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?
-
A.
x2 – 5x – 10 = 0 -
B.
x2 – 20x + 360 = 0 -
C.
x2 – 21x – 270 = 0 -
D.
3x2 – 65x + 362 = 0
Correct Answer: Option C
Explanation
Tunde and Shola can do the work in 18 days.
Both will do the work in (frac{1}{18}) days.
But Tunde can do the whole work in x days; Hence he does (frac{1}{x}) of the work in 1 day.
Shola does the work in (x + 15) days; hence, he does (frac{1}{x + 15}) of the work in 1 day.
(frac{1}{x} + frac{1}{x + 15} = frac{1}{18})
(frac{2x + 15}{x^{2} + 15x} = frac{1}{18})
(x^{2} + 15x = 36x + 270)
(x^{2} + 15x – 36x – 270 = 0)
(x^{2} – 21x – 270 = 0)