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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.HardLevel 55
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The price of one pen is (p) and one notebook is (q). If (3p+2q=185) and (2p+5q=215), what is the value of (q)?

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Answer and explanation

Correct answer: ₹25

Using elimination, multiply the first equation by 5 and the second equation by 2: \(15p+10q=925\) and \(4p+10q=430\). Subtracting gives \(11p=495\), so \(p=45\). Substituting in \(3p+2q=185\), we get \(135+2q=185\), hence \(2q=50\) and \(q=25\). Therefore, the correct answer is ₹25. Substituting ₹20 does not satisfy both equations together. Exam tip: in elimination, make the coefficients of one variable equal before subtracting the equations.

Related tags

Pair Of Linear EquationsElimination MethodSubstitution MethodWord ProblemsPrice CalculationClass 10 Mathematics

Frequently asked questions

What is the correct answer to this question?

₹25

Why is this the correct answer?

Using elimination, multiply the first equation by 5 and the second equation by 2: \(15p+10q=925\) and \(4p+10q=430\). Subtracting gives \(11p=495\), so \(p=45\). Substituting in \(3p+2q=185\), we get \(135+2q=185\), hence \(2q=50\) and \(q=25\). Therefore, the correct answer is ₹25. Substituting ₹20 does not satisfy both equations together. Exam tip: in elimination, make the coefficients of one variable equal before subtracting the equations.

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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10 more MCQs
  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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