Class 10 Quadratic Word Problems: Work and Pipes — practice questions with answers

Quadratic Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Two taps together fill a tank in 9 3/8 hours. The larger tap takes 10 hours less than the smaller one to fill it alone. How long does the larger tap take alone?

A25 hours
B10 hours
C18 3/4 hours
D15 hours

Show answer

Answer: D) 15 hours

Larger:

x

, smaller:

x + 10

\frac{1}{x} + \frac{1}{x + 10} = \frac{8}{75}

gives

4 x^{2} - 35 x - 375 = 0

, i.e.

(x - 15) (4 x + 25) = 0

. So

x = 15

2. An inlet fills a tank in x hours and an outlet empties it in x + 3 hours. With both open the tank fills in 18 hours. Find x.

A9 hours
B6 hours
C3 hours
D18 hours

Show answer

Answer: B) 6 hours

\frac{1}{x} - \frac{1}{x + 3} = \frac{1}{18}

3 \times 18 = x (x + 3)

x^{2} + 3 x - 54 = 0

(x - 6) (x + 9) = 0

3. Two taps together fill a bathtub in 2 hours; one alone takes 3 hours longer than the other. How long does the slower tap take?

A3 hours
B5 hours
C4 hours
D6 hours

Show answer

Answer: D) 6 hours

\frac{1}{x} + \frac{1}{x + 3} = \frac{1}{2}

x^{2} - x - 6 = 0

x = 3

. Slower: 6 hours.

4. Two looms together weave an order in 24 hours; one alone takes 14 hours longer than the other. How long does the faster loom take?

A56 hours
B42 hours
C28 hours
D24 hours

Show answer

Answer: B) 42 hours

\frac{1}{x} + \frac{1}{x + 14} = \frac{1}{24}

x^{2} - 34 x - 336 = 0

(x - 42) (x + 8) = 0

x = 42

5. Two tractors together plough a farm in 30 hours. One alone takes 11 hours longer than the other. How long does the faster tractor take alone?

A66 hours
B30 hours
C44 hours
D55 hours

Show answer

Answer: D) 55 hours

\frac{1}{x} + \frac{1}{x + 11} = \frac{1}{30}

x^{2} - 49 x - 330 = 0

(x - 55) (x + 6) = 0

x = 55

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