Ratio, Proportion, Indices, LogarithmMCQPYQ Nov 18Question 788 of 305
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3x−2:5x+6\displaystyle 3x-2:5x+6 the duplicate ratio of 2:3\displaystyle 2:3 then find the value x\displaystyle x.

Options

A2\displaystyle 2
B6\displaystyle 6
C5\displaystyle 5
D9\displaystyle 9
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Correct Answer

✅ Option b — 6\displaystyle 6

All Options:

  • A2\displaystyle 2
  • B6\displaystyle 6
  • C5\displaystyle 5
  • D9\displaystyle 9

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Detailed Solution & Explanation

The problem states that the ratio 3x−2:5x+6\displaystyle 3x-2:5x+6 is the duplicate ratio of 2:3\displaystyle 2:3. First, let's understand the concept of a duplicate ratio. If a ratio is a:b\displaystyle a:b, its duplicate ratio is a2:b2\displaystyle a^2:b^2. In this case, the given ratio is 2:3\displaystyle 2:3. The duplicate ratio of 2:3\displaystyle 2:3 is 22:32\displaystyle 2^2:3^2. 22:32=4:92^2:3^2 = 4:9 Now, according to the problem statement, the ratio 3x−2:5x+6\displaystyle 3x-2:5x+6 is equal to the duplicate ratio of 2:3\displaystyle 2:3. Therefore, we can set up the following equation: 3x−25x+6=49\frac{3x-2}{5x+6} = \frac{4}{9} To solve for x\displaystyle x, we will cross-multiply: 9(3x−2)=4(5x+6)9(3x-2) = 4(5x+6) Distribute the numbers on both sides of the equation: 27x−18=20x+2427x - 18 = 20x + 24 Now, we need to gather all terms involving x\displaystyle x on one side of the equation and all constant terms on the other side. Subtract 20x\displaystyle 20x from both sides: 27x−20x−18=2427x - 20x - 18 = 24 7x−18=247x - 18 = 24 Next, add 18\displaystyle 18 to both sides of the equation: 7x=24+187x = 24 + 18 7x=427x = 42 Finally, divide both sides by 7\displaystyle 7 to find the value of x\displaystyle x: x=427x = \frac{42}{7} x=6x = 6 We can verify this solution by substituting x=6\displaystyle x=6 back into the original ratio: 3x−2=3(6)−2=18−2=16\displaystyle 3x-2 = 3(6)-2 = 18-2 = 16 5x+6=5(6)+6=30+6=36\displaystyle 5x+6 = 5(6)+6 = 30+6 = 36 The ratio becomes 16:36\displaystyle 16:36. Simplifying this ratio by dividing both terms by their greatest common divisor, which is 4\displaystyle 4: 16÷4:36÷4=4:9\displaystyle 16 \div 4 : 36 \div 4 = 4:9. This matches the duplicate ratio of 2:3\displaystyle 2:3, which is 4:9\displaystyle 4:9. Thus, our value of x=6\displaystyle x=6 is correct. Comparing our result with the given options: (A) 2\displaystyle 2 (B) 6\displaystyle 6 (C) 5\displaystyle 5 (D) 9\displaystyle 9 Our calculated value x=6\displaystyle x=6 matches Option B. Hence, **Option B** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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