A bookseller sold 'a' number of Geography textbooks at the rate of x per book, 'a + 2' number of History textbooks at the rate of (x + 2) per book…

Correct Option (2)

The total sale is calculated by summing the sales from each category of textbooks.

• Sale from Geography textbooks = Number of books × Price per book = a × x = ax
• Sale from History textbooks = Number of books × Price per book = (a + 2) × (x + 2) = ax + 2a + 2x + 4
• Sale from Mathematics textbooks = Number of books × Price per book = (a – 2) × (x – 2) = ax – 2a – 2x + 4

Total Sale = (Sale from Geography) + (Sale from History) + (Sale from Mathematics)

Total Sale = ax + (ax + 2a + 2x + 4) + (ax – 2a – 2x + 4)

Combine like terms:

• Terms with 'ax': ax + ax + ax = 3ax
• Terms with 'a': +2a – 2a = 0
• Terms with 'x': +2x – 2x = 0
• Constant terms: +4 + 4 = 8

Therefore, the Total Sale = 3ax + 8.

Incorrect Options:

The calculated total sale is 3ax + 8. The other options do not match this derived expression.

• Option 1 (3x + 3a): This expression is incorrect as it does not account for the product of 'a' and 'x' terms (ax) and the constant terms derived from the multiplication of binomials.
• Option 3 (9zr): This option introduces variables 'z' and 'r' which are not present in the problem statement. It is an irrelevant expression.
• Option 4 (x³a³): This expression incorrectly suggests a cubic relationship between 'x' and 'a', which is not derived from the sum of the sales calculations. It does not reflect the total sale.