Q.8 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:
(A) 22
(B) 66
(C) 88
(D) 110
The total number of students in the three classes at the beginning is 88.
Problem Setup
Let the original numbers of students be 3x, 13x, and 6x. After adding 18 to each, they become 3x+18, 13x+18, and 6x+18, matching the ratio 15:35:21.
Solving Equations
Set up proportions: (3x+18)/15 = (13x+18)/35
Cross-multiplying gives: 35(3x+18) = 15(13x+18)
Simplifying to: 105x+630 = 195x+270, so 360 = 90x and x = 4.
Total students: 22x = 88
Option Analysis
| Option | Total | Possible Split | New Split | Matches New Ratio? |
|---|---|---|---|---|
| (A) 22 | 22 | ~1:13:1 (wrong) | Wrong | No |
| (B) 66 | 66 | 18:39:9 (wrong) | 36:57:27 | No |
| (C) 88 | 88 | 12:52:24 | 30:70:42 | Yes 15:35:21 |
| (D) 110 | 110 | 15:65:30 (wrong) | 33:83:48 | No |
Introduction to Students Three Classes Ratio Problem
In competitive exams like GATE and CSIR NET, ratio proportion questions test quick algebraic skills. This problem states: “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. Find the total number of students originally.” Options: (A) 22, (B) 66, (C) 88, (D) 110. Master this students three classes ratio 3:13:6 added 18 scenario for better scores.
Step-by-Step Solution Breakdown
- Assume original students: 3x, 13x, 6x.
- After addition:
3x+18 : 13x+18 : 6x+18 = 15:35:21 - Use first two:
(3x+18)/15 = (13x+18)/35 - Cross-multiply:
35(3x+18) = 15(13x+18) 105x+630 = 195x+270630-270 = 195x-105x360 = 90x, sox=4- Original: 12, 52, 24. Total: 88
- Verify new: 30:70:42 = 15:35:21
Exam Tips for Ratio Problems
- Simplify ratios first (new 15:35:21 already simplest).
- Difference method: New – old ratios show multiples (12,22,15 parts for 18 students).
- Practice similar: 2:3:5 +40 becomes 4:5:7 (total 200).
- Target GATE CSIR NET with these students three classes ratio techniques.
