The number of students in three classes is in the ratio \(3:13:6\). If 18 students are added to each class, the ratio changes to \(15:35:21\).
The total number of students in all the three classes in the beginning was:
The total number of students in all the three classes in the beginning was:
Show Hint
- 22
- 66
- 88
- 110
The Correct Option is C
Solution and Explanation
Step 1: Assume the initial numbers of students.
Let the number of students in the three classes initially be
\[
3x,\; 13x,\; 6x.
\]
Step 2: Add 18 students to each class.
After adding 18 students to each class, the numbers become
\[
3x+18,\; 13x+18,\; 6x+18.
\]
Step 3: Use the new ratio.
According to the question,
\[
\frac{3x+18}{15} = \frac{13x+18}{35} = \frac{6x+18}{21}.
\]
Step 4: Solve using the first two terms.
\[
\frac{3x+18}{15} = \frac{13x+18}{35}
\]
\[
35(3x+18) = 15(13x+18)
\]
\[
105x + 630 = 195x + 270
\]
\[
360 = 90x $\Rightarrow$ x = 4.
\]
Step 5: Find the total number of students initially.
\[
3x + 13x + 6x = 22x = 22 \times 4 = 88.
\]
% Final Answer
Final Answer: \[ \boxed{88} \]
Top Questions on Ratio and Proportion
Health insurance plays a vital role in ensuring financial protection and access to quality healthcare. In India, however, the extent and nature of health insurance coverage vary significantly between urban and rural areas. While urban populations often have better access to organized insurance schemes, employer-provided coverage, and awareness about health policies, rural populations face challenges such as limited outreach of insurance schemes, inadequate infrastructure, and lower awareness levels. This urban-rural divide in health insurance coverage highlights the broader issue of healthcare inequality, making it essential to analyze the factors contributing to this gap and explore strategies for more inclusive health protection. A state-level health survey was conducted.
The survey covered 1,80,000 adults across urban and rural areas. Urban residents formed 55% of the sample (that is, 99,000 people) while rural residents made up 45% (that is, 81,000 people). In each area, coverage was classified under four heads – Public schemes, Private insurance, Employer-provided coverage, and Uninsured. In urban areas, Public coverage accounted for 28% of the urban population, Private for 22%, Employer for 18%, and the remaining 32% were Uninsured. In rural areas, where formal coverage is generally lower, Public coverage stood at 35%, Private at 10%, Employer at 8%, while 47% were Uninsured.
For this survey, “Insured” includes everyone covered by Public + Private + Employer schemes, and “Uninsured” indicates those with no coverage at all. Officials noted that public schemes remain the backbone of rural coverage, while employer and private plans are relatively more prevalent in urban centres. (250 words)
- CLAT - 2026
- Quantitative Aptitude
- Ratio and Proportion
- A and B bought lands on the Moon from an eStore, both with the same diameter but A’s land is square-shaped, and B’s land is circular. What is the ratio of the areas of their respective lands?
- XAT - 2025
- Quantitative Ability and Data Interpretation
- Ratio and Proportion
- If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes?
- GMAT - 2025
- Quantitative Aptitude
- Ratio and Proportion
- The ratio of the number of students in the morning shift and afternoon shift of a school was $13 : 9$. After 21 students moved from the morning shift to the afternoon shift, this ratio became $19 : 14$. Next, some new students joined the morning and afternoon shifts in the ratio $3 : 8$ and then the ratio of the number of students in the morning shift and the afternoon shift became $5 : 4$. The number of new students who joined is:
- CAT - 2025
- Quantitative Aptitude
- Ratio and Proportion
- The ratio of the number of coins in boxes A and B was 17:7. After 108 coins were shifted from box A to box B, this ratio became 37:20. The number of coins that needs to be shifted further from A to B, to make this ratio 1:1, is
- CAT - 2025
- Quantitative Aptitude
- Ratio and Proportion
Questions Asked in GATE CS exam
In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and the line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?
Note: The figure shown is representative
- GATE CS - 2025
- Geometry
- If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which one among the given options is the most appropriate code for BEACH?
- GATE CS - 2025
- GATE IN - 2025
- GATE MT - 2025
- GATE NM - 2025
- GATE TF - 2025
- Logical and Analytical Reasoning Skills
A square paper, shown in figure (I), is folded along the dotted lines as shown in figures (II) and (III). Then a few cuts are made as shown in figure (IV). Which one of the following patterns will be obtained when the paper is unfolded?
- GATE CS - 2025
- Paper Folding and Cutting
Consider the relationships among P, Q, R, S, and T:
• P is the brother of Q.
• S is the daughter of Q.
• T is the sister of S.
• R is the mother of Q.
The following statements are made based on the relationships given above.
(1) R is the grandmother of S.
(2) P is the uncle of S and T.
(3) R has only one son.
(4) Q has only one daughter.
Which one of the following options is correct?- GATE CS - 2025
- Blood Relations
- The average marks obtained by a class in an examination were calculated as 30.8. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42. After correcting the marks, the average becomes 31.4. How many students does the class have?
- GATE CS - 2025
- Average