SSC CHSL Tier 1 2021 Quantitative Aptitude Questions with Solutions

Explanation

The volume of a cube is given by the formula V = a³, where a is the length of its side.

Given: a³ = 5832 cm³

Taking the cube root on both sides: a = 18 cm

The total surface area of a cube is given by the formula: Total Surface Area = 6a²

Substituting the value of a: Total Surface Area = 6 × 18² Total Surface Area = 6 × 324 Total Surface Area = 1944 cm²

Explanation

The expression 3 sinA - 4 sin³A is the standard trigonometric identity for the triple angle of the sine function.

By using the angle sum formula, sin(3A) can be written as sin(2A + A). Expanding this using the sine addition formula yields sin2A cosA + cos2A sinA. Substituting the double angle formulas sin2A = 2 sinA cosA and cos2A = 1 - 2 sin²A, the expression becomes 2 sinA cos²A + (1 - 2 sin²A) sinA. Replacing cos²A with 1 - sin²A results in 2 sinA (1 - sin²A) + sinA - 2 sin³A, which simplifies directly to 3 sinA - 4 sin³A.

Explanation

To find the required difference, identify the highest number of cakes sold by bakery F and the lowest number of cakes sold by bakery B from the table.

For bakery F, the sales on the given days are 175, 205, 255, 240, and 308. The highest number of cakes sold by bakery F in a single day is 308.

For bakery B, the sales on the given days are 205, 275, 314, 295, and 260. The lowest number of cakes sold by bakery B in a single day is 205.

The difference between these two values is: 308 - 205 = 103

Explanation

By the division algorithm, if a positive integer N is divided by 7 with a remainder of 3, it can be expressed in the form:

N = 7k + 3

where k is a non-negative integer.

To find an expression that yields a remainder of 0 when divided by 7, we need to add a value to N that makes the resulting expression a multiple of 7. Adding 4 to N gives:

N + 4 = 7k + 3 + 4 N + 4 = 7k + 7 N + 4 = 7(k + 1)

Since 7(k + 1) is a multiple of 7, the number N + 4 is completely divisible by 7, leaving a remainder of 0.

Explanation

Correct Answer: B

Dividing the given equation x² - 8x + 1 = 0 by x, we get: x - 8 + 1/x = 0 x + 1/x = 8

Squaring both sides of this equation: (x + 1/x)² = 8² x² + 2 + 1/x² = 64 x² + 1/x² = 62

Squaring both sides once more: (x² + 1/x²)² = 62² x⁴ + 2 + 1/x⁴ = 3844 x⁴ + 1/x⁴ = 3842

Multiplying the entire equation by x⁴: x⁸ + 1 = 3842x⁴

Rearranging the terms gives: x⁸ - 3842x⁴ + 1 = 0

Explanation

The future population after a given number of years under a constant growth rate can be calculated using the compound growth formula:

A = P × (1 + r/100)ⁿ

In this formula, P represents the present population, r is the annual growth rate, and n is the number of years.

Given: Present population, P = 16000 Growth rate, r = 5% per annum Time, n = 2 years

Substituting these values into the formula:

A = 16000 × (1 + 5/100)² A = 16000 × (1 + 1/20)² A = 16000 × (21/20)² A = 16000 × (441/400) A = 40 × 441 A = 17640

Explanation

The expression is evaluated by breaking it down into three parts:

First term: 56% of 4800 = 56/100 × 4800 = 56 × 48 = 2688

Second term: {(9.3 × 2.8) + √(65.61)} Since 9.3 × 2.8 = 26.04 and √(65.61) = 8.1: 26.04 + 8.1 = 34.14

Third term: 48% of (81 + 8) = 48% of 89 = 48/100 × 89 = 42.72

Combining these values: 2688 - 34.14 - 42.72 = 2611.14

Explanation

When a journey covers two equal distances at different speeds, say v₁ and v₂, the average speed for the entire journey is given by the harmonic mean of the speeds:

Average Speed = 2v₁v₂ / (v₁ + v₂)

Substituting the given values, v₁ = 60 km/h and v₂ = 40 km/h:

Average Speed = (2 × 60 × 40) / (60 + 40) Average Speed = 4800 / 100 Average Speed = 48 km/h

This calculation directly yields the average speed of the car for the entire journey.

Explanation

Wages are distributed in proportion to the share of work completed by each individual.

A can complete the task in 12 days, which means A's daily work rate is 1/12 of the total work. Since A works for only 2 days, the fraction of work completed by A is 2 × (1/12) = 1/6.

Since B completes the entire remaining portion of the work, B's share of the total work is 1 - 1/6 = 5/6.

