EquationsMCQPYQ May 18Question 985 of 221
All Questions

If 3x+y+2x−y=−1\displaystyle 3x+y+2x−y\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = -1 and 1x+y−1x−y=43\displaystyle 1x+y−1x−y=43\displaystyle \frac{1}{x+y} - \frac{1}{x-y} = \frac{4}{3} then (x,y)\displaystyle (x, y) is:

Select Your Answer (Keyboard: A, B, C, D)
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — (1,2)\displaystyle (1, 2)

All Options:

  • A(2,1)\displaystyle (2, 1)
  • B(1,2)\displaystyle (1, 2)
  • C(−1,2)\displaystyle (-1, 2)
  • D(−2,1)\displaystyle (-2, 1)

Detailed Solution & Explanation

Let u=1x+y\displaystyle u = 1x+y\displaystyle \frac{1}{x+y} and v=1x−y\displaystyle v = 1x−y\displaystyle \frac{1}{x-y}. The given system of equations can be written as: 3u+2v=−1— (Equation 1)3u + 2v = -1 \quad — (Equation 1)\displaystyle \text{--- (Equation 1)} u−v=43— (Equation 2)u - v = 43\displaystyle \frac{4}{3} \quad — (Equation 2)\displaystyle \text{--- (Equation 2)} Multiplying Equation 2 by 2\displaystyle 2, we get: 2u−2v=83— (Equation 3)2u - 2v = 83\displaystyle \frac{8}{3} \quad — (Equation 3)\displaystyle \text{--- (Equation 3)} Adding Equation 1 and Equation 3: (3u+2v)+(2u−2v)=−1+83(3u + 2v) + (2u - 2v) = -1 + 83\displaystyle \frac{8}{3} 5u=53  ⟹  u=135u = 53\displaystyle \frac{5}{3} \implies u = 13\displaystyle \frac{1}{3} Substituting u=13\displaystyle u = 13\displaystyle \frac{1}{3} in Equation 2: 13−v=43  ⟹  v=13−43=−113−v=43\displaystyle \frac{1}{3} - v = \frac{4}{3} \implies v = 13−43\displaystyle \frac{1}{3} - \frac{4}{3} = -1 Now, substituting back u\displaystyle u and v\displaystyle v: 1x+y=13  ⟹  x+y=3— (Equation 4)1x+y=13\displaystyle \frac{1}{x+y} = \frac{1}{3} \implies x + y = 3 \quad — (Equation 4)\displaystyle \text{--- (Equation 4)} 1x−y=−1  ⟹  x−y=−1— (Equation 5)1x−y\displaystyle \frac{1}{x-y} = -1 \implies x - y = -1 \quad — (Equation 5)\displaystyle \text{--- (Equation 5)} Adding Equation 4 and Equation 5: 2x=2  ⟹  x=12x = 2 \implies x = 1 Substituting x=1\displaystyle x = 1 in Equation 4: 1+y=3  ⟹  y=21 + y = 3 \implies y = 2 So, (x,y)=(1,2)\displaystyle (x, y) = (1, 2). Hence, **Option B** is the correct answer.

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.

More Questions from Equations

2x+510+3x+1015=5\displaystyle \frac{2x+5}{10} + \frac{3x+10}{15} = 5, find x\displaystyle x

Find value of x2−10x+1\displaystyle x^2 - 10x + 1 if x=15−26\displaystyle x = 15−26\displaystyle \frac{1}{5-2\sqrt{6}}

The cost of 2\displaystyle 2 oranges and 3\displaystyle 3 apples is $28$. If the cost of an apple is doubled then the cost of $3orangesand\displaystyle oranges and5$ apples is $75$. The original cost of 7\displaystyle 7 oranges and 4\displaystyle 4 apples (in Rs) is:

In a multiple choice question paper consisting of $100questionsof\displaystyle questions of1\displaystyle mark each, a candidate gets $60\% marks. If the candidate attempted all questions and there was a penalty of $0.25$ marks for wrong answers is:

The values of x\displaystyle x and y\displaystyle y satisfying the equations 3x+y+2x−y=3\displaystyle 3x+y+2x−y=3\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = 3 and 2x+y+3x−y=233\displaystyle 2x+y+3x−y=233\displaystyle \frac{2}{x+y} + \frac{3}{x-y} = \frac{23}{3} given by

A plumber can be paid either $600\displaystyle and $50 per hour or $170$ per hour. If the job takes '$n$' hour, for what value of '$n$' the second method earns better wages for the plumber?

Ready to Master Equations?

Practice all 221 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free