Quantitative Aptitude PYQs

Shortcut Trick

Solve the bracket and multiplication simultaneously for speed.

Product: 72 × 2 = 144

Bracket: 61 − 28 = 33

Combine: 144 − 19 + 33 + 35 = 125 + 68 = 193

∴ The correct answer is 193.

Alternate Method

Given: 72 × 2 − 19 + (61 − 28) + 35

Formula Used: BODMAS Rule

⇒ 72 × 2 − 19 + (33) + 35 (Solving Bracket)

⇒ 144 − 19 + 33 + 35 (Solving Multiplication)

⇒ 125 + 33 + 35 (Solving first Subtraction)

⇒ 158 + 35 (Solving first Addition)

⇒ 193

∴ The correct answer is 193.

Additional Information

BODMAS Rule Priority

The order of operations is Brackets (B), Orders (O), Division (D), Multiplication (M), Addition (A), and Subtraction (S). Note that DM and AS have equal priority and are solved from left to right.

Types of Brackets

Brackets are solved in the order: Bar/Vinculum, Parentheses ( ), Braces { }, and then Square Brackets [ ].

Shortcut Trick

Solve the expression using the VBODMAS priority order.

⇒ 76 − 33 + (28 × 2) + (36 ÷ 3) − 22 + 19

⇒ 76 − 33 + 56 + 12 − 22 + 19

⇒ (76 + 56 + 12 + 19) − (33 + 22) = 163 − 55 = 108

∴ The correct answer is 108.

Alternate Method

Given:

76 − 33 + 28 of 2 + 36 ÷ 3 − (22) + 19

Formula Used:

Follow the BODMAS rule: Brackets, Of, Division, Multiplication, Addition, Subtraction.

Calculations:

⇒ 76 − 33 + (28 × 2) + (36 ÷ 3) − 22 + 19 (Solving Of and Division)

⇒ 76 − 33 + 56 + 12 − 22 + 19

⇒ 43 + 56 + 12 − 22 + 19 (Solving Subtraction/Addition from left to right)

⇒ 99 + 12 − 22 + 19

⇒ 111 − 22 + 19

⇒ 89 + 19

⇒ 108

∴ The correct answer is 108.

Additional Information

BODMAS Rule

It specifies the order of operations: Brackets ((), {}, []), Orders (powers/roots), Division, Multiplication, Addition, and Subtraction.

The 'Of' Operator

The word 'of' represents multiplication but must be performed before regular division and multiplication in the hierarchy.

Addition and Subtraction Grouping

For faster calculation, group all positive numbers and all negative numbers separately, then find the final difference.

Shortcut Trick

Solve the expression following the BODMAS priority: Bracket, Of, Division, Multiplication, Addition, and Subtraction.

Step 1: Of → 17 × 2 = 34

Step 2: Division → 44 ÷ 4 = 11

Step 3: Multiplication → 29 × 1 = 29

Step 4: 78 − 33 + 29 + 11 + 34 − 19 = 152 − 52 = 100

∴ The correct answer is 100.

Alternate Method

Given: 78 − 33 + 29 × 1 + 44 ÷ 4 + (17 of 2) − 19

Following the BODMAS rule step-by-step:

⇒ 78 − 33 + 29 × 1 + 44 ÷ 4 + 34 − 19

⇒ 78 − 33 + 29 × 1 + 11 + 34 − 19

⇒ 78 − 33 + 29 + 11 + 34 − 19

⇒ (78 + 29 + 11 + 34) − (33 + 19)

⇒ 152 − 52

⇒ 100

∴ The correct answer is 100.

Additional Information

BODMAS Rule

It is an acronym to help remember the order of mathematical operations: Brackets, Of (orders/powers), Division, Multiplication, Addition, and Subtraction.

The 'Of' Operation

In simplification, the term of is treated as multiplication but is prioritized higher than division and standard multiplication symbols.

Calculation Tip

While performing addition and subtraction, it is often faster to group all positive terms and negative terms separately before the final subtraction.

