Civil Service Exam (Subprofessional) Numerical Ability — Word Problems — Speed/Distance/Age, Discount & InterestExam Answer Templates

Marks

2

Topic

Discount

Difficulty

easy

Template Id

T1

Examiner Tip

Always show the discount amount calculation separately before finding selling price

Model Answer

Given: Marked Price = ₱2,500, Discount = 15% Discount Amount = 15% of ₱2,500 = 0.15 × 2,500 = ₱375 Selling Price = Marked Price - Discount Amount = ₱2,500 - ₱375 = ₱2,125

Question Type

short_answer

Answer Structure

• Line 1: Write given values and identify what to find [0.5 marks]
• Line 2: Calculate discount amount using percentage [1 mark]
• Line 3: Calculate selling price and state final answer [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Not showing discount calculation step
• Incorrect percentage calculation
• Missing peso sign in answer

Key Phrases To Include

• Given
• Discount Amount
• Selling Price
• ₱

Marks

2

Topic

Simple Interest

Difficulty

easy

Template Id

T2

Examiner Tip

Always write the formula first, then substitute - this shows understanding

Model Answer

Given: Principal (P) = ₱8,000, Rate (R) = 6% per annum, Time (T) = 3 years Using Simple Interest formula: I = PRT/100 I = (8,000 × 6 × 3)/100 = 144,000/100 = ₱1,440

Question Type

short_answer

Answer Structure

• Line 1: Write given values clearly [0.5 marks]
• Line 2: State the simple interest formula [0.5 marks]
• Line 3: Substitute values and calculate [1 mark]

Scoring Breakdown

Common Mark Deductions

• Using wrong formula
• Calculation errors
• Not converting percentage properly

Key Phrases To Include

• Simple Interest formula
• I = PRT/100
• ₱

Marks

1

Topic

Speed, Distance, Time

Difficulty

easy

Template Id

T3

Examiner Tip

For 1-mark questions, write formula and answer in one clean line

Model Answer

Speed = Distance/Time = 240 km ÷ 4 hours = 60 km/h

Question Type

very_short_answer

Answer Structure

• Single line: Apply speed formula and calculate [1 mark]

Scoring Breakdown

Common Mark Deductions

• Missing units
• Wrong formula
• Calculation error

Key Phrases To Include

• Speed =
• Distance/Time
• km/h

Marks

3

Topic

Age Problems

Difficulty

medium

Template Id

T4

Examiner Tip

Always verify your answer by checking if it satisfies the original condition

Model Answer

Let son's present age = x years Then Ram's present age = 3x years Given: Sum of their ages = 48 years So, x + 3x = 48 4x = 48 x = 12 Therefore, Son's age = 12 years, Ram's age = 3 × 12 = 36 years

Question Type

short_answer

Answer Structure

• Line 1: Define variable for unknown age [0.5 marks]
• Line 2-3: Set up equation based on given condition [1 mark]
• Line 4-5: Solve the equation [1 mark]
• Line 6: State both ages clearly [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Not defining variables clearly
• Setting up wrong equation
• Not stating both final ages

Key Phrases To Include

• Let
• present age
• years
• Therefore

Marks

3

Topic

Speed, Distance, Time

Difficulty

medium

Template Id

T5

Examiner Tip

Remember: average speed is NOT the average of individual speeds - use total distance/total time

Model Answer

Given: Distance each way = 300 km, Time for first journey = 5 hours, Time for return journey = 6 hours Total distance covered = 300 + 300 = 600 km Total time taken = 5 + 6 = 11 hours Average speed = Total distance/Total time = 600/11 = 54.55 km/h (approximately)

Question Type

short_answer

Answer Structure

• Line 1: Write all given information [0.5 marks]
• Line 2: Calculate total distance [0.5 marks]
• Line 3: Calculate total time [0.5 marks]
• Line 4: Apply average speed formula and calculate [1.5 marks]

Scoring Breakdown

Common Mark Deductions

• Adding speeds instead of using distance/time
• Not considering return journey
• Incorrect formula usage

Key Phrases To Include

• Average speed
• Total distance
• Total time
• km/h

Marks

3

Topic

Compound Interest

Difficulty

medium

Template Id

T6

Examiner Tip

Show the exponential calculation step-by-step to avoid errors

Model Answer

Given: Principal (P) = ₱5,000, Rate (R) = 8% per annum, Time (T) = 2 years Using compound interest formula: A = P(1 + R/100)^T A = 5,000(1 + 8/100)² = 5,000(1.08)² = 5,000 × 1.1664 = ₱5,832 Compound Interest = A - P = ₱5,832 - ₱5,000 = ₱832

Question Type

short_answer

Answer Structure

• Line 1: Write given values [0.5 marks]
• Line 2: State compound interest formula [0.5 marks]
• Line 3: Calculate amount [1.5 marks]
• Line 4: Find compound interest by subtracting principal [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Using simple interest formula
• Calculation errors in exponents
• Not subtracting principal from amount

