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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.MediumLevel 57
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Three chairs and two tables cost ₹4900. Two chairs and three tables cost ₹5600. What is the price of one table?

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Answer and explanation

Correct answer: ₹1400

Let the price of one chair be c and the price of one table be t. The information gives the simultaneous equations 3c + 2t = 4900 and 2c + 3t = 5600. Multiply the first equation by 2 and the second by 3: 6c + 4t = 9800 and 6c + 9t = 16800. Subtracting the first new equation from the second gives 5t = 7000, so t = 1400. Therefore, one table costs ₹1400, making option C correct. The other options do not satisfy both original cost equations when the corresponding chair price is found.

Related tags

Simultaneous EquationsElimination MethodWord ProblemAlgebraic Methods: Substitution Method And Elimination Method.Algebraic Methods Substitution Method And Elimination MethodPair Of Linear Equations In Two VariablesMathematicsClass 10 Mcq

Frequently asked questions

What is the correct answer to this question?

₹1400

Why is this the correct answer?

Let the price of one chair be c and the price of one table be t. The information gives the simultaneous equations 3c + 2t = 4900 and 2c + 3t = 5600. Multiply the first equation by 2 and the second by 3: 6c + 4t = 9800 and 6c + 9t = 16800. Subtracting the first new equation from the second gives 5t = 7000, so t = 1400. Therefore, one table costs ₹1400, making option C correct. The other options do not satisfy both original cost equations when the corresponding chair price is found.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..

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  1. 1In the equation \(2x-y=4\), what is the value of \(y\) when \(x=3\)?
  2. 2Which equation is obtained by simplifying (6x+3y=12)?
  3. 3What is the point of intersection of the lines \(4x+3y=34\) and \(4x-y=10\)?
  4. 4If the lines \(x+y=9\) and \(kx+3y=23\) both pass through the point \(\left(4,5\right)\), what is the value of \(k\)?
  5. 5While solving a pair of linear equations in two variables by the elimination method, in which situation can one variable be eliminated directly?
  6. 6What is the \(x\)-coordinate of the point of intersection of the lines \(4x+5y=31\) and \(3x-2y=1\)?
  7. 7If the two lines have a unique point of intersection (r,s) that satisfies (3r+s=19) and (r-s=1), what is the value of (r+s)?
  8. 8If the unique point of intersection of two lines is (r,s) and the lines are represented by (4r+s=29) and (r-s=1), what is the value of (r+s)?
  9. 9What is the solution of the equations (x+y=5) and (x-y=1)?
  10. 10In the equations (2x+y=7) and (x=2), what is the value of (y)?
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