A company offers two salary schemes for a 10-year period, Year 1 to Year 10 inclusive - Edexcel - A-Level Maths Pure - Question 1 - 2012 - Paper 1

For Salary Scheme 2, we know:

• The first salary in Year 1 is £(P + 1800).
• It increases by £T each year.

Using the same formula for the sum of an arithmetic series:

• First term = £(P + 1800)
• Common difference = £T
• Number of terms = 10

Thus: $S_{10} = \frac{10}{2} [2(P + 1800) + (10 - 1)T]$

We know that the total for both schemes is the same, hence:

Setting the two total equations equal: $10P + 1215 = 5 (2(P + 1800) + 9T)$

Solving this equation will give us the value of T. After simplifying, we find: $50T = 400$ $T = 400$.

From the condition of Salary Scheme 2 for Year 10, we have:

• Salary in Year 10 = £(P + 1800 + 9T)
• We know T = 400.
• So, the equation becomes: $P + 1800 + 3600 = 29850$ [ P + 5400 = 29850
  ] $P = 29850 - 5400$ $P = 24450$