Key Phrases To Include

• Compound interest formula
• A = P(1 + R/100)^T
• Amount
• Compound Interest

Marks

5

Topic

Discount and Profit

Difficulty

hard

Template Id

T7

Examiner Tip

Break complex word problems into clear steps and verify your final answer

Model Answer

Given: Selling Price = ₱1,800, Discount = 10%, Required Profit = 20% Step 1: Find the marked price for current scenario Selling Price = Marked Price - Discount ₱1,800 = MP - 10% of MP = MP - 0.1MP = 0.9MP Marked Price = ₱1,800 ÷ 0.9 = ₱2,000 Step 2: Find cost price from current selling price If no profit/loss: SP = CP + 0 (assuming current SP gives some profit) Actually, let's work backwards: If SP = ₱1,800 with 10% discount, then MP = ₱2,000 Let's assume this ₱1,800 gives some profit. We need to find what MP should be for 20% profit. Step 3: Find cost price For 20% profit: SP should be 1.2 times CP So if we want 20% profit, and SP after 10% discount should achieve this: Let required MP = x SP after discount = 0.9x For 20% profit: 0.9x = 1.2 × CP We need more information about current profit to solve this completely. Alternative approach: If ₱1,800 is the desired SP for 20% profit: CP = ₱1,800 ÷ 1.2 = ₱1,500 For 10% discount to give SP of ₱1,800: Required MP = ₱1,800 ÷ 0.9 = ₱2,000

Question Type

long_answer

Answer Structure

• Step 1: Identify what is given and what needs to be found [1 mark]
• Step 2: Find the relationship between SP, discount, and MP [1 mark]
• Step 3: Calculate cost price using profit percentage [1 mark]
• Step 4: Calculate required marked price [1 mark]
• Step 5: Verify the answer [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not showing step-by-step approach
• Confusing profit and discount calculations
• Not verifying final answer

Key Phrases To Include

• Given
• Step
• Marked Price
• Cost Price
• Profit
• Discount
• Therefore

Marks

3

Topic

Age Problems

Difficulty

medium

Template Id

T8

Examiner Tip

Verify your answer by substituting back: Father will be 56, son will be 28, and 56 = 2 × 28 ✓

Model Answer

Given: Father's present age = 42 years, Son's present age = 14 years Let after x years, father will be twice as old as his son Father's age after x years = 42 + x Son's age after x years = 14 + x According to condition: 42 + x = 2(14 + x) 42 + x = 28 + 2x 42 - 28 = 2x - x 14 = x Therefore, after 14 years, the father will be twice as old as his son.

Question Type

short_answer

Answer Structure

• Line 1: Write given information [0.5 marks]
• Line 2-3: Express ages after x years [0.5 marks]
• Line 4: Set up equation based on condition [1 mark]
• Line 5-7: Solve the equation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Wrong equation setup
• Algebraic errors
• Not clearly stating the final answer

Key Phrases To Include

• Let
• after x years
• According to condition
• Therefore

Marks

2

Topic

Simple Interest

Difficulty

medium

Template Id

T9

Examiner Tip

Remember that Amount = Principal + Interest, so derive the combined formula

Model Answer

Given: Amount (A) = ₱8,800, Time (T) = 3 years, Rate (R) = 10% per annum Using A = P + I and I = PRT/100 A = P + PRT/100 = P(1 + RT/100) ₱8,800 = P(1 + 10×3/100) = P(1 + 0.3) = 1.3P P = ₱8,800 ÷ 1.3 = ₱6,769.23 (approximately)

Question Type

short_answer

Answer Structure

• Line 1: Write given values [0.5 marks]
• Line 2-3: Use amount formula with simple interest [1 mark]
• Line 4: Calculate principal [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Using wrong formula
• Not combining amount and interest formulas properly

Key Phrases To Include

• Amount
• Principal
• Simple interest
• A = P + I

Marks

2

Topic

Speed, Distance, Time

Difficulty

easy

Template Id

T10

Examiner Tip

Find speed first, then use it to calculate the required time

Model Answer

Given: Distance₁ = 60 km, Time₁ = 4 hours, Distance₂ = 105 km Speed = Distance₁/Time₁ = 60/4 = 15 km/h Time₂ = Distance₂/Speed = 105/15 = 7 hours

Question Type

short_answer

Answer Structure

• Line 1: Write given information [0.5 marks]
• Line 2: Calculate speed from first journey [0.75 marks]
• Line 3: Calculate time for second journey [0.75 marks]

Scoring Breakdown

Common Mark Deductions

• Not calculating speed first
• Direct proportion errors

Key Phrases To Include

• Speed =
• Distance/Time
• km/h
• hours

Marks

1

Topic

Discount

Difficulty

easy

Template Id

T11

Examiner Tip

Use the formula: Discount% = (Discount Amount/Marked Price) × 100

Model Answer

Discount% = [(MP - SP)/MP] × 100 = [(5,000 - 4,250)/5,000] × 100 = (750/5,000) × 100 = 15%

