Linear InequalitiesPYQ Sept 25Question 4109 of 73
All Questions

The region specified by the inequalities 10x+29y≥40\displaystyle 10x+29y \ge 40 and 15x−4y≤25\displaystyle 15x-4y \le 25 includes the point

Options

A(1,1.25)\displaystyle (1, 1.25)
B(3,2.25)\displaystyle (3, 2.25)
C(2.5,2.5)\displaystyle (2.5, 2.5)
D(4,1.25)\displaystyle (4, 1.25)
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — (1,1.25)\displaystyle (1, 1.25)

All Options:

  • A(1,1.25)\displaystyle (1, 1.25)
  • B(3,2.25)\displaystyle (3, 2.25)
  • C(2.5,2.5)\displaystyle (2.5, 2.5)
  • D(4,1.25)\displaystyle (4, 1.25)

Detailed Solution & Explanation

We are given two inequalities: 1) 10x+29y≥40\displaystyle 10x + 29y \ge 40 2) 15x−4y≤25\displaystyle 15x - 4y \le 25
Let us test the given points to see which one satisfies both inequalities:
**Point (1, 1.25):** Substitute x=1,y=1.25\displaystyle x = 1, y = 1.25: - First inequality: 10(1)+29(1.25)=10+36.25=46.25≥40\displaystyle 10(1) + 29(1.25) = 10 + 36.25 = 46.25 \ge 40 (True) - Second inequality: 15(1)−4(1.25)=15−5=10≤25\displaystyle 15(1) - 4(1.25) = 15 - 5 = 10 \le 25 (True) Since both inequalities are satisfied, the point (1,1.25)\displaystyle (1, 1.25) lies in the specified region.
Let us check the other options to confirm: - For (3,2.25)\displaystyle (3, 2.25): 15(3)−4(2.25)=45−9=36≰25\displaystyle 15(3) - 4(2.25) = 45 - 9 = 36 \not\le 25 (False) - For (2.5,2.5)\displaystyle (2.5, 2.5): 15(2.5)−4(2.5)=37.5−10=27.5≰25\displaystyle 15(2.5) - 4(2.5) = 37.5 - 10 = 27.5 \not\le 25 (False) - For (4,1.25)\displaystyle (4, 1.25): 15(4)−4(1.25)=60−5=55≰25\displaystyle 15(4) - 4(1.25) = 60 - 5 = 55 \not\le 25 (False)
Hence, **Option A** is the correct answer.

About This Chapter: Linear Inequalities

Paper

Paper 3: Quantitative Aptitude

Weightage

1-3 Marks

Key Topics

Linear Inequalities in one & two variables

This chapter covers Linear Inequalities in one & two variables and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 1-3 Marks weightage. Focus on understanding core concepts rather than memorizing.

More Questions from Linear Inequalities

On solving the inequalities 5x+y≤100\displaystyle 5x + y \le 100, x+y≤60\displaystyle x + y \le 60, x≥0\displaystyle x \ge 0, y≥0\displaystyle y \ge 0, we get the following solution:

An employer recruits experienced (x)\displaystyle (x) and fresh workmen (y)\displaystyle (y) for his under the condition that he cannot employ more than 11\displaystyle 11 people x\displaystyle x and y\displaystyle y can be related by the inequality.

The solution set of the equations x+2>0\displaystyle x + 2 > 0 and 2x−6>0\displaystyle 2x - 6 > 0 is

On solving the inequalities; we get 6x+y≥18\displaystyle 6x + y \ge 18, x+4y≥12\displaystyle x + 4y \ge 12, 2x+y≥10\displaystyle 2x + y \ge 10

Solve for x\displaystyle x of the inequalities 2≤3x−25≤4\displaystyle 2 \le \frac{3x - 2}{5} \le 4 where x∈N\displaystyle x \in N

The common region in the graph of the inequalities x+y≤4\displaystyle x + y \le 4, x−y≤4\displaystyle x - y \le 4, x≥2\displaystyle x \ge 2 is

Ready to Master Linear Inequalities?

Practice all 73 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free