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Ratio and Proportion
Proportions
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NTPC Graduate Tier 1 2025 Shift-3 📅 06 Jun, 2025

When x is added to each of 20, 34, 11 and 16, then the numbers so obtained, in this order, are in proportion. Then, if $3x:y::y:(2x-6)$, and $y>0$ what is the value of y?

A
29
B
10
C
18
D
2
Result Summary
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NTPC Graduate Tier 1
2025 • 06 Jun, 2025 • Shift-3
When x is added to each of 20, 34, 11 and 16, then the numbers so obtained, in this order, are in proportion. Then, if $3x:y::y:(2x-6)$, and $y>0$ what is the value of y?
Correct Answer
18
Formulating the Proportion: According to the problem, $(20+x) / (34+x) = (11+x) / (16+x)$.Solving for x: Cross-multiplying gives $(20+x)(16+x) = (34+x)(11+x)$. ......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Ratio and Proportion
Chapter -
Ref. Topic Proportions
Pg. No -
💡 Analysis & Explanation
Formulating the Proportion ▼
According to the problem, $(20+x) / (34+x) = (11+x) / (16+x)$.
Solving for x ▼
Cross-multiplying gives $(20+x)(16+x) = (34+x)(11+x)$. Expanding this: $320 + 36x + x^2 = 374 + 45x + x^2$. Canceling $x^2$ from both sides: $320 + 36x = 374 + 45x$. Rearranging terms yields $9x = 320 - 374$, so $9x = -54$. Wait, let me re-calculate. $320 + 20x + 16x + x^2 = 320 + 36x + x^2$. Right side: $34 \times 11 + 34x + 11x + x^2 = 374 + 45x + x^2$. Yes. $9x = -54 \Rightarrow x = -6$. Let me check if adding a negative number makes them in proportion. $20-6 = 14$; $34-6 = 28$; $11-6 = 5$; $16-6 = 10$. Ratio is $14/28 = 1/2$. Ratio is $5/10 = 1/2$. Yes, they are in proportion. So $x = -6$.
Calculating y ▼
We are given $3x : y :: y : (2x - 6)$. This means $y^2 = 3x(2x - 6)$. Substituting $x = -6$: $y^2 = 3(-6) [2(-6) - 6] = -18 [-12 - 6] = -18 \times -18 = 324$. Since $y > 0$, $y = \sqrt{324} = 18$.
Conclusion ▼
The value of y is 18.
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