Class 10 Problems on Quadratic Equations Mock Test (ICSE)

Topics in Problems on Quadratic Equations

• Problems on numbers
• Problems on ages
• Problems on time, speed and work
• Problems on geometry and mensuration

Problems on Quadratic Equations practice questions with answers

1. Q1Multiple choice·1 mark
   The sum of the reciprocals of Rehman's ages (in years) $3$ years ago and $5$ years from now is $\frac{1}{3}$. If his present age is $x$ years, the quadratic equation representing this is:

   1. (a)$x^2 - 4x - 21 = 0$
   2. (b)$x^2 + 4x - 21 = 0$
   3. (c)$x^2 - 4x + 21 = 0$
   4. (d)$x^2 + 4x + 21 = 0$
   Show answer and step marks

   1. Correct option: (a) $x^2 - 4x - 21 = 0$. Given $\frac{1}{x-3} + \frac{1}{x+5} = \frac{1}{3} \Rightarrow \frac{2x+2}{x^2+2x-15} = \frac{1}{3} \Rightarrow 6x+6 = x^2+2x-15 \Rightarrow x^2-4x-21 = 0$.+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   A train travels $360\text{ km}$ at a uniform speed. If the speed had been $5\text{ km/h}$ more, it would have taken $1$ hour less for the same journey. If the original speed of the train is $x\text{ km/h}$, the equation that represents this situation is:

   1. (a)$\frac{360}{x+5} - \frac{360}{x} = 1$
   2. (b)$\frac{360}{x} + \frac{360}{x+5} = 1$
   3. (c)$\frac{360}{x} - \frac{360}{x-5} = 1$
   4. (d)$\frac{360}{x} - \frac{360}{x+5} = 1$
   Show answer and step marks

   1. Correct option: (d) $\frac{360}{x} - \frac{360}{x+5} = 1$. Original time minus new time equals $1$ hour.+1

   Answer: (d)
3. Q3Multiple choice·1 mark
   The sum of the squares of two consecutive natural numbers is $313$. If the smaller number is $x$, the quadratic equation representing this condition is:

   1. (a)$2x^2 + 2x - 313 = 0$
   2. (b)$2x^2 + 2x - 312 = 0$
   3. (c)$2x^2 - 312 = 0$
   4. (d)$2x^2 - 2x - 313 = 0$
   Show answer and step marks

   1. Correct option: (b) $2x^2 + 2x - 312 = 0$. The numbers are $x$ and $x+1$. Sum of squares is $x^2 + (x+1)^2 = 313 \Rightarrow 2x^2 + 2x + 1 = 313 \Rightarrow 2x^2 + 2x - 312 = 0$.+1

   Answer: (b)
4. Q4Multiple choice·1 mark
   The length of a rectangular garden is $3\text{ m}$ more than its breadth. If the area of the garden is $108\text{ m}^2$, the breadth of the garden is:

   1. (a)$12\text{ m}$
   2. (b)$6\text{ m}$
   3. (c)$8\text{ m}$
   4. (d)$9\text{ m}$
   Show answer and step marks

   1. Correct option: (d) $9\text{ m}$. Setting breadth as $x$, length is $x+3$. Then $x(x+3) = 108 \Rightarrow x^2+3x-108 = 0 \Rightarrow (x+12)(x-9) = 0$. Since breadth cannot be negative, $x = 9\text{ m}$.+1

   Answer: (d)

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