EquationsMCQMTP Nov 18Question 1015 of 221
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A number consist of three digit of which the middle one is zero and the sum of other digits is 9. The number formed by interchanging the first and third digits is more than the original number by 297 find the number?

Chapter 2 Diagram

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — 306

All Options:

  • A306
  • B309
  • C603
  • D307

Detailed Solution & Explanation

Let the three-digit number be represented as x0y\displaystyle x0y, where x\displaystyle x is the hundreds digit, 0\displaystyle 0 is the tens digit, and y\displaystyle y is the units digit. The value of this original number is: 100x+0×10+y=100x+y100x + 0 ×\displaystyle \times 10 + y = 100x + y According to the first condition, the sum of the hundreds and units digits is 9: x+y=9— (Equation 1)x + y = 9 \quad — (Equation 1)\displaystyle \text{--- (Equation 1)} The number formed by interchanging the first and third digits is y0x\displaystyle y0x, which has a value of: 100y+x100y + x According to the second condition, the new number is more than the original number by 297: (100y+x)−(100x+y)=297(100y + x) - (100x + y) = 297 99y−99x=29799y - 99x = 297 y−x=3— (Equation 2)y - x = 3 \quad — (Equation 2)\displaystyle \text{--- (Equation 2)} We can solve Equations 1 and 2 simultaneously: Adding Equation 1 and Equation 2: (x+y)+(y−x)=9+3(x + y) + (y - x) = 9 + 3 2y=12  ⟹  y=62y = 12 \implies y = 6 Now substitute y=6\displaystyle y = 6 into Equation 1: x+6=9  ⟹  x=3x + 6 = 9 \implies x = 3 Thus, the original number is $306$. *(Note: If the question meant the reversed/interchanged number, that would be 603, which is option C. However, 'the number' refers to the original number, which is 306, option A.)* **Correct Option: (a)**

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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