Civil Service Exam (Subprofessional) Numerical Ability — Ratio, Proportion & PercentageFlash Cards

What is a ratio and how is it expressed?

A ratio is a relationship between two numbers or quantities that compares their sizes. It can be expressed in three ways: 1) Using colon notation (3:4), 2) Using fraction form (3/4), and 3) Using words ('3 to 4'). Example: If there are 15 boys and 10 girls in a class, the ratio of boys to girls is 15:10 or 3:2.

What is a proportion and when are two ratios proportional?

A proportion states that two ratios are equal. Two ratios are proportional if their cross products are equal. For ratios a:b and c:d, they are proportional if a×d = b×c. Example: 5:10 and 3:6 are proportional because 5×6 = 10×3 = 30.

Define percentage and explain its relationship to fractions and decimals.

Percentage means 'per hundred' and is expressed with the % symbol. It represents a fraction with denominator 100. Conversions: 1) Fraction to %: multiply by 100, 2) Decimal to %: multiply by 100, 3) % to decimal: divide by 100. Example: 3/4 = 0.75 = 75%.

How do you solve for an unknown term in a proportion using cross multiplication?

Step 1: Set up the proportion (a:b = c:x). Step 2: Cross multiply (a×x = b×c). Step 3: Solve for x (x = bc/a). Example: Find x in 5:x = 3:9. Cross multiply: 3x = 5×9 = 45. Therefore, x = 45/3 = 15.

What is the formula for finding a percentage of a number?

Formula: Percentage of a number = (Rate/100) × Base. Where Rate is the percentage value, and Base is the whole amount. Example: Find 25% of 200. Solution: (25/100) × 200 = 0.25 × 200 = 50.

How do you find what percentage one number is of another?

Formula: Rate = (Part/Whole) × 100%. Steps: 1) Identify the part and whole, 2) Divide part by whole, 3) Multiply by 100. Example: 150 out of 250 students are female. Rate = (150/250) × 100% = 0.6 × 100% = 60%.

How do you find the original price when given a discounted price and discount rate?

Formula: Original Price = Discounted Price ÷ (100% - Discount Rate). Steps: 1) Convert discount rate to decimal, 2) Subtract from 1, 3) Divide discounted price by result. Example: Item costs ₱1,200 after 20% discount. Original = 1,200 ÷ (1 - 0.20) = 1,200 ÷ 0.80 = ₱1,500.

In a school of 500 students, the ratio of boys to girls is 3:2. How many boys and girls are there?

Step 1: Total ratio parts = 3 + 2 = 5. Step 2: Each part = 500 ÷ 5 = 100 students. Step 3: Boys = 3 × 100 = 300, Girls = 2 × 100 = 200. Verification: 300 + 200 = 500 ✓.

A shirt originally costs ₱800 but is sold at 25% discount. What is the sale price?

Method 1: Discount amount = 25% × ₱800 = 0.25 × 800 = ₱200. Sale price = ₱800 - ₱200 = ₱600. Method 2: Sale price = 800 × (100% - 25%) = 800 × 0.75 = ₱600.

If a product is marked up by 30% from its cost price of ₱200, what is the selling price?

Markup amount = 30% × ₱200 = 0.30 × 200 = ₱60. Selling price = Cost price + Markup = ₱200 + ₱60 = ₱260. Alternative: Selling price = 200 × (100% + 30%) = 200 × 1.30 = ₱260.

What is the formula for calculating profit percentage?

Profit % = (Selling Price - Cost Price) / Cost Price × 100%. Example: Item bought for ₱500, sold for ₱650. Profit = ₱650 - ₱500 = ₱150. Profit % = (150/500) × 100% = 30%.

A car depreciates by 15% each year. If it's worth ₱500,000 initially, what's its value after depreciation?

Depreciated value = Original value × (100% - Depreciation rate) = ₱500,000 × (100% - 15%) = ₱500,000 × 0.85 = ₱425,000. The car loses ₱75,000 in value.

How do you calculate tax on a purchase?

Total amount = Original price × (100% + Tax rate). Example: Item costs ₱1,000 with 12% VAT. Tax amount = ₱1,000 × 0.12 = ₱120. Total = ₱1,000 + ₱120 = ₱1,120. Or directly: ₱1,000 × 1.12 = ₱1,120.

Compare direct proportion and inverse proportion.

Direct Proportion: When one quantity increases, the other increases proportionally (y = kx). Example: More workers, more output. Inverse Proportion: When one quantity increases, the other decreases proportionally (xy = k). Example: More speed, less time for same distance.

A recipe calls for flour and sugar in ratio 4:1. If you use 200g flour, how much sugar is needed?

Set up proportion: 4:1 = 200:x. Cross multiply: 4x = 1 × 200 = 200. Solve: x = 200/4 = 50g. Therefore, 50g of sugar is needed for 200g of flour.

If 5 machines can produce 100 items in 2 hours, how many items can 8 machines produce in 3 hours?

Step 1: Find rate per machine per hour = 100 ÷ (5 × 2) = 10 items/machine/hour. Step 2: Calculate for 8 machines in 3 hours = 8 × 3 × 10 = 240 items. Or use proportion: (5×2):100 = (8×3):x, so x = 240.

What is the difference between markup and margin?

Markup: Percentage added to cost price. Formula: (Selling Price - Cost Price) / Cost Price × 100%. Margin: Percentage of selling price that is profit. Formula: (Selling Price - Cost Price) / Selling Price × 100%. Same profit amount, different base for calculation.

In a mixture of 60L, juice and water are in ratio 2:3. How much water should be added to make ratio 1:2?

Current: Juice = 24L, Water = 36L (from 2:3 ratio). Target ratio 1:2 means water = 2 × juice = 2 × 24 = 48L. Additional water needed = 48 - 36 = 12L.

Express the ratio 1.5:2.5:3.5 in simplest form.

Method: Multiply all terms by 10 to eliminate decimals: 15:25:35. Find GCD of 15, 25, 35 = 5. Divide by GCD: 15÷5:25÷5:35÷5 = 3:5:7. Therefore, simplest form is 3:5:7.

A student scored 85% on a test with 40 questions. How many questions were answered correctly?

Questions answered correctly = 85% × 40 = 0.85 × 40 = 34 questions. Verification: 34 out of 40 = 34/40 = 0.85 = 85% ✓. The student answered 34 questions correctly and got 6 wrong.