Shortcut Trick

Identify and solve BODMAS components mentally: Bracket (18 − 14 = 4), Of (21 × 2 = 42), and Division (33 ÷ 3 = 11).

Notice the cancellation: The expression contains −42 and + (21 of 2), which is −42 + 42 = 0.

Remaining calculation: 96 + 11 + 4 = 111.

∴ The correct answer is 111.

Alternate Method

Given: 96 − 42 + 33 ÷ 3 + 21 of 2 + (18 − 14)

Formula Used: Apply the VBODMAS rule (Vinculum, Bracket, Of, Division, Multiplication, Addition, Subtraction).

⇒ 96 − 42 + 33 ÷ 3 + 21 of 2 + 4 (Solving Bracket: 18 − 14)

⇒ 96 − 42 + 33 ÷ 3 + 42 + 4 (Solving Of: 21 × 2)

⇒ 96 − 42 + 11 + 42 + 4 (Solving Division: 33 ÷ 3)

⇒ 54 + 11 + 42 + 4 (Solving Subtraction: 96 − 42)

⇒ 65 + 42 + 4 (Solving Addition: 54 + 11)

⇒ 107 + 4 = 111

∴ The correct answer is 111.

Additional Information

BODMAS Hierarchy

The rule ensures a unique solution to mathematical expressions by following the sequence: Brackets, Orders/Of, Division, Multiplication, Addition, and Subtraction.

Sign Convention

When multiple addition and subtraction operations are present, they are performed from left to right, although results remain the same if all additions are grouped first.

Of Operator Significance

The 'of' operator acts like multiplication but holds a higher precedence than division, meaning it must be calculated before any division in the expression.

Shortcut Trick

In a parallelogram, the sum of any two adjacent angles is always 180° (they are supplementary).

Adjacent Angle = 180° − Given Angle

Adjacent Angle = 180° − 60° = 120°

∴ The correct answer is 120°.

Alternate Method

Given: One angle of the parallelogram = 60°

Formula Used: Consecutive interior angles formed by a transversal crossing parallel lines are supplementary. For a parallelogram ABCD, ∠A + ∠B = 180°.

Calculations:

⇒ Let the angles of the parallelogram be ∠A, ∠B, ∠C, and ∠D.

⇒ Given ∠A = 60°.

⇒ Since AD || BC and AB || DC, the adjacent angles are supplementary.

⇒ ∠A + ∠B = 180°

⇒ 60° + ∠B = 180°

⇒ ∠B = 180° − 60°

⇒ ∠B = 120°

∴ The correct answer is 120°.

Additional Information

Opposite Angles Property

In any parallelogram, the opposite angles are always equal in measure. If one angle is 60°, its opposite angle is also 60°.

Angle Sum Property

The sum of all four interior angles of a parallelogram (or any quadrilateral) is always 360°.

Consecutive Angles

Any two consecutive angles of a parallelogram are supplementary, meaning their sum is 180°.

Shortcut Trick

The Least Common Multiple (LCM) of a set of numbers can be found by taking the LCM of the LCMs of its subsets.

LCM(A, B, C, D) = LCM[LCM(A, B), LCM(C, D)]

Given: LCM(A, B) = 15 and LCM(C, D) = 25

Required LCM = LCM(15, 25)

LCM(15, 25) = 75

∴ The correct answer is 75.

Alternate Method

Given:

LCM of A and B = 15

LCM of C and D = 25

Formula Used:

The Associative Property of LCM states: LCM(a, b, c, d) = LCM(LCM(a, b), LCM(c, d)).

Calculations:

⇒ To find the LCM of 15 and 25, we use Prime Factorization.

⇒ 15 = 3¹ × 5¹

⇒ 25 = 5 × 5 = 5²

⇒ LCM is the product of the highest power of all prime factors involved.

⇒ LCM(15, 25) = 3¹ × 5²

⇒ LCM = 3 × 25

⇒ LCM = 75

∴ The correct answer is 75.

Additional Information

Fundamental LCM Property

The Least Common Multiple (LCM) is the smallest positive integer that is perfectly divisible by every number in the given set.

