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**BUSINESS MATHEMATICS & EVALUATION**

**Direction:** Read and understand each item carefully, then solve for what is being asked.

1. Julia buys a notebook with a cost of P45. The rate of mark-up based on cost is 25%. Find the:
a. Selling price
b. Mark-up

2. Peter decides to impose a mark-up of P5 on each pen he sells to his classmates and friends. This represents a 20% mark-up based on the selling price. Find the:
a. Cost
b. Selling price

Answer :

Sure, let's break down the solution step by step for each part of the problem.

### Part 1: Julia's Notebook

Given:
- Cost of the notebook: P45
- Mark-up rate based on cost: 25% (or 0.25 in decimal form)

Find:
(a) Mark-up amount
(b) Selling price

#### Steps to solve:
1. Calculate the Mark-up Amount:
- The mark-up amount is calculated by multiplying the cost by the mark-up rate.
- Mark-up Amount = Cost × Mark-up Rate
- Mark-up Amount = P45 × 0.25
- Mark-up Amount = P11.25

2. Calculate the Selling Price:
- The selling price is the sum of the cost and the mark-up amount.
- Selling Price = Cost + Mark-up Amount
- Selling Price = P45 + P11.25
- Selling Price = P56.25

Answer:
(a) Mark-up amount: P11.25
(b) Selling price: P56.25

### Part 2: Peter's Pen

Given:
- Mark-up on each pen: P5
- Mark-up rate based on selling price: 20% (or 0.20 in decimal form)

Find:
(a) Cost price of the pen
(b) Selling price of the pen

#### Steps to solve:
1. Calculate the Cost Price:
- We know the mark-up amount and the mark-up rate. To find the cost price, we can rearrange the formula for mark-up rate:
- Mark-up Rate = Mark-up Amount / Cost Price
- Using the given mark-up rate based on selling price:
- Mark-up Amount = Selling Price × Mark-up Rate
- But since we are given the mark-up rate based on the selling price, we reframe it:
- Mark-up Amount = Selling Price × Mark-up Rate
- So Selling Price = Cost Price + Mark-up
- As we have a mark-up amount based on selling price (which is P5 representing 20% of selling price):
- P5 = 0.20 × Selling Price
- Solving for Selling Price
- Selling Price = P5 / 0.20
- Selling Price = P25

Now, since P5 is 20% of the selling price, we can find:
- Cost Price + P5 (markup) = P25 (selling price)
- Cost Price = P25 - P5 = P20

2. Calculate the Selling Price:
- As we have found above the selling price is P25

Answer:
(a) Cost price: P25
(b) Selling price: P30

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Rewritten by : Barada