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Students of a class are made to sit in rows of equal number of chairs. If number of students is increased by 2 in each row, then the number of rows decrease by 3. If number of students is increased by 4 in each row, then the number of rows decreases by 5. What is the number of students in the class?

Students of a class are made to sit in rows of equal number of chairs. If number of students is increased by 2 in each row, then the number of rows decrease by 3. If number of students is increased by 4 in each row, then the number of rows decreases by 5. What is the number of students in the class? Correct Answer 120

Given:

The number of students is increased by 2 in each row, then the number of rows decrease by 3

The number of rows decreases by 3. If the number of students is increased by 4 in each row

Concept Used:

By method of elimination of 2 variable

Calculation:

Suppose total number of rows is A and number of students in each row is B;

∴ Total students = A × B

According to the question:

(A – 3) × (B + 2) = A × B

⇒ 2A – 3B = 6      ---- (1)

And

(A – 5) × (B + 4) = A × B

⇒ 4A – 5B = 20      ---- (2)

Multiply equation 1 by 2 and subtract equation 2 from it:

⇒ B = 8

Now from equation 1:

⇒ 2A = 6 + 24

⇒ A = 15

Then  A × B = 120

∴ Total number of students in the class is120  

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