Class 10 Quadratic Word Problems — practice questions with answers

Algebra — Quadratics · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. The product of two consecutive positive integers is 56. Which equation models this?

Ax(x+1) = 56
Bx + (x+1) = 56
Cx(x-1) = 56
Dx² + 56 = 0

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Answer: A) x(x+1) = 56

Let the integers be x and x+1. Their product is x(x+1) = 56.

2. The base of a triangle is 4 cm more than its height. If its area is 48 sq cm, which equation gives the height x?

A $\frac{1}{2} x (x + 4) = 48$
Bx(x+4) = 48
C $\frac{1}{2} (x) (x - 4) = 48$
Dx² + 4 = 48

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Answer: A)

\frac{1}{2} x (x + 4) = 48

Area of triangle =

\frac{1}{2}

base height =

\frac{1}{2} (x + 4) (x) = 48

3. The sum of two numbers is 15 and the sum of their reciprocals is

\frac{3}{10}

. The larger number is:

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Answer: C) 10

x + (15-x) = 15;

\frac{1}{x} + \frac{1}{15 - x} = \frac{3}{10}

\frac{15}{x ( 15 - x )} = \frac{3}{10}

, x(15-x)=50, x²-15x+50=0, (x-5)(x-10)=0. Larger = 10.

4. If twice a number is added to three times its square, the result is 65. The positive value of the number is:
Find it.

A $\frac{13}{3}$
B5
C13
D-5

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Answer: A)

\frac{13}{3}

3x² + 2x = 65, 3x² + 2x - 65 = 0, (3x-13)(x+5)=0. Positive value

x = \frac{13}{3}

5. In a flight of 600 km, an aircraft was slowed by bad weather. Its average speed was reduced by 200 km/h and the time of flight increased by 30 minutes. The original speed of the aircraft (km/h) is:
Form and solve the equation.

A540
B1200
C600
D660

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Answer: C) 600

\frac{600}{x - 200} - \frac{600}{x} = \frac{1}{2}

\frac{600 ( 200 )}{x ( x - 200 )} = \frac{1}{2}

, 240000 = x(x-200)/2... 240000*2 = x²-200x, x² -200x -240000 = 0, (x-600)(x+400)=0. x = 600 km/h.

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