When x is added to each of 30, 15, 21 and 11, then the numbers so obtained, in this order, are in proportion. Then, if 6x : y :: y : (3x - 9), and y > 0, what is the value of y?

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NTPC Graduate Tier 1

2025 • 06 May, 2025 • Shift-1

When x is added to each of 30, 15, 21 and 11, then the numbers so obtained, in this order, are in proportion. Then, if 6x : y :: y : (3x - 9), and y > 0, what is the value of y?

Correct Answer

Equation Setup: To make the numbers proportional when 'x' is added, the ratios equate to (30+x)/(15+x) = (21+x)/(11+x).Solving for x: Cross-multiplying yields (......

💡 Analysis & Explanation

Equation Setup ▼

To make the numbers proportional when 'x' is added, the ratios equate to (30+x)/(15+x) = (21+x)/(11+x).

Solving for x ▼

Cross-multiplying yields (30+x)(11+x) = (21+x)(15+x), which expands to 330 + 41x + x² = 315 + 36x + x². Solving this linear equation gives 5x = -15, hence x = -3.

Evaluating y ▼

The second proportion is 6(-3) : y :: y : (3(-3)-9). This substitutes to -18 : y :: y : -18, meaning -18/y = y/-18.

Final Calculation ▼

Cross-multiplying gives y² = 324. Since the problem specifies y > 0, the square root is strictly positive.

Conclusion ▼

Taking the positive root, y equals 18.

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When x is added to each of 30, 15, 21 and 11, then the numbers so obtained, in this order, are in proportion. Then, if 6x : y :: y : (3x - 9), and y > 0, what is the value of y?