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 and ‘a – 2’ number of mathematics text books at the rate of (x –2) per book. What is his total sale in

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.