and March. We are given the production for January and how the production in February and March relates to the previous months.

Understanding the Factory Production Data

We are given the following information about the factory's production:

• Production in January is explicitly given.
• Production in February is a certain amount more than in January.
• Production in March is a certain amount less than in February.

Our goal is to find the sum of the production for all three months.

Calculating Production in Each Month

Let's break down the calculation for each month:

• January Production: The factory produced 18,58,509 cassettes in January.
• February Production: The factory produced 7623 more cassettes in February than in January. To find the production in February, we add 7623 to the January production.

  Production in February = Production in January + 7623

  Production in February \( = 18,58,509 + 7623 \)

  Production in February \( = 18,66,132 \)

  So, the factory produced 18,66,132 cassettes in February.
• March Production: The factory produced 25,838 less cassettes in March than in February. To find the production in March, we subtract 25,838 from the February production.

  Production in March = Production in February - 25838

  Production in March \( = 18,66,132 - 25838 \)

  Production in March \( = 18,40,294 \)

  So, the factory produced 18,40,294 cassettes in March.

Summary of Monthly Production

Let's summarize the production for each month in a table:

Total Production Calculation

To find the total production in all three months, we add the production from January, February, and March.

Total Production = Production in January + Production in February + Production in March

Total Production \( = 18,58,509 + 18,66,132 + 18,40,294 \)

Let's perform the addition:

\[ \begin{array}{@{}c@{\,}c@{}c@{}c@{}c@{}c@{}c} & 1 & 8 & 5 & 8 & 5 & 0 & 9 \\ & 1 & 8 & 6 & 6 & 1 & 3 & 2 \\ + & 1 & 8 & 4 & 0 & 2 & 9 & 4 \\ \hline & 5 & 5 & 6 & 4 & 9 & 3 & 5 \\ \end{array} \]

The total production in all three months is 55,64,935.

Comparing with Options

We compare our calculated total production with the given options:

• A. 55,57,312
• B. 59,83,245
• C. 55,64,935
• D. 56,08,988

Our calculated total production, 55,64,935, matches option C.

Revision Table - Factory Production Analysis

Additional Information - Solving Word Problems

Solving word problems like this one involves several steps:

• Read Carefully: Understand what information is given and what needs to be found. Identify the quantities and their relationships.
• Plan: Determine the steps needed to solve the problem. This usually involves identifying which operations (addition, subtraction, multiplication, division) are required and in what order.
• Calculate: Perform the mathematical operations carefully, paying attention to place values, especially with large numbers.
• Check: Review your calculations to minimize errors. Ensure your final answer makes sense in the context of the problem.
• State the Answer: Clearly state your final answer.

In this problem, we used addition and subtraction to find the production for each month and then added the monthly totals to find the grand total production.