LCM and HCF Relationship

For any two numbers x and y, the product of their HCF and LCM is equal to the product of the numbers: HCF(x, y) × LCM(x, y) = x × y.

LCM of Co-prime Numbers

If two numbers are co-prime (having no common factors other than 1), their LCM is simply the product of the two numbers.

Shortcut Trick

To find the LCM of three numbers A, B, and C, we use the property: LCM(A, B, C) = LCM[LCM(A, B), C].

Given LCM(A, B) = 30 and C = 18.

We need to find the LCM of 30 and 18.

Check the multiples of the larger number (30): 30 × 1 = 30 (not divisible by 18), 30 × 2 = 60 (not divisible by 18), 30 × 3 = 90 (divisible by 18).

∴ The correct answer is 90.

Alternate Method

Given:

LCM of A and B = 30

Value of C = 18

Formula Used:

The Least Common Multiple (LCM) of three numbers is the LCM of the LCM of any two of those numbers and the third number.

Calculations:

⇒ Prime factorization of 30 = 2 × 3 × 5

⇒ Prime factorization of 18 = 2 × 3 × 3 = 2 × 3²

⇒ To find the LCM, take the highest power of each prime factor present in both numbers:

⇒ Highest power of 2 = 2¹

⇒ Highest power of 3 = 3²

⇒ Highest power of 5 = 5¹

⇒ LCM(30, 18) = 2¹ × 3² × 5¹

⇒ LCM = 2 × 9 × 5 = 90

∴ The correct answer is 90.

Additional Information

LCM and HCF Relation

For any two numbers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

LCM of Fractions

To calculate the LCM of fractions, use the formula: LCM = LCM(Numerators) ÷ HCF(Denominators).

Divisibility Rule

The HCF of a set of numbers always completely divides their LCM.

Shortcut Trick

The Highest Common Factor (HCF) of any set of numbers must always be a factor of their Least Common Multiple (LCM).

Given LCM = 150.

Check the options to see which number divides 150 exactly: 150 ÷ 15 = 10 (Integer).

Other options (20, 35, 28) do not divide 150 without leaving a remainder.

∴ The correct answer is 15.

Alternate Method

Given:

LCM = 150

Property: In any pair of numbers, the LCM is always a multiple of the HCF. Conversely, the HCF must divide the LCM completely.

Let us test each option:

⇒ Option (1): 150 ÷ 15 = 10 (Divisible)

⇒ Option (2): 150 ÷ 20 = 7.5 (Not divisible)

⇒ Option (3): 150 ÷ 35 = 4.28 (Not divisible)

⇒ Option (4): 150 ÷ 28 = 5.35 (Not divisible)

⇒ Since only 15 is a factor of 150, it can be the HCF.

∴ The correct answer is 15.

Additional Information

Product Rule of LCM and HCF

For any two numbers A and B, the product of the numbers is equal to the product of their HCF and LCM: A × B = HCF(A, B) × LCM(A, B).

HCF of Coprime Numbers

The Highest Common Factor of two coprime numbers is always 1, and their LCM is simply the product of the two numbers.

Range of HCF and LCM

The HCF is always less than or equal to the smallest number in the set, while the LCM is always greater than or equal to the largest number in the set.

Shortcut Trick

Loss of 18% = ₹81

1% = 81 ÷ 18 = 4.5

Selling Price (SP) = 100% − 18% = 82%

Selling Price (SP) = 82 × 4.5 = ₹369

∴ The correct answer is ₹369.

Alternate Method

Given:

Loss = ₹81

Loss Percentage = 18%

Formula Used:

Loss % = (Loss ÷ Cost Price) × 100

Selling Price (SP) = Cost Price (CP) − Loss

Calculations:

⇒ 18 = (81 ÷ CP) × 100

⇒ CP = (81 × 100) ÷ 18

⇒ CP = 4.5 × 100 = ₹450

⇒ SP = 450 − 81

⇒ SP = ₹369

∴ The correct answer is ₹369.

