Quantitative Aptitude PYQs

Shortcut Trick

Identify numbers between 308 and 320: 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319.

Eliminate even numbers and numbers ending in 5: 309, 311, 313, 317, 319.

Check divisibility: 309 (3+0+9=12, div by 3), 319 (11 × 29).

Remaining prime numbers: 311, 313, 317.

∴ The correct answer is 3.

Alternate Method

Given: Range of numbers from 308 to 320.

Formula Used: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Calculations:

⇒ Numbers in range: {309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319}

⇒ 309: 3 + 0 + 9 = 12 (Divisible by 3) → Composite

⇒ 311: Not divisible by 2, 3, 5, 7, 11, 13, 17 (√311 ≈ 17.6) → Prime

⇒ 313: Not divisible by 2, 3, 5, 7, 11, 13, 17 (√313 ≈ 17.7) → Prime

⇒ 317: Not divisible by 2, 3, 5, 7, 11, 13, 17 (√317 ≈ 17.8) → Prime

⇒ 319: 11 × 29 = 319 → Composite

⇒ Even numbers (310, 312, 314, 316, 318) and 315 are Composite.

⇒ Total prime numbers = 3 (311, 313, 317).

∴ The correct answer is 3.

Additional Information

Prime Number Definition

Numbers with exactly two factors (1 and the number itself). 2 is the only even prime number.

Divisibility Test for 11

Difference between the sum of digits at odd places and even places is 0 or divisible by 11. For 319: (3+9) − 1 = 11.

Checking Primes

To check if N is prime, test divisibility by primes up to √N.

Shortcut Trick

Successive effective Compound Interest rate for 2 years at 20% = 20 + 20 + (20 × 20)/100 = 44%.

Total Amount = 100% (Principal) + 44% (Interest) = 144% of Principal.

Amount = 1.44 × 7800 = ₹11,232.

∴ The correct answer is ₹11,232.

Alternate Method

Given:

Principal (P) = ₹7,800

Rate (R) = 20% per annum

Time (n) = 2 years (compounded annually)

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 7800 × (1 + 20/100)²

⇒ A = 7800 × (1 + 1/5)²

⇒ A = 7800 × (6/5)²

⇒ A = 7800 × (36/25)

⇒ A = 312 × 36

⇒ A = ₹11,232

∴ The correct answer is ₹11,232.

Additional Information

Compound Interest Formula

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

Effective Rate for 2 Years

Equivalent rate for 2 years at R% compound interest is [2R + R²/100]%.

Difference between CI and SI for 2 years

Difference = P(R/100)². For 20% on ₹7,800, Difference = 7800 × (20/100)² = ₹312.

Shortcut Trick

Total work (LCM of 3, 2, 6) = 6 units.

Efficiency of A = 2, B = 3, C = 1.

Total Efficiency = 2 + 3 + 1 = 6 units/day.

Twice the work = 6 × 2 = 12 units.

Time taken = 12 ÷ 6 = 2 days.

∴ The correct answer is 2 days.

Alternate Method

Given:

Time taken by A = 3 days, B = 2 days, C = 6 days.

Formula Used:

Total Work = LCM of individual days; Efficiency = Work ÷ Time; Time = Work ÷ Efficiency

Calculations:

⇒ Combined Efficiency of A + B + C = 2 + 3 + 1 = 6 units/day

⇒ Target Work = 2 × Total Work = 2 × 6 = 12 units

⇒ Time taken together = 12 ÷ 6 = 2 days

∴ The correct answer is 2 days.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete a task. Efficiency = Work ÷ Time.

Pipes & Cisterns

Similar to time and work, but involves negative work (leakage/outlet pipes). Net efficiency = Σ Filling efficiency − Σ Emptying efficiency.

Work & Wages

Wages are generally distributed in the ratio of the efficiency of the workers if they work for the same duration.

