Acca Arithmeticworked problems for accumulator maths
Chapters

Chapter 5

Percentages on top

Some slips show a percentage added to winnings. The arithmetic depends on what the percentage is applied to. The terms here are invented to show the calculation; they describe no real offer and are not a reason to take one.

Problems 24–27 · 1 warm-up · 2 steady · 1 stretch

stake₦1,000profit₦4,400+10%₦440return ₦5,840
Problem 24: 10% added to profit, not to the stake.

Problem 24: 10% added to profit

Warm-up

Invented terms: 10% is added to the profit of an accumulator. Using problem 1 (stake ₦1,000, combined odds 5.40), what is the total return?

Profit before
₦4,400
Added
10% of profit
Show working for problem 24
  1. Added amount: ₦4,400 × 0.10 = ₦440.
  2. Return: ₦1,000 + ₦4,400 + ₦440 = ₦5,840.

Answer ₦5,840.

Problem 25: Profit or return?

Steady

Suppose instead that 10% were added to the whole return, stake included. How much more is that than adding it to profit?

Return before
₦5,400
Show working for problem 25
  1. On the return: ₦5,400 × 1.10 = ₦5,940.
  2. On profit (problem 24): ₦5,840.
  3. Difference: ₦100, which is 10% of the ₦1,000 stake.

Answer ₦100 more. The wording “profit” or “return” decides it.

Problem 26: The odds it amounts to

Steady

Express the return of problem 24 as effective combined odds.

Return
₦5,840
Stake
₦1,000
Show working for problem 26
  1. ₦5,840 ÷ ₦1,000 = 5.84.

Answer 5.84, against 5.40 without the addition.

Problem 27: A minimum-odds condition

Stretch

Invented terms: the addition applies only if every leg is priced at 1.30 or more. A treble is 1.25 × 1.60 × 2.00, stake ₦1,000. Does it qualify, and what is the return if all win?

Legs
1.25 × 1.60 × 2.00
Condition
each leg 1.30 or more
Show working for problem 27
  1. Leg 1 is 1.25, below 1.30, so the condition fails.
  2. Return without any addition: ₦1,000 × 1.25 × 1.60 × 2.00 = ₦4,000.

Answer It does not qualify; the return is ₦4,000.