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JAMB Mathematics 1984 Question 21

Question 21

Quadratic Equations

Tunde and Shola can do a piece of work in 18 days. Tunde can do it alone in x days, whilst Shola takes 15 days longer to do it alone. Which of the following equations is satisfied by x?

  1. A.x2 − 5x − 18 = 0
  2. B.x2 − 20x + 360 = 0
  3. C.x2 − 21x − 270 = 0
  4. D.2x2 + 42x − 190 = 0
  5. E.3x2 − 31x + 150 = 0.
Show the answer and explanation

Answer: C (x2 − 21x − 270 = 0)

Explanation

In one day they do 1/x + 1/(x + 15) = 1/18 of the work. Multiplying out: 18(2x + 15) = x(x + 15), which gives x² − 21x − 270 = 0.