Rita purchased 9 pens and 7 pencils for ₹66. Megha also bought 5 pens and 11 pencils of the same kind for ₹58. What is the cost of 3 pencils?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → ₹9
The two purchases give two equations in two unknowns. Making the pen terms equal in both equations and subtracting leaves the pencils alone.
The two purchases (one pen costs ₹\(p\) and one pencil ₹\(c\)):
Rita: \(9p+7c=66\) (1)
Megha: \(5p+11c=58\) (2)
Making the pen terms equal (45 pens in each):
Multiplying (1) by 5: \(45p+35c=330\) (3)
Multiplying (2) by 9: \(45p+99c=522\) (4)
Subtracting (3) from (4) (the \(p\) terms cancel):
\(64c=192\)
So one pencil costs ₹3
Cost of 3 pencils \(=3\times3=\) ₹9