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CAT 2019 Slot 1 · Quant · Linear Equations · easy

3 pens and 5 pencils cost ₹72, while 5 pens and 3 pencils cost ₹88. What is the cost of 2 pens and 7 pencils?

Single correct option

3 pens and 5 pencils cost ₹72, while 5 pens and 3 pencils cost ₹88. What is the cost of 2 pens and 7 pencils?
  1. A. ₹70
  2. B. ₹64
  3. C. ₹76
  4. D. ₹68
Show answer and solution

Answer: (A) ₹70

Add the two equations: 8(pen + pencil) = 160 ⇒ pen + pencil = 20.
Subtract: 2(pen − pencil) = 16 ⇒ pen − pencil = 8.

So pen = ₹14, pencil = ₹6.

2 pens + 7 pencils = 28 + 42 = ₹70.

Tip: When the coefficients are swapped (3,5 and 5,3), adding and subtracting the equations is the fastest route.
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Original question written in the CAT 2019 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake