EquationsMCQMTP Jun 23 Series IQuestion 1031 of 221
All Questions

The sum of the two numbers is 80 and the sum of their squares is 34. Taking one number as x\displaystyle x from an equation in x\displaystyle x and hence find the numbers. The numbers are:

Options

A(7, 10)
B(4, 4)
C(3, 5)
D(2, 6)
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Correct Answer

✅ Option c — (3, 5)

All Options:

  • A(7, 10)
  • B(4, 4)
  • C(3, 5)
  • D(2, 6)

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Detailed Solution & Explanation

Note: There is a typo in the question text. The sum of the two numbers is 8\displaystyle 8, not 80\displaystyle 80. Let's solve with the correct sum of 8\displaystyle 8.
Let one number be x\displaystyle x. Since the sum is 8\displaystyle 8, the other number is 8−x\displaystyle 8 - x.
The sum of their squares is 34\displaystyle 34. We form the equation in x\displaystyle x:
x2+(8−x)2=34x^2 + (8 - x)^2 = 34
x2+64−16x+x2=34x^2 + 64 - 16x + x^2 = 34
2x2−16x+30=02x^2 - 16x + 30 = 0
Dividing the entire equation by 2:
x2−8x+15=0x^2 - 8x + 15 = 0
Factoring the quadratic equation:
(x−3)(x−5)=0(x - 3)(x - 5) = 0
This gives x=3\displaystyle x = 3 or x=5\displaystyle x = 5.
If x=3\displaystyle x = 3, the other number is 8−3=5\displaystyle 8 - 3 = 5.
If x=5\displaystyle x = 5, the other number is 8−5=3\displaystyle 8 - 5 = 3.
Thus, the two numbers are (3,5)\displaystyle (3, 5).
**Option c**

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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