Shortcut Trick

Present ratio Rohit : Father = 2 : 5 (difference = 3)

Future ratio (after 4 years) = 12 : 27 = 4 : 9 (difference = 5)

Equalize differences: Present (2:5) × 5 = 10 : 25 | Future (4:9) × 3 = 12 : 27

Ratio increase of 2 units (12 − 10 or 27 − 25) represents 4 years ⇒ 1 unit = 2 years.

Father's present age = 25 × 2 = 50 years. Age 5 years ago = 50 − 5 = 45 years.

∴ The correct answer is 45 years.

Alternate Method

Given: Present ratio = 2 : 5, Ratio after 4 years = 12 : 27.

Formula: Let Rohit's age be 2x and Father's age be 5x.

⇒ (2x + 4) / (5x + 4) = 12 / 27

⇒ (2x + 4) / (5x + 4) = 4 / 9

⇒ 9 × (2x + 4) = 4 × (5x + 4)

⇒ 18x + 36 = 20x + 16

⇒ 2x = 20 ⇒ x = 10

⇒ Father's present age = 5x = 5 × 10 = 50 years.

⇒ Father's age 5 years ago = 50 − 5 = 45 years.

∴ The correct answer is 45 years.

Additional Information

Ratio Difference Equality

When the same number of years is added to two people, the age difference between them remains constant. Adjust the ratios by multiplying to keep the difference parts equal.

Present vs. Past/Future Age

If present age is A, then age 'n' years ago is A − n and age after 'm' years is A + m.

Cross-Multiplication Method

Used for solving ratio changes: (Initial Ratio) → (Change) → (Final Ratio). Helpful in problems involving additions or subtractions from both quantities.

Shortcut Trick

Total amount to be deducted = 32 + 60 + 71 = ₹163.

Remaining sum = 8413 − 163 = ₹8250.

Ratio of shares = 5 : 11 : 14 | Total ratio parts = 5 + 11 + 14 = 30.

Value of 1 unit = 8250 ÷ 30 = ₹275.

Difference between B and C (ratio units) = 14 − 11 = 3 units.

Difference in actual shares = (3 × 275) + (71 − 60) = 825 + 11 = ₹836.

∴ The correct answer is ₹836.

Alternate Method

Given: Total sum = ₹8,413. Deductions: S = ₹32, B = ₹60, C = ₹71. Ratio after deduction = 5 : 11 : 14.

Formula Used: Share = (Ratio part × Total remaining sum / Sum of ratios) + Deducted amount.

⇒ Total Deductions = 32 + 60 + 71 = ₹163

⇒ Remaining Sum = 8413 − 163 = ₹8250

⇒ Let the parts be 5x, 11x, and 14x

⇒ 5x + 11x + 14x = 8250

⇒ 30x = 8250 → x = 275

⇒ Actual share of B = 11 × 275 + 60 = 3025 + 60 = ₹3085

⇒ Actual share of C = 14 × 275 + 71 = 3850 + 71 = ₹3921

⇒ Difference = 3921 − 3085 = ₹836

∴ The correct answer is ₹836.

Additional Information

Ratio Division with Constants

When fixed amounts are subtracted or added before dividing a sum, always calculate the net change to the total sum first before applying the ratio parts.

Direct Difference Shortcut

The difference between two shares (A and B) can be calculated as (Difference in Ratio Parts × Unit Value) + (Difference in respective deducted/added constants).

Shortcut Trick

In a right-angled triangle, tan θ represents the ratio of Height to Base.

Given tan θ = 4/3, let Height = 4 units and Base = 3 units.

According to the question, Base = 108 feet.

3 units → 108 feet ⇒ 1 unit = 36 feet.

Height = 4 units ⇒ 4 × 36 = 144 feet.

∴ The correct answer is 144 feet.

Alternate Method

Given: Distance from point A to building (Base) = 108 feet, Angle of elevation = θ, tan θ = 4/3.

Formula Used: tan θ = Perpendicular (Height) ÷ Base

⇒ Let the height of the building be h.