Additional Information

Cost Price (CP)

The price at which an article is purchased. It is the base for calculating Profit % or Loss %.

Profit Percentage Formula

Profit % = [(Selling Price − Cost Price) ÷ Cost Price] × 100.

Selling Price for Profit

To find SP when Profit % is given: SP = CP × (100 + Profit %) ÷ 100.

Shortcut Trick

Ratio of Smaller number (S) to Larger number (L) is inversely proportional to their percentage values.

S : L = 20% : 40% = 1 : 2

Sum of ratios = 1 + 2 = 3 units

3 units = 750 ⇒ 1 unit = 250

Larger number = 2 units = 2 × 250 = 500

∴ The correct answer is 500.

Alternate Method

Given: Sum of numbers = 750, 40% of Smaller = 20% of Larger.

Formula Used: Percentage = (Value / Total) × 100

Let the smaller number be S and the larger number be L.

⇒ 40% × S = 20% × L

⇒ (40/100) × S = (20/100) × L

⇒ 2 × S = 1 × L ⇒ L = 2S

⇒ S + L = 750

⇒ S + 2S = 750

⇒ 3S = 750 ⇒ S = 250

⇒ Larger number (L) = 2 × 250 = 500

∴ The correct answer is 500.

Additional Information

Percentage Equivalence

If x% of A = y% of B, then the ratio of the numbers is A : B = y : x. This is a common shortcut for direct ratio conversion.

Dividing a Sum into Ratios

To divide a total sum T into ratio a : b, the parts are calculated as [a / (a + b)] × T and [b / (a + b)] × T.

Linear Equations in Two Variables

Problems involving the sum of two numbers can always be modeled using x + y = Total and solved by substituting one variable in terms of the other.

Shortcut Trick

Let the initial Cost Price be 100 units, then the initial Selling Price is 75 units (25% loss).

New Cost Price = 100 + 40% = 140 units.

New Selling Price at 15% loss = 140 × 0.85 = 119 units.

Required percentage increase in Selling Price (y) = [(119 − 75) ÷ 75] × 100.

y = (44 ÷ 75) × 100 = 176 ÷ 3 = 58.67.

∴ The correct answer is 58.67.

Alternate Method

Given:

Initial Loss = 25%

Increase in Cost Price = 40%

New Loss = 15%

Formula Used:

Selling Price (SP) = Cost Price (CP) × (100 − Loss%)/100

Percentage Increase = [(Final Value − Initial Value) ÷ Initial Value] × 100

Calculations:

⇒ Assume initial Cost Price = 100

⇒ Initial Selling Price = 100 − 25% of 100 = 75

⇒ New Cost Price = 100 + 40% of 100 = 140

⇒ New Selling Price = 140 × (100 − 15)/100

⇒ New Selling Price = 140 × 85/100 = 119

⇒ Increase in Selling Price = 119 − 75 = 44

⇒ Percentage increase (y) = (44 ÷ 75) × 100

⇒ y = (44 × 4) ÷ 3 = 176 ÷ 3

⇒ y = 58.666... ≈ 58.67

∴ The correct answer is 58.67.

Additional Information

Profit and Loss Relationship

Selling Price is calculated as CP × (100 + P%)/100 for profit and CP × (100 − L%)/100 for loss.

Percentage Change

The percentage change between two values is always calculated using the original value as the base: [(New − Old) ÷ Old] × 100.

Effective Change

When both CP and SP change, the new profit/loss percentage depends on the final ratio of the updated SP and CP values.

Shortcut Trick

Time for S to complete 3/4 work = 18 days

Time for S to complete full work = 18 × (4/3) = 24 days

Since R is 3 times as efficient as S, he takes 1/3^rd of the time.

Time taken by R = 24 ÷ 3 = 8 days

∴ The correct answer is 8 days.

Alternate Method

Given:

S completes 3/4 part of work in 18 days.

R's Efficiency = 3 × S's Efficiency.

Formula:

Total Time = (Time taken for fraction) ÷ (Fraction of work)

Efficiency × Time = Total Work

⇒ Total days for S = 18 × (4 ÷ 3) = 24 days.

