EquationsMCQMTP Jun 23 Series IQuestion 1033 of 221
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If difference between a number and its positive square root is 12, the numbers are

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Correct Answer

✅ Option b — 16

All Options:

  • A9
  • B16
  • C25
  • DNone of these

Detailed Solution & Explanation

Let the number be x\displaystyle x. The positive square root of x\displaystyle x is x\displaystyle x\displaystyle \sqrt{x}.
According to the question:
x−x=12x - x=12\displaystyle \sqrt{x} = 12
Let x=t\displaystyle x=t\displaystyle \sqrt{x} = t where t>0\displaystyle t > 0. Then x=t2\displaystyle x = t^2.
t2−t−12=0t^2 - t - 12 = 0
Factoring the quadratic equation:
(t−4)(t+3)=0(t - 4)(t + 3) = 0
Since t\displaystyle t must be positive (as it represents a positive square root), we discard t=−3\displaystyle t = -3.
Thus, t=4\displaystyle t = 4.
Therefore, x=4  ⟹  x=16\displaystyle x=4\displaystyle \sqrt{x} = 4 \implies x = 16.
Checking: $16 - 16=16−4=12\displaystyle \sqrt{16} = 16 - 4 = 12$.
**Option b**

About This Chapter: Equations

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Linear, Quadratic and Cubic Equations

This chapter covers Linear, Quadratic and Cubic Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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