← Quantitative Aptitude

Ratio & Proportion — Questions with Solutions

4 solved Ratio & Proportion questions from Quantitative Aptitude, as asked in SSC CGL and other SSC exams. Read the answer and explanation below, then practise the full set in the practice section.

Practise this topic

Q1. A 54,000 grant is distributed among Research, Teaching, and Administration in a 6:8:4 ratio. Teaching department uses 5,000 for equipment and 3,000 for books, then distributes the rest to four faculty members in a 4:3:2:1 ratio. How much does the faculty member with the smallest share receive?

54,000 के अनुदान को अनुसंधान, शिक्षण और प्रशासन के बीच 6:8:4 के अनुपात में वितरित किया जाता है। शिक्षण विभाग उपकरण के लिए 5,000 और पुस्तकों के लिए 3,000 का उपयोग करता है, फिर शेष राशि को चार संकाय सदस्यों में 4:3:2:1 के अनुपात में वितरित करता है। सबसे छोटा हिस्सा पाने वाले संकाय सदस्य को कितना मिलता है?

  1. A. 1,600
  2. B. 1,800
  3. C. 2,000
  4. D. 2,200

Solution

Total ratio = 18 units = 54000 $\implies$ 1 unit = 3000. Teaching share = $8 \times 3000 = 24000$. After spending 8000 (5000+3000), remainder = 16000. Distributed in 4:3:2:1 (Total 10 units). Smallest share (1 unit) = 1600.

Q2. The mean proportional of $8a^2$ and $\frac{18}{a^4}$, where $a$ is a positive number, is:

जहाँ $a$ एक धनात्मक संख्या है, $8a^2$ और $\frac{18}{a^4}$ का मध्यानुपाती (mean proportional) क्या है?

  1. A. $\frac{12}{a^2}$
  2. B. $12a$
  3. C. $12a^2$
  4. D. $\frac{12}{a}$

Solution

Mean proportional = $\sqrt{(8a^2) \times (18/a^4)} = \sqrt{144 / a^2} = 12/a$.

Q3. What is the value of D, if A: C :: B: D in the given table? (A=25, B=40, C=30, D=?)

दी गई तालिका में यदि $A : C :: B : D$ है, तो D का मान क्या है? (A=25, B=40, C=30, D=?)

  1. A. $56$
  2. B. $48$
  3. C. $45$
  4. D. $42$

Solution

$\frac{A}{C} = \frac{B}{D} \Rightarrow \frac{25}{30} = \frac{40}{D} \Rightarrow \frac{5}{6} = \frac{40}{D} \Rightarrow D = \frac{40 \times 6}{5} = 48$.

Q4. If x varies inversely as y and x=2 when y=6, then the value of y when x=3 is:

  1. A. 2
  2. B. 3
  3. C. 4
  4. D. 6

Solution

Since x is inversely proportional to y, x * y = constant (k). So, k = 2 * 6 = 12. When x = 3, 3 * y = 12, which gives y = 4.