⇒ Let Efficiency of S = 1 unit/day.

⇒ Total Work = Efficiency × Days = 1 × 24 = 24 units.

⇒ Efficiency of R = 3 × Efficiency of S = 3 × 1 = 3 units/day.

⇒ Days taken by R alone = Total Work ÷ Efficiency of R

⇒ Days taken by R alone = 24 ÷ 3 = 8 days.

∴ The correct answer is 8 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. If the ratio of efficiency is x : y, then the ratio of time taken is y : x.

Total Work Calculation

Total Work = Number of Days × Efficiency. For fractional work, Full Work Time = (Time for Part) × (Reciprocal of the Part).

Combined Efficiency

When multiple people work together, their efficiencies are added: E_total = E₁ + E₂ + ... + E_n.

Shortcut Trick

Total work = LCM(18, 24, 36) = 72 units.

2(M + R + P) combined efficiency = (72 ÷ 18) + (72 ÷ 24) + (72 ÷ 36) = 4 + 3 + 2 = 9.

Combined efficiency of M, R, and P = 9 ÷ 2 = 4.5 units/day.

Work done in 4 days = 4.5 × 4 = 18 units.

Required part of work = 18 ÷ 72 = 1/4.

∴ The correct answer is 1/4.

Alternate Method

Given: M and R = 18 days, R and P = 24 days, P and M = 36 days.

Formula Used: Efficiency = Total Work ÷ Time; Total work done = Combined Efficiency × Time.

⇒ Sum of efficiencies = 2 × (M + R + P) = 4 + 3 + 2 = 9 units/day.

⇒ Efficiency of (M + R + P) working together = 9 ÷ 2 = 4.5 units/day.

⇒ Work completed in 4 days = 4.5 × 4 = 18 units.

⇒ Part of work done = 18 ÷ 72 = 1/4.

∴ The correct answer is 1/4.

Additional Information

Combined Efficiency of Pairs

When people work in pairs (AB, BC, CA), the sum of their individual efficiencies is found by dividing the sum of pair efficiencies by 2.

Work & Wages Principle

Wages are distributed based on the Efficiency × Time product for each person, which represents the actual work done.

Fractional Work

The part of work done in 'n' days is calculated as (Combined Efficiency × n) ÷ Total Work.

Shortcut Trick

Speed of boat in still water is the average of downstream and upstream speeds.

Speed = (Downstream + Upstream) ÷ 2

Speed = (42 + 36) ÷ 2 = 78 ÷ 2 = 39 km/hr

∴ The correct answer is 39 km/hr.

Alternate Method

Given:

Downstream Speed (D) = 42 km/hr

Upstream Speed (U) = 36 km/hr

Formula Used:

Speed of boat in still water (x) = (D + U) ÷ 2

Speed of stream (y) = (D − U) ÷ 2

Calculations:

⇒ x = (42 + 36) ÷ 2

⇒ x = 78 ÷ 2

⇒ x = 39 km/hr

∴ The correct answer is 39 km/hr.

Additional Information

Speed of Stream

The rate at which the water flows is given by y = (Downstream speed − Upstream speed) ÷ 2. In this case, y = (42 − 36) ÷ 2 = 3 km/hr.

Downstream and Upstream Logic

Downstream Speed = Speed of boat (x) + Speed of stream (y). Upstream Speed = Speed of boat (x) − Speed of stream (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.

Shortcut Trick

Speed of Stream = Still Water Speed − Upstream Speed

⇒ Speed of Stream = 23 − 17

⇒ Speed of Stream = 6 km/hr

∴ The correct answer is 6 km/hr.

Alternate Method

Given:

Speed of the boat in still water (u) = 23 km/hr

Upstream speed of the boat (u − v) = 17 km/hr

Formula Used:

Upstream Speed = Speed in Still Water − Speed of Stream

Calculations:

Let the speed of the stream be v km/hr.

⇒ 17 = 23 − v

⇒ v = 23 − 17

⇒ v = 6 km/hr

∴ The correct answer is 6 km/hr.

Additional Information

Downstream Speed

It is the net speed of the boat when it travels in the direction of the stream: Downstream Speed = u + v.

Speed in Still Water

If downstream and upstream speeds are known: u = (Downstream + Upstream) ÷ 2.

Speed of Stream

If downstream and upstream speeds are known: v = (Downstream − Upstream) ÷ 2.

Shortcut Trick

Upstream Speed = Downstream Speed − 2 × Stream Speed

Upstream Speed = 35 − 2(5) = 25 km/hr

Total Time = (350 ÷ 35) + (150 ÷ 25) = 10 + 6 = 16 hr

∴ The correct answer is 16 hr.

Alternate Method

Given: Downstream Speed = 35 km/hr, Stream Speed = 5 km/hr, Downstream Distance = 350 km, Upstream Distance = 150 km.

Formula Used: Time = Distance ÷ Speed | Boat Speed (u) = Downstream − Stream | Upstream = u − Stream

⇒ Boat Speed in Still Water (u) = 35 − 5 = 30 km/hr

⇒ Upstream Speed (v) = 30 − 5 = 25 km/hr

⇒ Time taken for Downstream = 350 ÷ 35 = 10 hr

⇒ Time taken for Upstream = 150 ÷ 25 = 6 hr

⇒ Total Time = 10 + 6 = 16 hr

∴ The correct answer is 16 hr.

Additional Information

Boat Speed and Stream Speed Calculation

Boat speed in still water (u) = (Downstream Speed + Upstream Speed) ÷ 2. Stream speed (v) = (Downstream Speed − Upstream Speed) ÷ 2.

Average Speed in Boats and Streams

When the boat covers the same distance downstream and upstream, the Average Speed = (u² − v²) ÷ u, where u is boat speed and v is stream speed.

Upstream and Downstream Logic

Downstream speed is always greater than upstream speed because the stream supports the boat movement in the former and opposes it in the latter.

Shortcut Trick

Use the ratio of Marked Price (MP) to Cost Price (CP):

MP / CP = (100 + Profit%) / (100 − Discount%)

MP / 10000 = (100 + 40) / (100 − 30) = 140 / 70 = 2 / 1

MP = 10000 × 2 = ₹20000

∴ The correct answer is ₹20000.

Alternate Method

Given:

Cost Price (CP) = ₹10000

Profit Percentage = 40%

Discount Percentage = 30%

Formula Used:

Selling Price (SP) = CP × (100 + Profit%)/100

Marked Price (MP) = SP × 100 / (100 − Discount%)

Calculations:

⇒ SP = 10000 × (100 + 40) / 100

⇒ SP = 10000 × 140 / 100 = ₹14000

⇒ 14000 = MP × (100 − 30) / 100

⇒ 14000 = MP × 70 / 100

⇒ MP = (14000 × 100) / 70

⇒ MP = 200 × 100 = ₹20000

∴ The correct answer is ₹20000.

Additional Information

Relationship between CP and MP

The direct formula is CP / MP = (100 − Discount%) / (100 + Profit%). If there is a loss, use (100 − Loss%).

Markup Percentage

Markup % is the percentage by which the cost price is increased to set the marked price. Markup % = [(MP − CP) / CP] × 100.

Successive Discounts

If two discounts d₁% and d₂% are given, the equivalent single discount is [d₁ + d₂ − (d₁ × d₂)/100]%.

Shortcut Trick

The Marked Price (MP) is calculated as SP ÷ (1 − d), where d is the discount in decimal form.

Compare denominators: 0.9, 0.75, 0.55, and 0.8. A smaller denominator increases the final value.

Option 3: 6000 ÷ 0.55 ≈ 10909.09 (Highest SP with the highest discount %).

Option 4: 6250 ÷ 0.8 = 7812.5 (High SP but much lower discount %).

By inspection, Case 3 has the lowest multiplier (0.55) relative to its high base price.

∴ The correct answer is Rs. 6000 and 45% discount.

Alternate Method

Given: Selling Price (SP) and Discount Percentage for four different cases.