⇒ tan θ = h ÷ 108

⇒ 4/3 = h ÷ 108

⇒ h = (4 × 108) ÷ 3

⇒ h = 4 × 36

⇒ h = 144 feet.

∴ The correct answer is 144 feet.

Additional Information

Trigonometric Ratios

In a right-angled triangle: sin θ = P/H, cos θ = B/H, and tan θ = P/B.

Angle of Elevation

It is the angle formed by the line of sight with the horizontal when looking upwards at an object.

Pythagorean Triplet

For tan θ = 4/3, the sides follow the (3, 4, 5) triplet where Hypotenuse² = Base² + Height².

Shortcut Trick

Let the original price be 100.

Successive changes: 100 × 0.70 × 0.60 × 0.55 × 1.65

⇒ 100 × 0.42 × 0.55 × 1.65 ⇒ 23.1 × 1.65 = 38.115

Net Change = 100 − 38.115 = 61.885% ≈ 61.89% decrease.

∴ The correct answer is Decreases by 61.89%.

Alternate Method

Given: Successive decreases of 30%, 40%, 45% and an increase of 65%.

Formula: Final Price = Initial Price × (1 − d₁/100) × (1 − d₂/100) × (1 − d₃/100) × (1 + i₁/100)

⇒ Final Price = 100 × (1 − 0.30) × (1 − 0.40) × (1 − 0.45) × (1 + 0.65)

⇒ Final Price = 100 × 0.70 × 0.60 × 0.55 × 1.65

⇒ Final Price = 100 × 0.38115 = 38.115

⇒ Percentage Decrease = (100 − 38.115)/100 × 100 = 61.885%

∴ The correct answer is Decreases by 61.89%.

Additional Information

Successive Percentage Formula

For two successive changes a% and b%, the net effective change is (a + b + ab/100)%. Use negative values for decrease.

Multiplying Factor Method

A decrease of x% is equivalent to multiplying the value by (1 − x/100), while an increase of x% is equivalent to multiplying by (1 + x/100).

Base Change Property

When comparing the final value back to the original base, the percentage change is calculated as (Difference ÷ Original Value) × 100.

Shortcut Trick

Ratio of Total Surface Area (TSA) of cylinders = [r × (r + h)] / [R × (R + H)]

Given: Original Cylinder (R, H) = (4, 6) and Small Cylinder (r, h) = (2, 3)

Required Ratio = [2 × (2 + 3)] / [4 × (4 + 6)]

Required Ratio = [2 × 5] / [4 × 10] = 10 / 40 = 1 / 4

∴ The correct answer is 1 : 4.

Alternate Method

Given:

Radius of Original Cylinder (R) = 4 cm

Height of Original Cylinder (H) = 6 cm

Radius of Small Cylinder (r) = 2 cm

Height of Small Cylinder (h) = 3 cm

Formula Used:

Total Surface Area of a Cylinder = 2πr(r + h)

Calculations:

⇒ Total Surface Area (TSA) of Original Cylinder = 2 × π × 4 × (4 + 6)

⇒ TSA of Original Cylinder = 2 × π × 4 × 10 = 80π cm²

⇒ Total Surface Area (TSA) of one small cylinder = 2 × π × 2 × (2 + 3)

⇒ TSA of small cylinder = 2 × π × 2 × 5 = 20π cm²

⇒ Required Ratio = TSA of small cylinder : TSA of original cylinder

⇒ Required Ratio = 20π : 80π = 1 : 4

∴ The correct answer is 1 : 4.

Additional Information

Curved Surface Area (CSA) of Cylinder

The area of only the curved part is given by CSA = 2πrh.

Volume of Cylinder

The space occupied by the cylinder is Volume = πr²h.

Melting and Recasting

When a solid is melted and recast, the total Volume remains constant. Number of items = Total Volume ÷ Volume of one new item.

Shortcut Trick

The Selling Price (SP) is calculated by subtracting the Discount from the Cost Price (CP) when the discount is applied to the CP.

