Question

There are 3 college campuses in Delhi, Mumbai and Bangalore having 1200, 1500 and 1100 students respectively. Delhi campus teaches Public Policy and Russian, Mumbai campus teaches Finance and German while Bangalore campus teaches IT and Japanese. Each student either learns a Language or a non-language subject but not both. Number of students learning Russian are 1.5 times to that of Japanese. Number of students learning French and Japanese only are 100 more than number of students learning French and Russian only which is 100 more than the ones learning all 3 languages. Number of students learning only French are 50 less than 1.5 times the students learning only Japanese and only Russian combined. Number of students learning Japanese only and Japanese and Russian only are 200 each and all the ones learning all are 100. If only the ones learning single language are campus students and other are all from distance learning programs, then answer the following: 5) How many students are learning French only?​

Answer 1

To find the number of students learning French only, let's break down the given information step by step:

1. The total number of students in the three campuses is 1200 + 1500 + 1100 = 3,800.

2. Let's assume the number of students learning Russian is R, and the number of students learning Japanese is J.

3. According to the given information, the number of students learning Russian is 1.5 times the number of students learning Japanese: R = 1.5J.

4. The number of students learning French and Japanese only is 100 more than the number of students learning French and Russian only, and this is 100 more than the number of students learning all three languages.

Let's denote the number of students learning all three languages as A.

So, the number of students learning French and Russian only is A - 100, and the number of students learning French and Japanese only is A + 100.

5. The number of students learning only French is 50 less than 1.5 times the number of students learning only Japanese and only Russian combined.

So, the number of students learning only French is 1.5(J + R) - 50.

6. The number of students learning Japanese only and Japanese and Russian only are both 200, and the number of students learning all three languages is 100.

Now, we have enough information to solve the problem.

Let's summarize the information we have so far:

- Total number of students: 3,800.

- Number of students learning Russian: R.

- Number of students learning Japanese: J.

- Number of students learning all three languages: A = 100.

- Number of students learning French and Russian only: A - 100.

- Number of students learning French and Japanese only: A + 100.

- Number of students learning only French: 1.5(J + R) - 50.

To find the number of students learning French only, we need to subtract the students who are learning French and Russian only and French and Japanese only from the number of students learning only French:

Number of students learning French only = (1.5(J + R) - 50) - (A - 100) - (A + 100).

Substituting the value of A (100) into the equation, we get:

Number of students learning French only = (1.5(J + R) - 50) - (100 - 100) - (100 + 100).

Simplifying further:

Number of students learning French only = 1.5(J + R) - 50 - 0 - 200.

Number of students learning French only = 1.5(J + R) - 250.

So, the number of students learning French only is 1.5 times the number of students learning only Japanese and only Russian combined, minus 250.

Explanation: