Quantitative Aptitude PYQs

Shortcut Trick

Speed ratio = 5 : 6 → Time ratio = 6 : 5 (since distance is constant).

Difference in time ratio parts = 6 − 5 = 1 unit.

Given 1 unit = 25 minutes.

Usual time = 5 units = 5 × 25 = 125 minutes.

∴ The correct answer is 125 min.

Alternate Method

Given: New speed = 5/6 of normal speed, Time delay = 25 minutes.

Formula Used: Distance = Speed × Time. If distance is constant, Speed ∝ 1/Time.

⇒ Let normal speed be S and usual time be T.

⇒ Normal Distance = S × T

⇒ New Distance = (5/6)S × (T + 25)

⇒ S × T = (5/6)S × (T + 25)

⇒ T = 5/6(T + 25)

⇒ 6T = 5T + 125

⇒ T = 125 minutes.

∴ The correct answer is 125 min.

Additional Information

Inverse Proportion of Speed and Time

When the distance is constant, the ratio of speeds is inversely proportional to the ratio of time taken: S₁/S₂ = T₂/T₁.

Late/Early Concept Shortcut

Usual Time = (Late Time × Numerator) ÷ (Difference between Numerator and Denominator) = (25 × 5) ÷ (6 − 5) = 125 min.

Average Speed

If a person covers two equal distances at speeds x and y, the average speed is 2xy/(x+y).

Shortcut Trick

संख्या 6336 के लिए 11 की विभाज्यता की जाँच करें।

विषम स्थानों के अंकों का योग = 6 + 3 = 9

सम स्थानों के अंकों का योग = 3 + 6 = 9

अंतर = 9 − 9 = 0

चूँकि अंतर 0 है, इसलिए संख्या पहले से ही 11 से विभाज्य है।

∴ The correct answer is 0.

Alternate Method

दिया गया है: संख्या = 6336

प्रयुक्त सूत्र: यदि (विषम स्थानों के अंकों का योग) − (सम स्थानों के अंकों का योग) = 0 या 11 का गुणज हो, तो संख्या 11 से विभाज्य होती है।

⇒ विषम स्थानों का योग (1^st + 3^rd) = 6 + 3 = 9

⇒ सम स्थानों का योग (2^nd + 4^th) = 3 + 6 = 9

⇒ अंतर = 9 − 9 = 0

⇒ चूँकि अंतर 0 है, इसलिए संख्या 11 से पूर्णतः विभाज्य है।

⇒ अतः, संख्या में 0 जोड़ने या घटाने पर वह 11 से विभाज्य बनी रहेगी।

∴ The correct answer is 0.

Additional Information

9 की विभाज्यता का नियम

यदि किसी संख्या के सभी अंकों का योग 9 से विभाज्य है, तो वह संख्या 9 से विभाज्य होती है (यहाँ 6+3+3+6 = 18, जो 9 से विभाज्य है)।

11 की विभाज्यता का नियम

एकांतर अंकों के योग का अंतर 0 या 11 का गुणज होना चाहिए।

99 की विभाज्यता

यदि कोई संख्या 9 और 11 दोनों से विभाज्य है, तो वह उनके गुणनफल 99 से भी विभाज्य होगी।

Shortcut Trick

Rate = 16% = 4/25 ⇒ Ratio of Principal to Amount for 1 year = 25 : 29.

For 2 years, the ratio becomes 25² : 29² = 625 : 841.

Given 625 units = ₹7500 ⇒ 1 unit = ₹12.

Total Amount = 841 units × 12 = ₹10,092.

∴ The correct answer is ₹10,092.

Alternate Method

Given:

Principal (P) = ₹7,500

Rate of Interest (R) = 16% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 7500 × (1 + 16/100)²

⇒ A = 7500 × (116/100) × (116/100)

⇒ A = 7500 × (29/25) × (29/25)

⇒ A = (7500 ÷ 625) × (29 × 29)

⇒ A = 12 × 841

⇒ A = 10092

∴ The correct answer is ₹10,092.

Additional Information

Effective Rate of Interest

For 2 years at R%, the effective compound interest rate is R + R + (R×R)/100. For 16%, it is 16 + 16 + 2.56 = 34.56%.

CI vs SI Difference

The difference between Compound Interest and Simple Interest for 2 years is given by P(R/100)².

Successive Percentage Change

Compound interest is essentially a successive percentage increase on the initial principal value over the given time periods.

Shortcut Trick

Use the direct empirical relationship formula: Mean = (3 × Median − Mode) ÷ 2.

Substitute the given values: (3 × 31 − 72.8) ÷ 2.

⇒ (93 − 72.8) ÷ 2 = 20.2 ÷ 2 = 10.1.

∴ The correct answer is 10.1.

Alternate Method

Given:

Mode of the data = 72.8

Median of the data = 31

Formula Used:

The Empirical Relationship between measures of central tendency is:

Mode = 3 × Median − 2 × Mean

Calculations:

⇒ 72.8 = 3 × 31 − 2 × Mean

⇒ 72.8 = 93 − 2 × Mean

⇒ 2 × Mean = 93 − 72.8

⇒ 2 × Mean = 20.2

⇒ Mean = 20.2 ÷ 2

⇒ Mean = 10.1

∴ The correct answer is 10.1.

Additional Information

Empirical Formula for Skewed Distributions

For moderately asymmetrical distributions, the relationship is Mean − Mode = 3(Mean − Median), which simplifies to Mode = 3 Median − 2 Mean.

Types of Skewness

In a Symmetric Distribution, Mean = Median = Mode. In a Positively Skewed distribution, Mean > Median > Mode. In a Negatively Skewed distribution, Mode > Median > Mean.

Measures of Central Tendency

Mean is the average, Median is the middle value, and Mode is the most frequent value in a data set.

Shortcut Trick

Total amount to be divided = ₹10,896.

Total deductions = 91 + 4 + 57 = ₹152.

Remaining amount = 10,896 − 152 = ₹10,744.

Divide ₹10,744 in ratio 3 : 8 : 6 (Total units = 17).

Difference between B and C shares (after deduction) = 8 − 6 = 2 units.

Difference between original shares = (Value of 2 units) + (Difference in deductions) = (10,744 ÷ 17 × 2) + (4 − 57) = 1,264 − 53 = ₹1,211.

∴ The correct answer is ₹1,211.

Alternate Method

Given: Total sum = ₹10,896. Deductions from A, B, C are ₹91, ₹4, ₹57. Ratio after deduction = 3 : 8 : 6.

Calculations:

⇒ Sum of ratio parts = 3 + 8 + 6 = 17 units

⇒ Total deduction = 91 + 4 + 57 = ₹152

⇒ Remaining amount = 10,896 − 152 = ₹10,744

⇒ Value of 1 unit = 10,744 ÷ 17 = ₹632

⇒ B's share after deduction = 8 × 632 = ₹5,056

⇒ B's original share = 5,056 + 4 = ₹5,060

⇒ C's share after deduction = 6 × 632 = ₹3,792

⇒ C's original share = 3,792 + 57 = ₹3,849

⇒ Required Difference = 5,060 − 3,849 = ₹1,211

∴ The correct answer is ₹1,211.

Additional Information

Ratio and Proportion

If a sum S is divided in ratio a:b:c, the shares are [a/(a+b+c)]×S, [b/(a+b+c)]×S, and [c/(a+b+c)]×S respectively.

Deduction problems

Always subtract the specific deductions from the total sum before applying the ratio units to find the individual shares.

Shortcut Trick

Product of fractions method: 1/10 × 2/5 × 1/3 × Number = 512

Number = 512 × 10 × 5/2 × 3

Number = 512 × 5 × 5 × 3 = 512 × 75

Number = 38400

∴ The correct answer is 38400.

Alternate Method

Given:

10% of 40% of 1/3 of a number = 512

Let the number be x.

⇒ (10/100) × (40/100) × (1/3) × x = 512

⇒ (1/10) × (2/5) × (1/3) × x = 512

⇒ (2/150) × x = 512

⇒ x = (512 × 150) ÷ 2

⇒ x = 256 × 150

⇒ x = 38400

∴ The correct answer is 38400.

Additional Information

Percentage to Fraction Conversion

To simplify calculations, convert percentages to fractions: 10% = 1/10, 20% = 1/5, 25% = 1/4, 40% = 2/5, and 50% = 1/2.

Successive Percentage Application

When multiple percentages are applied to a single value, the result is the product of the individual multiplying factors times the original value.

Base Value Concept

Always identify the base value (the number x) to which percentages and fractions are being applied to avoid calculation errors.

Shortcut Trick

The given expression follows the algebraic identity (a³ + b³) ÷ (a² − ab + b²) = (a + b).

Here, let a = 0.45 and b = 0.2.

Value = a + b = 0.45 + 0.2 = 0.65.

Converting decimal to fraction: 0.65 = 65/100 = 13/20.

∴ The correct answer is 13/20.

Alternate Method

Given:

Expression: ((0.45)³ + (0.2)³) ÷ ((0.45)² − 0.45 × 0.2 + (0.2)²)

Formula Used:

Sum of two cubes: x³ + y³ = (x + y)(x² − xy + y²)

Calculations:

⇒ Let x = 0.45 and y = 0.2.

⇒ Numerator = (0.45 + 0.2) × ((0.45)² − (0.45 × 0.2) + (0.2)²)

⇒ Expression = [(0.45 + 0.2) × ((0.45)² − 0.45 × 0.2 + (0.2)²)] ÷ [(0.45)² − 0.45 × 0.2 + (0.2)²]

⇒ Cancelling common terms in numerator and denominator: Expression = 0.45 + 0.2

⇒ Expression = 0.65

⇒ 0.65 = 65 ÷ 100

⇒ Simplifying the fraction by dividing by 5: 13/20

∴ The correct answer is 13/20.

Additional Information

Difference of Cubes Identity

The formula for the difference of two cubes is a³ − b³ = (a − b)(a² + ab + b²).

Decimal to Fraction Conversion

To convert a decimal to a fraction, place the number over its place value (e.g., 0.65 = 65/100) and simplify to the lowest terms.

BODMAS Rule

Always follow the order of operations: Brackets, Orders (powers/roots), Division/Multiplication, and Addition/Subtraction.

Shortcut Trick

Apply the Empirical Formula directly: Mode = 3 × Median − 2 × Mean.

Rearranging for Mean: 2 × Mean = 3 × Median − Mode.

Calculation: 2 × Mean = 3 × 58 − 70.2 = 174 − 70.2 = 103.8.

Final Step: Mean = 103.8 ÷ 2 = 51.9.

∴ The correct answer is 51.9.

Alternate Method

Given:

Mode of the data = 70.2

Median of the data = 58

Formula Used:

The relationship between Mean, Median, and Mode is given by the empirical formula:

Mode = 3 × Median − 2 × Mean

Calculations:

⇒ 70.2 = 3 × 58 − 2 × Mean

⇒ 70.2 = 174 − 2 × Mean

⇒ 2 × Mean = 174 − 70.2

⇒ 2 × Mean = 103.8

⇒ Mean = 103.8 ÷ 2

⇒ Mean = 51.9

∴ The correct answer is 51.9.

Additional Information

Symmetrical Distribution

In a perfectly symmetrical distribution, the values of Mean, Median, and Mode are identical (Mean = Median = Mode).

Skewed Distribution

For a Positively Skewed distribution, Mean > Median > Mode. For a Negatively Skewed distribution, Mode > Median > Mean.

Karl Pearson's Coefficient

The empirical formula is used for moderately asymmetrical distributions to estimate a missing measure of central tendency.

Shortcut Trick

Simplify ratio: 4/10 : 20/18 : 20/11 → 2/5 : 10/9 : 20/11.

Multiply by LCM(5, 9, 11) = 495: (2/5 × 495) : (10/9 × 495) : (20/11 × 495) = 198 : 550 : 900.

Difference (900 − 198) units = 702 units → 39.

1 unit = 39 ÷ 702 = 1/18.

Largest number = 900 × (1/18) = 50.

∴ The correct answer is 50.

Alternate Method

Given: Ratio of three numbers = 4/10 : 20/18 : 20/11

⇒ Simplified Ratio = 2/5 : 10/9 : 20/11

⇒ Multiplying by LCM of denominators (495):

⇒ First Number = 2/5 × 495 = 198

⇒ Second Number = 10/9 × 495 = 550

⇒ Third Number = 20/11 × 495 = 900

⇒ Difference between Greatest and Smallest = 900 − 198 = 702 units

⇒ 702 units = 39

⇒ 1 unit = 39/702 = 1/18

⇒ Largest number = 900 units = 900 × (1/18) = 50

∴ The correct answer is 50.

Additional Information

Ratio Simplification

To convert a fractional ratio a/b : c/d into integers, multiply each term by the Least Common Multiple (LCM) of the denominators b and d.

Proportional Parts

If a total quantity is divided in ratio a:b:c, the value of the largest part is [Maximum(a,b,c) / (a+b+c)] × Total.

Comparison of Fractions

For two fractions a/b and c/d, cross multiply (a×d and b×c) to quickly determine which is larger without finding common denominators.

Shortcut Trick

Net percentage change formula = a + b + (ab/100)

Here, increase in height (a) = +20% and decrease in base (b) = −15%

Net change = 20 − 15 + [(20 × −15) ÷ 100]

Net change = 5 − 3 = +2%

Positive sign indicates an increase.

∴ The correct answer is Increase by 2%.

Alternate Method

Given:

Initial Height (H₁) = 100, New Height (H₂) = 120

Initial Base (B₁) = 100, New Base (B₂) = 85

Calculations:

⇒ Initial Area (A₁) = 1/2 × B₁ × H₁ = 1/2 × 100 × 100 = 5000

⇒ New Area (A₂) = 1/2 × B₂ × H₂ = 1/2 × 85 × 120 = 85 × 60 = 5100

⇒ Area Change = 5100 − 5000 = 100

⇒ Percentage Change = (Change ÷ Original Area) × 100

⇒ Percentage Change = (100 ÷ 5000) × 100 = 2%

∴ The correct answer is Increase by 2%.

Additional Information

Area of Triangle

Basic formula: Area = 1/2 × base × height. Changes in both parameters lead to a cumulative effect on the area.

Successive Percentage Change

When a value depends on the product of two variables, the net % change is given by x + y + xy/100, where x and y are the percentage changes in those variables.

Base Change Rule

If one dimension increases by x% and the other decreases by y%, the net effect is an increase if (x − y − xy/100) is positive.

Shortcut Trick

Effective Rate of Interest for 2 years at 10% compounded annually = 10 + 10 + (10 × 10)/100 = 21%.

Total Amount = 100% (Principal) + 21% (Interest) = 121% of Principal.

Amount = 8,300 × (121/100) = 83 × 121.

Amount = ₹10,043.

∴ The correct answer is ₹10,043.

Alternate Method

Given:

Principal (P) = ₹8,300

Rate (R) = 10% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 8300 × (1 + 10/100)²

⇒ A = 8300 × (110/100) × (110/100)

⇒ A = 8300 × 1.1 × 1.1

⇒ A = 8300 × 1.21

⇒ A = 83 × 121

⇒ A = ₹10,043

∴ The correct answer is ₹10,043.

Additional Information

Effective Rate for Compound Interest

For a rate R% for 2 years, the effective interest rate is R + R + (R × R)/100.

Difference between CI and SI

For 2 years, the difference between Compound Interest and Simple Interest is P × (R/100)².

Compound Interest Formula

Interest (CI) = Amount − Principal = P[(1 + R/100)ⁿ − 1].

Shortcut Trick

Savings = 20% ⇒ Expenditure = 100% − 20% = 80%

Given, 80% → ₹320

1% → ₹4

Total Income (100%) → 100 × 4 = ₹400

∴ The correct answer is ₹400.

Alternate Method

Given:

Savings percentage = 20%

Expenditure = ₹320

Formula: Income = Expenditure + Savings

⇒ Let Total Income be x

⇒ Savings = 20% of x = 0.20x

⇒ Expenditure = Income − Savings

⇒ 320 = x − 0.20x

⇒ 320 = 0.80x

⇒ x = 320 ÷ 0.80

⇒ x = 400

∴ The correct answer is ₹400.

Additional Information

Income Components

Income is always the sum of Expenditure and Savings. If any two are known, the third can be calculated.

Percentage Base Change

When Savings % is given, the Expenditure % is always (100 − Savings %). Here, 100% represents the Total Income.

Ratio Method

20% Savings = 1/5 of Income. This means if Income is 5 units, Savings is 1 unit and Expenditure is 4 units.

Shortcut Trick

49 = 7²

(49)ⁿ = (7²)ⁿ = 7²ⁿ

Expression = (7²ⁿ × 7) ÷ 7²ⁿ

Cancel ⇒ = 7

∴ Answer = 7¹

Alternate Method

Given:

((49)ⁿ × 7) ÷ (7²ⁿ)

Concept Used:

Laws of exponents

Calculation:

⇒ 49 = 7²

⇒ (49)ⁿ = (7²)ⁿ = 7²ⁿ

⇒ Substitute ⇒ (7²ⁿ × 7) ÷ 7²ⁿ

⇒ = 7²ⁿ⁺¹ ÷ 7²ⁿ

⇒ = 7^{(2n+1 − 2n)}

⇒ = 7¹

∴ The correct answer is 7¹.

Additional Information

Exponent Rule

a^m × aⁿ = a^m+n

Division Rule

a^m ÷ aⁿ = a^m−n

Power of Power

(a^m)ⁿ = a^mn

Shortcut Tip

Always convert numbers to same base first

Shortcut Trick

Let TV cost = 100, then Washing Machine (WM) cost = 75.

Initial total cost of 6 WM and 3 TV = (6 × 75) + (3 × 100) = 450 + 300 = 750.

New WM cost = 75 × 1.88 = 141; New TV cost = 100 × 0.43 = 43.

New total cost = (6 × 141) + (3 × 43) = 846 + 129 = 975.

Percentage change = [(975 − 750) ÷ 750] × 100 = (225 ÷ 750) × 100 = 30%.

∴ The correct answer is Increase by 30%.

Alternate Method

Given: Cost of WM is 25% less than TV. WM cost ↑ 88%, TV cost ↓ 57%. Formulas: New Value = Old Value × (100 ± Change%) ÷ 100 | %Change = (New − Old) ÷ Old × 100.

⇒ Let TV cost = 100x and WM cost = 75x. ⇒ Initial cost of 6 WM and 3 TV = 6(75x) + 3(100x) = 450x + 300x = 750x. ⇒ Final cost = 6(75x × 1.88) + 3(100x × 0.43) = 6(141x) + 3(43x) = 846x + 129x = 975x. ⇒ Change = 975x − 750x = 225x. ⇒ %Change = (225x ÷ 750x) × 100 = 30%.

∴ The correct answer is Increase by 30%.

Additional Information

Percentage Change in Weighted Average

When multiple items with different initial costs and quantities undergo price changes, the total percentage change is the weighted average of individual percentage changes based on their initial total value contributions.

Cost Price Scaling

Using a base value of 100 for the reference item (TV) simplifies calculations involving percentage increases and decreases.

Shortcut Trick

Ratio of investments of Laxmi, Dhruv, and Gauri = 13 : 6 : 12.

Sum of ratio parts = 13 + 6 + 12 = 31 units.

Total profit = ₹37,200, which represents 75% of the total investment.

Total Investment = (37,200 ÷ 75) × 100 = ₹49,600.

Dhruv investment = (Investment ratio of Dhruv ÷ Total ratio sum) × Total Investment.

Dhruv investment = (6 ÷ 31) × 49,600 = 6 × 1,600 = ₹9,600.

∴ The correct answer is ₹9,600.

Alternate Method

Given → Investment ratio = 13 : 6 : 12 | Profit = ₹37,200 | Profit = 75% of Investment. Formulas: Total Investment = (Profit ÷ Profit%) × 100 | Individual Investment = (Individual Ratio ÷ Total Ratio) × Total Investment.

⇒ Let the investments be 13x, 6x, and 12x. Total investment = 31x. ⇒ According to the question, 75% of 31x = 37,200. ⇒ (75 ÷ 100) × 31x = 37,200. ⇒ (3 ÷ 4) × 31x = 37,200. ⇒ 31x = (37,200 × 4) ÷ 3 = 12,400 × 4 = 49,600. ⇒ x = 49,600 ÷ 31 = 1,600. ⇒ Dhruv investment = 6x = 6 × 1,600 = ₹9,600.

∴ The correct answer is ₹9,600.

Additional Information

Partnership Basics

In a partnership, if the time period of investment is the same for all partners, the profit is shared in the ratio of their investments.

Profit and Investment Relationship

Profit = Investment × Time. If Time is constant, Profit ∝ Investment. Profit percentage is calculated on the Total Capital invested.

Shortcut Trick

Total Quantity = 52 + 47 = 99 books

Total Expenditure = 1120 + 905 = ₹2025

Average Price = 2025 ÷ 99 = 225 ÷ 11

225 ÷ 11 ≈ 20.45

∴ The correct answer is ₹20.45.

Alternate Method

Given:

Books from Shop 1 = 52 | Price = ₹1120

Books from Shop 2 = 47 | Price = ₹905

Formula Used:

Average = (Total Sum of Observations) ÷ (Total Number of Observations)

Calculations:

⇒ Total number of books = 52 + 47 = 99

⇒ Total amount spent = ₹1120 + ₹905 = ₹2025

⇒ Average price per book = 2025 ÷ 99

⇒ Average price = (2025 ÷ 9) ÷ (99 ÷ 9) = 225 ÷ 11

⇒ Average price = 20.4545...

⇒ Rounding off to two decimal places, we get 20.45

∴ The correct answer is ₹20.45.

Additional Information

Weighted Average Concept

When two groups with different quantities (n₁, n₂) and different averages (A₁, A₂) are combined, the total average is calculated as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Rounding Off Rules

To round to two decimal places, check the third decimal digit. If it is 5 or more, add 1 to the second decimal digit. If it is less than 5, keep the second decimal digit as it is.

Simplified Division

Always check for common factors in the numerator and denominator to simplify calculations. Here, 2025 and 99 are both divisible by 9 (Sum of digits 2+0+2+5=9 and 9+9=18).

Shortcut Trick

The unit digit of the given edge is 1.

The volume of a cube is calculated as (Edge)³.

The unit digit of the result must be 1³ = 1.

Only option (3) ends with the digit 1.

∴ The correct answer is 68921 m³.

Alternate Method

Given: Edge (a) of the cube = 41 m

Formula: Volume (V) of a cube = a³

⇒ V = 41 × 41 × 41

⇒ V = 1681 × 41

⇒ V = 68921 m³.

∴ The correct answer is 68921 m³.

Additional Information

Total Surface Area of a Cube

The total area of all six square faces is given by the formula 6a².

Diagonal of a Cube

The length of the longest space diagonal connecting opposite corners is a√3.

Lateral Surface Area

The area of the four vertical side faces of the cube is 4a².

Shortcut Trick

In any quadrilateral, the angle formed by the bisectors of two adjacent angles is equal to half the sum of the other two angles.

∠STR = (∠P + ∠Q) ÷ 2

25.5° = (∠P + ∠Q) ÷ 2 ⇒ ∠P + ∠Q = 51°

Ratio P : Q = 8 : 9 ⇒ Sum = 17 units = 51° ⇒ 1 unit = 3°

Difference = 9 − 8 = 1 unit = 3°.

∴ The correct answer is 3°.

Alternate Method

Given:

∠STR = 25.5°

Ratio ∠P : ∠Q = 8 : 9

Formula Used:

Sum of interior angles of a triangle = 180°

Sum of interior angles of a quadrilateral = 360°

Calculations:

⇒ In ▵STR, ∠TSR + ∠TRS + ∠STR = 180°

⇒ Since ST and RT are angle bisectors, ∠TSR = ∠S ÷ 2 and ∠TRS = ∠R ÷ 2

⇒ (∠S ÷ 2) + (∠R ÷ 2) + 25.5° = 180°

&rArr

Shortcut Trick

Average Speed when time intervals are equal is simply the Arithmetic Mean of the speeds.

Since each interval is exactly 1 hour, Average Speed = (158 + 110) ÷ 2

⇒ 268 ÷ 2 = 134 km/hr

∴ The correct answer is 134 km/hr.

Alternate Method

Given:

Distance in 1^st hour (D₁) = 158 km

Distance in 2^nd hour (D₂) = 110 km

Time taken for each part (t₁, t₂) = 1 hour

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = 158 + 110 = 268 km

⇒ Total Time = 1 + 1 = 2 hours

⇒ Average Speed = 268 ÷ 2

⇒ Average Speed = 134 km/hr

∴ The correct answer is 134 km/hr.

Additional Information

Equal Distance Case

If a car travels equal distances at speeds x and y, then Average Speed = 2xy ÷ (x + y).

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Relative Speed

When two objects move in the same direction, relative speed is (u − v). In opposite directions, it is (u + v).

Shortcut Trick

Net change formula for Mark-up (a) and Discount (b) is [a − b − (ab ÷ 100)].

Here, a = 10% (Mark-up) and b = 80% (Discount).

Net Profit/Loss % = 10 − 80 − (10 × 80 ÷ 100)

⇒ −70 − 8 = −78%

The negative sign indicates a Loss of 78%.

∴ The correct answer is 78%.

Alternate Method

Given: Mark-up% = 10%, Discount% = 80%.

Formulas: MP = CP × (100 + Mark-up%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100 | Loss% = [(CP − SP) ÷ CP] × 100

⇒ Let the Cost Price (CP) be 100.

⇒ Marked Price (MP) = 100 + 10% of 100 = 110.

⇒ Selling Price (SP) = 110 − 80% of 110 = 110 − 88 = 22.

⇒ Loss = CP − SP = 100 − 22 = 78.

⇒ Loss Percentage = (78 ÷ 100) × 100 = 78%.

∴ The correct answer is 78%.

Additional Information

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP × (100 − D)%.

Effective Percentage Change

When a value is increased by x% and then decreased by y%, the net change is [x − y − (xy/100)]%.