Multiplier for SP = CP × (100 − Discount%) ÷ 100

SP = 2800 × (100 − 87) ÷ 100

SP = 2800 × 13 ÷ 100 = 28 × 13

SP = 364

∴ The correct answer is ₹364.

Alternate Method

Given: Cost Price (CP) = ₹2,800 and Discount% = 87%.

Formulas: Discount Value = (Discount% ÷ 100) × CP | SP = CP − Discount Value

⇒ Discount Value = (87 ÷ 100) × 2800

⇒ Discount Value = 87 × 28 = 2436

⇒ SP = 2800 − 2436

⇒ SP = 364

∴ The correct answer is ₹364.

Additional Information

Cost Price and Discount

Usually, Discount is calculated on the Marked Price (MP). However, if the question specifies that the discount is given on the Cost Price (CP), we treat the CP as the base value for calculations.

Profit/Loss Scenarios

If the SP is less than the CP (as in this case due to a high discount on CP), the shopkeeper incurs a Loss. Loss = CP − SP.

Shortcut Trick

Total Volume of new cube = 2³ + 12³ + 16³

⇒ Volume = 8 + 1728 + 4096 = 5832 cm³

Side of the new cube (a) = ³√5832 = 18 cm

Total Surface Area = 6 × 18² = 6 × 324 = 1944 cm²

∴ The correct answer is 1944 cm².

Alternate Method

Given: Sides of the three metallic cubes are a₁ = 2 cm, a₂ = 12 cm, and a₃ = 16 cm.

Formula Used:

1. Volume of a cube = (side)³
2. Total Surface Area of a cube = 6 × (side)²

Calculations:

⇒ Volume of the first cube (V₁) = 2³ = 8 cm³

⇒ Volume of the second cube (V₂) = 12³ = 1728 cm³

⇒ Volume of the third cube (V₃) = 16³ = 4096 cm³

⇒ Total Volume of the new cube = V₁ + V₂ + V₃

⇒ Total Volume = 8 + 1728 + 4096 = 5832 cm³

⇒ Let the side of the new cube be 'A'. Then, A³ = 5832

⇒ A = ³√5832 = 18 cm

⇒ Total Surface Area of the new cube = 6 × A²

⇒ Total Surface Area = 6 × 18² = 6 × 324

⇒ Total Surface Area = 1944 cm²

∴ The correct answer is 1944 cm².

Additional Information

Volume of a Cube

The amount of space occupied by the cube is calculated as side³.

Lateral Surface Area (LSA)

The area of the four vertical faces of the cube is given by 4 × side².

Diagonal of a Cube

The longest distance between any two corners of a cube is side × √3.

Total Surface Area (TSA)

The sum of the areas of all six faces of the cube is 6 × side².

Shortcut Trick

Teacher's age = New Average + (Initial number of students × Increase in average)

Change in average = 13 − 12 = 1 year

Teacher's age = 13 + (30 × 1)

Teacher's age = 13 + 30 = 43 years

∴ The correct answer is 43 years.

Alternate Method

Given:

Number of students = 30

Initial average age = 12 years

Number of people including teacher = 30 + 1 = 31

New average age = 13 years

Formula Used:

Average = Sum of observations ÷ Number of observations

⇒ Sum = Average × Number of observations

Calculations:

⇒ Total age of 30 students = 30 × 12 = 360 years

⇒ Total age of 31 people (including teacher) = 31 × 13

⇒ Total age of 31 people = 403 years

⇒ Age of the teacher = (Total age of 31 people) − (Total age of 30 students)

⇒ Age of the teacher = 403 − 360

⇒ Age of the teacher = 43 years

∴ The correct answer is 43 years.

Additional Information

Weighted Average

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

Average with Replacement

If one person is replaced, the age of the new person = Age of replaced person + (Total items × Increase in Average).

Net Deviation Method

The sum of deviations of all observations from their arithmetic mean is always zero. This is useful for finding missing values in a dataset.

Shortcut Trick

Solve the nested square roots step-by-step starting from the innermost to the outermost.

