An examiner made a 24% error in recording a student's score. If 48 was recorded, find, correct to the nearest whole number, the actual score. The third and fifth terms of a Geometric Progression (G.P.) are 32 and 8 respectively. Find the eighth term.

here are the solutions to the questions:

1. An examiner made a 24% error in recording a student's score. If 48 was recorded, find, correct to the nearest whole number, the actual score.

Let the actual score be $A$. The recorded score is 48.
A 24% error means that the difference between the recorded score and the actual score is 24% of the actual score.
So, $|48 - A| = 0.24A$. This leads to two possible cases:

• Case 1: The recorded score (48) is 24% more than the actual score.

  Step 1: Set up the equation