Question

Select the correct alternative from the given choices. The ratio of the number of students in classes $A, B$ and $C$ is $3: 7: 8$. If 10 students leave $C$ and join $B$, the ratio of the number of students in $B$ and $C$ would be reversed. Find the total number of students in the classes $A, B$ and $C$. (A) 144 (B) 162 (C) 180 (D) 198

Name: Problem 15, Chapter 2: Computer Science and Information Technology
Uploaded: 2021-12-12T13:13:21-08:00
Duration: 1 min 37 s
Channel: Prabhu Ramji
Description: Select the correct alternative from the given choices. The ratio of the number of students in classes A, B and C is 3: 7: 8. If 10 students leave C and join B, the ratio of the number of students in B and C would be reversed. Find the total number of students in the classes A, B and C. (A) 144 (B) 162 (C) 180 (D) 198

   Select the correct alternative from the given choices.
The ratio of the number of students in classes $A, B$ and $C$ is $3: 7: 8$. If 10 students leave $C$ and join $B$, the ratio of the number of students in $B$ and $C$ would be reversed. Find the total number of students in the classes $A, B$ and $C$.
(A) 144
(B) 162
(C) 180
(D) 198

Computer Science and Information Technology

Trishna Knowledge… 2018 Edition

Chapter 2, Problem 15

Instant Answer

Solved by Expert Prabhu Ramji

12/12/2021

Step 1

Step 1: Let's denote the number of students in class A, B, and C as $3x$, $7x$, and $8x$ respectively according to the given ratio. Show more…

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Select the correct alternative from the given choices. The ratio of the number of students in classes $A, B$ and $C$ is $3: 7: 8$. If 10 students leave $C$ and join $B$, the ratio of the number of students in $B$ and $C$ would be reversed. Find the total number of students in the classes $A, B$ and $C$. (A) 144 (B) 162 (C) 180 (D) 198

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Key Concepts

Ratios and Proportions

Ratios express the relative sizes of two or more quantities and are used to divide a total amount into proportional parts. Understanding ratios allows you to represent quantities like the number of students in each class as multiples of a common factor.

Algebraic Formulation of Word Problems

Translating real-world problems into algebraic expressions involves assigning variables to unknown quantities—such as using a common multiplier for the ratio values—and setting up equations to mirror the changes described in the problem.

Linear Equations

Setting up and solving linear equations is essential when the problem involves adjustments to the quantities, such as moving students between classes, which then alters the given ratios. Solving these equations yields the value of the common multiplier and, ultimately, the total number of students.

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