First part: √289 = 17 → √(19 + 17) = √36 = 6 → √(250 + 6) = √256 = 16

Second part: √196 = 14 → √(11 + 14) = √25 = 5 → √(620 + 5) = √625 = 25

Final sum = 16 + 25 = 41

∴ The correct answer is 41.

Alternate Method

Given:

√(250 + √(19 + √289)) + √(620 + √(11 + √196))

Calculations:

⇒ Solve the innermost square roots first: √289 = 17 and √196 = 14

⇒ Substitute these values back into the expression:

⇒ √(250 + √(19 + 17)) + √(620 + √(11 + 14))

⇒ Simplify the addition inside the remaining inner roots:

⇒ √(250 + √36) + √(620 + √25)

⇒ Solve the next set of square roots: √36 = 6 and √25 = 5

⇒ Substitute these values back into the outermost roots:

⇒ √(250 + 6) + √(620 + 5)

⇒ Simplify the addition:

⇒ √256 + √625

⇒ Solve the final outermost square roots: √256 = 16 and √625 = 25

⇒ 16 + 25 = 41

∴ The correct answer is 41.

Additional Information

BODMAS Rule

Always follow the order of Brackets, Orders (powers and roots), Division, Multiplication, Addition, and Subtraction when simplifying arithmetic expressions.

Nested Square Roots

When simplifying continuous or nested radicals, always start evaluating from the innermost root and work your way outwards step-by-step until the outermost root is solved.

Perfect Squares 1 to 30

Memorizing squares up to 30 (e.g., 14² = 196, 16² = 256, 17² = 289, 25² = 625) significantly increases your calculation speed in simplification and number system problems.

Shortcut Trick

Check the options to see which pair satisfies both conditions: Sum = 50 and LCM = 429.

Option 1: 11 + 39 = 50. LCM of 11 and 39 (since 11 is prime and not a factor of 39) = 11 × 39 = 429.

Option 2: 16 + 34 = 50. LCM of 16 and 34 must be even (not 429).

Option 3: 4 + 46 = 50. LCM must be even (not 429).

Option 4: 9 + 41 = 50. LCM = 9 × 41 = 369 ≠ 429.

∴ The correct answer is 11, 39.

Alternate Method

Given: Sum of numbers (x + y) = 50, LCM(x, y) = 429.

Formula: Product of two numbers = HCF × LCM

⇒ Let the numbers be x and y.

⇒ Factorize 429: 429 = 3 × 11 × 13.

⇒ We need two factors whose sum is 50.

⇒ Possible pairs from factors: (11, 39) or (13, 33) etc.

⇒ 11 + 39 = 50. (Condition satisfied)

⇒ 13 + 33 = 46. (Condition not satisfied)

⇒ Therefore, the numbers are 11 and 39.

∴ The correct answer is 11, 39.

Additional Information

Relation between HCF and LCM

For any two numbers a and b, Product of numbers (a × b) = HCF(a, b) × LCM(a, b).

Co-prime Numbers

If two numbers are co-prime, their HCF is 1 and their LCM is equal to their product.

HCF property

The HCF of two numbers is always a factor of their LCM and also a factor of their sum and difference.

Shortcut Trick

Expenditure % = 100% − Savings %

Expenditure % = 100% − 25% = 75%

Monthly Expenditure = 75% of ₹7,700

Monthly Expenditure = 3/4 × 7,700 = 3 × 1,925 = ₹5,775

∴ The correct answer is ₹5,775.

Alternate Method

Given:

Total Monthly Salary = ₹7,700

Savings Rate = 25%

Formula Used:

Expenditure = Salary − Savings

⇒ Monthly Savings = 25% of ₹7,700

⇒ Monthly Savings = (25/100) × 7,700

⇒ Monthly Savings = 0.25 × 7,700 = ₹1,925

⇒ Monthly Expenditure = Total Salary − Monthly Savings

⇒ Monthly Expenditure = 7,700 − 1,925

⇒ Monthly Expenditure = ₹5,775

∴ The correct answer is ₹5,775.

