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Tunde and Shola can do a piece of work in 18 days. Tunde can...

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

View answer & explanation

Correct answer is C

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.

$\frac{1}{x} + \frac{1}{x + 15} = \frac{1}{18}$

$\frac{2x + 15}{x^{2} + 15x} = \frac{1}{18}$

$x^{2} + 15x = 36x + 270$

$x^{2} + 15x - 36x - 270 = 0$

$x^{2} - 21x - 270 = 0$

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