Detailed Solutions: Ratio and Proportion
Ratio and Proportion is one of the most important topics in Mathematics for SSC, Banking, Railway, NDA, and other competitive exams. Questions from this chapter are commonly asked in arithmetic and word-problem sections.
Here, you will find the Top 4 Important Ratio and Proportion Questions with Answers to strengthen your exam preparation.
What is Ratio and Proportion in Mathematics?
Ratio is the comparison of two quantities.
Example: 3 : 5
Proportion shows the equality of two ratios.
Example: 3 : 5 :: 6 : 10
These concepts are widely used in mixture, time and work, speed, percentage, and profit & loss problems.
Question: 1
एक स्कूल में लड़कों और लड़कियों का अनुपात 8:5 है। यदि लड़कियों की संख्या 160 है, तो कुल छात्रों की संख्या ज्ञात करें।
The ratio of boys to girls in a school is 8 : 5. If the number of girls is 160, find the total number of students.
[A] 160 [B] 416
[C] 320 [D] 256
⚡Solution:
Answer (b) : लड़कियों का अनुपात \(5x = 160 \Rightarrow x = 32\)
कुल छात्र = \(8x + 5x = 13x\)
कुल छात्र = 13 × 32 = 416
उत्तर: 416
Question: 2
4, 9 और 12 का चतुर्थ अनुपाती क्या है?
What is the fourth proportional to 4, 9 and 12?
[A] 27 [B] 108
[C] 36 [D] 48
⚡Solution:
Answer (a) : माना चतुर्थ अनुपाती \(x \)है।
\( \frac{4}{9} = \frac{12}{x}\)
\(\Rightarrow 4x = 108\)
\(\Rightarrow x = 27\)
Question: 3
दो संख्याएँ 3:5 के अनुपात में हैं। यदि प्रत्येक में से 9 घटाया जाए, तो वे 12:23 के अनुपात में हो जाती हैं। पहली संख्या ज्ञात करें।
Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, they become in the ratio 12 : 23. Find the first number.
[A] 99 [B] 11
[C] 33 [D] 12
⚡Solution:
Answer (c) : माना संख्याएँ \(3x\) और \(5x\) हैं।
Note: प्रत्येक में से 9 घटाया जाए, तो वे 12:23 के अनुपात में हो जाती हैं।
\(\frac{3x – 9}{5x – 9} = \frac{12}{23}\)
\(69x – 207 = 60x – 108\)
\(\Rightarrow 9x = 99\)
\(\Rightarrow x = 11\)
पहली संख्या = 3 × 11 = 33
Question: 4
A और B की आय का अनुपात 5:4 है और उनके खर्च का अनुपात 3:2 है। यदि प्रत्येक 1600 रुपये बचाता है, तो A की आय क्या है?
The ratio of A and B’s incomes is 5 : 4 and the ratio of their expenses is 3 : 2. If each saves Rs 1600, what is A’s income?
[A] ₹3200 [B] ₹8000
[C] ₹4800 [D] ₹4000
⚡Solution:
Answer (d) : माना A की आय 5p, और B की आय 4p है।
\(\frac{5p – 1600}{4p – 1600} = \frac{3}{2}\)
क्रॉस गुणा करने पर
\(10p – 3200 = 12p – 4800\)
\(\Rightarrow 2p = 1600\)
\(\Rightarrow p = 800\)
A की आय = 5 × 800 = 4000 रुपये।
Why Ratio and Proportion Questions Are Important for Exams
- Forms the base of arithmetic
- Used in mixture, time and work, speed, and profit-loss
- Frequently asked in SSC, Railway, Banking, and State exams
- High-scoring and concept-based topic
Conclusion
Practicing Ratio and Proportion important questions regularly will help you solve complex word problems easily and score higher in competitive exams.