Additional Information

Percentage Change

Percentage change = (New Value − Old Value) / Old Value × 100. It is used to calculate the percentage increase or decrease in salary or expenditure.

Successive Percentage

If a value changes by a% and then by b%, the effective change is (a + b + ab/100)%. This is useful in calculating multi-step salary increments or tax impacts.

Income, Savings and Expenditure Relation

Income is always the sum of Expenditure and Savings. If any two components are known, the third can be found using Income = Expenditure + Savings.

Shortcut Trick

If every observation in a data set is multiplied by a constant k, the new average is the old average multiplied by k.

Given k = 2 (doubled) and old average = 36.

⇒ New average = 36 × 2 = 72.

∴ The correct answer is 72.

Alternate Method

Given:

Total number of students = 12

Average marks of 12 students = 36

Formula Used:

Average = Sum of observations ÷ Number of observations

Sum of observations = Average × Number of observations

Calculations:

⇒ Total marks of 12 students = 36 × 12 = 432

⇒ Since marks of each student are doubled, the new sum will be double the old sum.

⇒ New total marks = 432 × 2 = 864

⇒ New Average = New total marks ÷ Number of students

⇒ New Average = 864 ÷ 12

⇒ New Average = 72

∴ The correct answer is 72.

Additional Information

Effect of Addition/Subtraction on Average

If a constant k is added or subtracted from each observation, the new average becomes (Old Average ± k).

Effect of Multiplication/Division on Average

If each observation is multiplied or divided by k, the new average becomes (Old Average × k) or (Old Average ÷ k) respectively.

Properties of Average

The average always lies between the minimum and maximum values of the data set. If all observations are equal to x, then the average is also x.

Shortcut Trick

Average Speed = (Distance₁ + Distance₂) ÷ (Time₁ + Time₂)

Average Speed = (209 + 83) ÷ (1 + 1)

Average Speed = 292 ÷ 2 = 146 km/hr.

∴ The correct answer is 146 km/hr.

Alternate Method

Given:

Distance covered in 1^st hour = 209 km

Distance covered in 2^nd hour = 83 km

Formula Used:

Average Speed = Total Distance Traveled ÷ Total Time Taken

Calculations:

⇒ Total Distance = 209 + 83 = 292 km

⇒ Total Time = 1 hour + 1 hour = 2 hours

⇒ Average Speed = 292 ÷ 2

⇒ Average Speed = 146 km/hr

∴ The correct answer is 146 km/hr.

Additional Information

Average Speed (Equal Distances)

If a journey covers two equal distances at speeds u and v, the average speed is (2 × u × v) ÷ (u + v).

Conversion Units

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

Relative Speed

For objects moving in the same direction, relative speed is the difference of speeds. In opposite directions, it is the sum of speeds.

Shortcut Trick

Let Total Capacity of tank = 12 units (LCM of 6 and 12).

Efficiency of A = +2 units/min and Efficiency of B = −1 unit/min.

Work done by A in 2 minutes = 2 × 2 = 4 units.

Remaining work = 12 − 4 = 8 units.

Combined efficiency (A + B) = 2 − 1 = 1 unit/min.

Time taken to fill remaining tank = 8 ÷ 1 = 8 minutes.

∴ The correct answer is 8 minutes.

Alternate Method

Given: Filling time of Pipe A = 6 mins, Emptying time of Pipe B = 12 mins.

⇒ Work done by Pipe A in first 2 minutes = 2 × 2 = 4 units

⇒ Remaining Capacity to be filled = 12 − 4 = 8 units

⇒ When both are open, Net Efficiency = 2 + (−1) = 1 unit/min

⇒ Time to fill remaining part = Remaining Capacity ÷ Net Efficiency

⇒ Time = 8 ÷ 1 = 8 minutes

∴ The correct answer is 8 minutes.

Additional Information

Negative Efficiency

In Pipes and Cisterns, an outlet pipe (drain pipe) is always assigned a negative efficiency because it reduces the volume of water in the tank.