Formula Used: Marked Price (MP) = (SP × 100) ÷ (100 − Discount %)

⇒ Case 1: MP = (4000 × 100) ÷ (100 − 10) = 400000 ÷ 90 ≈ ₹4444.44

⇒ Case 2: MP = (5000 × 100) ÷ (100 − 25) = 500000 ÷ 75 ≈ ₹6666.67

⇒ Case 3: MP = (6000 × 100) ÷ (100 − 45) = 600000 ÷ 55 ≈ ₹10909.09

⇒ Case 4: MP = (6250 × 100) ÷ (100 − 20) = 625000 ÷ 80 = ₹7812.50

Comparing all the results, Case 3 has the highest value.

∴ The correct answer is Rs. 6000 and 45% discount.

Additional Information

Marked Price and Discount

The Marked Price (MP) is also known as the list price or tag price. Discount is always calculated on the MP, and SP = MP − Discount.

Discount Percentage Formula

The percentage of discount is given by: Discount % = (Discount ÷ Marked Price) × 100.

Successive Discounts

When two discounts a% and b% are given, the Effective Discount = (a + b − (a × b) ÷ 100)%.

Shortcut Trick

Net discount % = a + b − (a × b)/100

Net discount = 20 + 30 − (20 × 30)/100 = 50 − 6 = 44%

Selling Price (SP) = 100% − 44% = 56% of Marked Price

56% = Rs. 4480 ⇒ 1% = 80 ⇒ 100% = Rs. 8000

∴ The correct answer is Rs. 8000.

Alternate Method

Given:

First discount (d₁) = 20%

Second discount (d₂) = 30%

Selling Price (SP) = Rs. 4480

Formula Used:

SP = MP × (100 − d₁)/100 × (100 − d₂)/100

Calculations:

⇒ SP = MP × (80/100) × (70/100)

⇒ 4480 = MP × (4/5) × (7/10)

⇒ 4480 = MP × (28/50)

⇒ 4480 = MP × (14/25)

⇒ MP = (4480 × 25) ÷ 14

⇒ MP = 320 × 25

⇒ MP = Rs. 8000

∴ The correct answer is Rs. 8000.

Additional Information

Successive Discount Formula

For two successive discounts of x% and y%, the single equivalent discount is (x + y − xy/100)%.

Relationship between MP, CP and Profit/Discount

The ratio of Marked Price to Cost Price is given by: MP/CP = (100 + Profit%)/(100 − Discount%).

Marked Price (MP) Definition

It is the price displayed on the label of an article, also known as the list price. Discount is always calculated on this price.

Shortcut Trick

Ratio of Height to Shadow is constant at the same time.

Boy's Ratio = 1.8 : 1.2 = 3 : 2

For the Building, Shadow = 8 m (which is 2 × 4)

Building Height = 3 × 4 = 12 m

∴ The correct answer is 12 m.

Alternate Method

Given:

Height of the Boy (H₁) = 1.8 m

Shadow of the Boy (S₁) = 1.2 m

Shadow of the Building (S₂) = 8 m

Formula Used:

In Similar Triangles (formed by sun rays), Height₁ / Shadow₁ = Height₂ / Shadow₂

Calculations:

⇒ H₁ / S₁ = H₂ / S₂

⇒ 1.8 / 1.2 = H₂ / 8

⇒ 3 / 2 = H₂ / 8

⇒ H₂ = (3 × 8) / 2

⇒ H₂ = 24 / 2

⇒ H₂ = 12 m

∴ The correct answer is 12 m.

Additional Information

Angle of Elevation

At any given time, the Sun's angle of elevation is the same for all objects in the same vicinity, making the triangles formed by objects and their shadows mathematically similar.

Properties of Similar Triangles

For two triangles to be similar, their corresponding sides must be in the same proportion. Here, Height/Shadow = tan(θ), where θ is the sun's altitude.

Ratio and Proportion

If a : b = c : d, then the product of means equals the product of extremes (ad = bc). This is used to find the unknown height directly.