The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables is Rs. 4000. Find the total price of 12 chairs and 3 tables.

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

The problem is solved by setting up a system of two linear equations based on the given information: 10C = 4T and 15C + 2T = 4000, where C is the price of a chair and T is the price of a table.
Using the substitution method, the first equation is simplified to T = 2.5C.
This expression for T is substituted into the second equation: 15C + 2(2.5C) = 4000, which simplifies to 20C = 4000.
Solving for C gives the price of one chair as Rs. 200.
Substituting C = 200 back into T = 2.5C gives the price of one table as Rs. 500.
The final calculation for 12 chairs and 3 tables is (12 × 200) + (3 × 500) = 2400 + 1500 = Rs. 3900.

Option A: This value is incorrect and likely results from a calculation error during one of the steps, such as incorrectly solving for the price of a chair or table.
Option B: This is an incorrect total. An arithmetic mistake, perhaps in the final multiplication or addition step, would lead to this answer.
Option D: This value is also incorrect. It may arise from misinterpreting the initial relationships, for example, incorrectly setting up the initial equations.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a system of linear equations from a word problem as background academic context rather than a clinical decision trigger.
This is a general aptitude question designed to test basic mathematical and logical reasoning skills.
While not directly clinical, such problem-solving abilities are fundamental for tasks like medication dosage calculations, interpreting lab results, and managing resources, which are part of the nursing profession.
What if the price of 15 chairs and 3 tables was Rs. 4500? The underlying method would be the same, but the values of C and T would change, leading to a different final answer.

How to Approach the Question

First, carefully read the word problem to identify the unknown quantities. Assign variables to these quantities, for instance, 'C' for the price of a chair and 'T' for the price of a table.
Translate the sentences into mathematical equations. 'The price of 10 chairs is equal to that of 4 tables' becomes 10C = 4T. 'The price of 15 chairs and 2 tables is Rs. 4000' becomes 15C + 2T = 4000.
You now have a system of two equations. Choose a method to solve them, such as substitution or elimination. Here, simplifying the first equation to T = 2.5C makes substitution straightforward.
Substitute the expression for one variable into the other equation. This will leave you with one equation and one variable, which you can solve.
Once you find the value of the first variable (C = 200), substitute it back into one of the original equations to find the value of the second variable (T = 500).
Finally, use the calculated prices for C and T to answer the specific question asked: find the total price of 12 chairs and 3 tables (12C + 3T).

Concept Tested & Keywords

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Practise the full RRB Staff Nurse Jaipur-6th June 2018

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