Question
Download Solution PDFStudy the given table carefully and answer the following question.
The table shows the percentage of students of four departments - Mechanical, Civil, Computer Science and Applied - with each student being in only one department. The table also shows the number of students of these four departments in five different colleges, with the total number of students being 2080.
| College | Students | Mechanical | Civil | Computer Science | Applied |
| IIT Delhi | 430 | - | 20% | - | 10% |
| IIT Kanpur | 350 | 20% | - | 25% | - |
| IIT Bombay | - | 20% | 18% | - | 32% |
| IIT Madras | - | - | 25% | 18% | 35% |
| IIT Guwahati | 400 | 20% | 22% | - | 20% |
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
Let the number of students in IIT Madras be x.
Then, the number of students in IIT Bombay = x × (100 - 20)/100
= 4/5x
The number of students in IIT Bombay and in IIT Madras = 2080 - (430 + 350 + 400)
= 2080 - 1180
= 900
⇒ x + 4/5x = 900
⇒ 9/5x = 900
⇒ x = 500
⇒ 4/5x → 500 × 4/5 = 400
The total number of students who study in the Applied department in these two colleges = 400 × 32% + 500 × 35%
= 128 + 175 = 303
The total number of students who study in the Civil department in these two colleges = 400 × 18% + 500 × 25%
= 72 + 125 = 197
Difference ⇒ 303 - 197
= 106
The answer is 106.
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