Combined Rate Formula

If one pipe fills in x hours and another empties in y hours (y > x), the net rate is (1/x − 1/y) per hour. The time taken to fill the tank is (xy)/(y − x).

Total Filling Time

Be careful to distinguish between remaining time and total time. Total time = Initial time (2 mins) + Remaining time (8 mins) = 10 mins.

Shortcut Trick

Marked Price (MP) is 100%.

If Discount is 25%, then Selling Price (SP) is 75% of MP.

SP = 2,000 × (75 ÷ 100).

SP = 2,000 × 0.75 = 1,500.

∴ The correct answer is ₹1,500.

Alternate Method

Given: Marked Price (MP) = ₹2,000, Discount% = 25%.
Formula: SP = MP × (100 − Discount%) ÷ 100.

⇒ Discount Value = 25% of 2,000
⇒ Discount Value = (25 ÷ 100) × 2,000 = 500
⇒ SP = MP − Discount
⇒ SP = 2,000 − 500 = 1,500

∴ The correct answer is ₹1,500.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on the label. Discount is always calculated on the Marked Price. Formula: SP = MP − Discount.

Successive Discount

If two discounts a% and b% are given, the equivalent discount is (a + b − ab ÷ 100)%.

Shortcut Trick

Investment ratio of Poonam, Qasim, and Rina = 192 : 120 : 88.

Simplified ratio (divided by 8) = 24 : 15 : 11.

Total ratio units = 24 + 15 + 11 = 50 units.

50 units correspond to the total profit of ₹4,93,600.

Value of 1 unit = 4,93,600 ÷ 50 = 9,872.

Rina's share (11 units) = 11 × 9,872 = ₹1,08,592.

∴ The correct answer is ₹1,08,592.

Alternate Method

Given: Investments of P = ₹1,92,000, Q = ₹1,20,000, R = ₹88,000. Total Profit = ₹4,93,600.

Formula: Profit Share = (Individual Investment × Time) ÷ (Total Investment × Time)

⇒ Ratio of Profit = 1,92,000 : 1,20,000 : 88,000

⇒ Simplified Ratio = 24 : 15 : 11

⇒ Sum of ratios = 24 + 15 + 11 = 50

⇒ Rina's share = (11 ÷ 50) × 4,93,600

⇒ Rina's share = 11 × 9,872 = 1,08,592

∴ The correct answer is ₹1,08,592.

Additional Information

Partnership Principle

When the time period of investment is the same for all partners, the profit is distributed solely in the ratio of their investments.

Variable Time Investment

If partners invest for different time periods, the profit ratio is calculated as (Capital₁ × Time₁) : (Capital₂ × Time₂).

Shortcut Trick

Direct application of Empirical Relationship between measures of central tendency:

2 × Mean = 3 × Median − Mode

⇒ 2 × Mean = 3 × 28 − 27.6

⇒ 2 × Mean = 84 − 27.6 = 56.4

⇒ Mean = 56.4 ÷ 2 = 28.2

∴ The correct answer is 28.2.

Alternate Method

Given:

Mode of the data = 27.6

Median of the data = 28

Formula Used:

Mode = 3 × Median − 2 × Mean

Calculations:

⇒ 27.6 = 3 × 28 − 2 × Mean

⇒ 27.6 = 84 − 2 × Mean

⇒ 2 × Mean = 84 − 27.6

⇒ 2 × Mean = 56.4

⇒ Mean = 56.4 ÷ 2

⇒ Mean = 28.2

∴ The correct answer is 28.2.

Additional Information

Symmetric Distribution

In a perfectly symmetrical distribution, the Mean, Median, and Mode are all equal (Mean = Median = Mode).

Positively Skewed Distribution

For a data set skewed to the right, the values generally follow the order: Mean > Median > Mode.

Negatively Skewed Distribution

For a data set skewed to the left, the values generally follow the order: Mean < Median < Mode.