Question Type

very_short_answer

Answer Structure

• Single line: Apply discount percentage formula and calculate [1 mark]

Scoring Breakdown

Common Mark Deductions

• Wrong formula
• Calculation errors
• Missing percentage sign

Key Phrases To Include

• Discount%
• MP - SP
• %

Marks

3

Topic

Simple Interest

Difficulty

medium

Template Id

T12

Examiner Tip

When money 'doubles itself', the interest earned equals the principal amount

Model Answer

Given: Amount = 2 × Principal (money doubles), Time = 8 years Let Principal = P, then Amount = 2P Simple Interest = Amount - Principal = 2P - P = P Using I = PRT/100 P = P × R × 8/100 Canceling P from both sides: 1 = R × 8/100 R = 100/8 = 12.5% Therefore, the rate of interest is 12.5% per annum.

Question Type

short_answer

Answer Structure

• Line 1: Interpret 'doubles itself' condition [0.5 marks]
• Line 2-3: Calculate simple interest [0.5 marks]
• Line 4-6: Apply simple interest formula and solve for rate [1.5 marks]
• Line 7: State final answer [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Not understanding doubling condition
• Algebraic manipulation errors

Key Phrases To Include

• doubles itself
• Amount = 2P
• Simple Interest
• per annum

Marks

3

Topic

Speed, Distance, Time

Difficulty

medium

Template Id

T13

Examiner Tip

For opposite directions, add the speeds; for same direction, subtract the speeds

Model Answer

Given: Speed of Car A = 60 km/h, Speed of Car B = 80 km/h, Final distance apart = 420 km Since cars travel in opposite directions, relative speed = 60 + 80 = 140 km/h Distance covered by both cars together = 420 km Time = Distance/Relative Speed = 420/140 = 3 hours Therefore, they will be 420 km apart after 3 hours.

Question Type

short_answer

Answer Structure

• Line 1: Write given information [0.5 marks]
• Line 2: Calculate relative speed for opposite directions [1 mark]
• Line 3-4: Apply time formula and calculate [1 mark]
• Line 5: State final answer [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Not adding speeds for opposite directions
• Using individual speeds instead of relative speed

Key Phrases To Include

• opposite directions
• relative speed
• Time =
• hours

Marks

5

Topic

Profit and Loss with Discount

Difficulty

hard

Template Id

T14

Examiner Tip

Handle profit and loss parts separately, then combine for overall result

Model Answer

Given: Total Cost Price = ₱8,000, 60% sold at 25% profit, 40% sold at 15% loss Step 1: Calculate cost prices of both parts CP of 60% goods = 60% of ₱8,000 = 0.6 × 8,000 = ₱4,800 CP of 40% goods = 40% of ₱8,000 = 0.4 × 8,000 = ₱3,200 Step 2: Calculate selling prices SP of first part = CP + 25% profit = ₱4,800 + 0.25 × 4,800 = ₱4,800 + ₱1,200 = ₱6,000 SP of second part = CP - 15% loss = ₱3,200 - 0.15 × 3,200 = ₱3,200 - ₱480 = ₱2,720 Step 3: Calculate total selling price and profit/loss Total SP = ₱6,000 + ₱2,720 = ₱8,720 Total CP = ₱8,000 Profit = SP - CP = ₱8,720 - ₱8,000 = ₱720 Step 4: Calculate profit percentage Profit % = (Profit/CP) × 100 = (720/8,000) × 100 = 9% Therefore, the shopkeeper has an overall profit of 9%.

Question Type

long_answer

Answer Structure

• Step 1: Divide total cost into two parts [1 mark]
• Step 2: Calculate selling prices for both parts [2 marks]
• Step 3: Find total selling price and profit [1 mark]
• Step 4: Calculate overall profit percentage [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not calculating parts separately
• Mixing up profit and loss calculations
• Incorrect percentage calculations

Key Phrases To Include

• Cost Price
• Selling Price
• Profit
• Loss
• Overall
• Therefore

Marks

2

Topic

Simple Interest

Difficulty

easy

Template Id

T15

Examiner Tip

Always find the interest amount first, then use the formula to find the unknown

Model Answer

Given: Principal = ₱2,000, Amount = ₱2,420, Time = 3 years Simple Interest = Amount - Principal = ₱2,420 - ₱2,000 = ₱420 Using I = PRT/100: 420 = (2,000 × R × 3)/100 420 = 6,000R/100 = 60R R = 420/60 = 7% Therefore, the rate is 7% per annum.

Question Type

short_answer

Answer Structure

• Line 1: Write given values and find simple interest [0.5 marks]
• Line 2-4: Apply simple interest formula and solve for rate [1.5 marks]

Scoring Breakdown

Common Mark Deductions

• Not finding interest first
• Algebraic errors in solving for R

Key Phrases To Include

• Simple Interest
• I = PRT/100
• per annum
• %