B's share of the total wage of ₹2,400 is calculated by multiplying B's share of work by the total wage: B's share = 5/6 × 2400 = 5 × 400 = 2000.

Explanation

When a solid cylinder is melted and recast into a solid cone, the volume of the material remains conserved.

Volume of cylinder = Volume of cone

Using the volume formulas: π r₁² h₁ = (1/3) π r₂² h₂

Here, the radius of the cylinder r₁ = 15 cm, the height of the cylinder h₁ = 12 cm, and the radius of the cone r₂ = 24 cm. Let h₂ be the height of the cone.

Substituting these values into the equation: 15² × 12 = (1/3) × 24² × h₂

225 × 12 = (1/3) × 576 × h₂

2700 = 192 × h₂

h₂ = 2700 / 192

h₂ = 225 / 16

h₂ = 14.0625 cm

Explanation

The relationship between the Cost Price (CP) and the Marked Price (MP) of an article is given by the formula:

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

Substituting the given values of discount (10%) and profit (12.5%):

CP/MP = (100 - 10)/(100 + 112.5) CP/MP = 90/112.5 CP/MP = 4/5

This means if the Cost Price is 4 units, the Marked Price is 5 units.

When the article is sold at the marked price with no discount, the Selling Price (SP) becomes equal to the Marked Price (MP).

SP = 5 units

Profit = SP - CP = 5 - 4 = 1 unit

Profit percentage = (Profit/CP) × 100% Profit percentage = (1/4) × 100% = 25%

Explanation

The relationship between distance, speeds, and the difference in travel time is given by the formula:

d = (s₁ × s₂ / (s₁ - s₂)) × Δt

where d is the distance, s₁ = 42 km/h is the initial speed, s₂ = 14 km/h is the reduced speed, and Δt is the difference in travel time.

Given that the train is late by 35 minutes, we convert this time difference into hours:

Δt = 35/60 hours = 7/12 hours

Substituting these values into the formula:

d = (42 × 14 / (42 - 14)) × (7 / 12)

d = (588 / 28) × (7 / 12)

d = 21 × 7 / 12

d = 147 / 12

d = 12.25 km

Explanation

Let the fourth number be x.

Using the given relations, the other three numbers can be expressed in terms of x: The third number is 3 times the fourth number, which is 3x. The second number is 1.5 times the third number, which is 1.5 × 3x = 4.5x. The first number is one-third of the second number, which is 4.5x / 3 = 1.5x.

The average of the four numbers is 10. Therefore, the sum of the four numbers is: Average × Count = 10 × 4 = 40

Summing the terms: 1.5x + 4.5x + 3x + x = 40 10x = 40 x = 4

Substituting x = 4 to find the values of all four numbers: First number = 1.5 × 4 = 6 Second number = 4.5 × 4 = 18 Third number = 3 × 4 = 12 Fourth number = 4

Comparing these values, the largest number is 18.

Explanation

Using the algebraic identity (a - b)² = a² - 2ab + b², the expression 144x² - 36x + 9/4 can be factored by identifying the components:

a² = 144x², which gives a = 12x b² = 9/4, which gives b = 3/2

Checking the middle term 2ab: 2ab = 2 × 12x × 3/2 = 36x

This matches the middle term of the given polynomial. Substituting these values into the identity yields: 144x² - 36x + 9/4 = (12x - 3/2)²

Explanation

The ratio of the total surface area (TSA) of a cylinder to its curved surface area (CSA) is given by their formulas:

TSA = 2πr(r + h) CSA = 2πrh

Taking the ratio of TSA to CSA: TSA / CSA = 2πr(r + h) / 2πrh = (r + h) / h

Given that the radius r = 9 cm and the height h = 25 cm, substituting these values into the simplified ratio formula yields: Ratio = (9 + 25) / 25 = 34 / 25

This simplifies to the ratio 34:25.

Explanation

For any three numbers a, b, and c, their fourth proportional x is defined by the relation:

a/b = c/x

Substituting the given values, a = 18, b = 36, and c = 52, we get:

18/36 = 52/x

Simplifying the fraction on the left side:

1/2 = 52/x

Solving for x:

x = 52 × 2 = 104

Explanation

The volume of the metal remains constant when the sphere is melted and drawn into a wire. Therefore, the volume of the solid metallic sphere is equal to the volume of the cylindrical wire.

The formula for the volume of a sphere is 4/3 × π × R³ and the volume of a cylinder is π × r² × L, where R is the radius of the sphere, r is the radius of the wire, and L is the length of the wire.

Given: Radius of the sphere, R = 15 cm Radius of the wire, r = 15 mm = 1.5 cm

Equating the volumes: 4/3 × π × R³ = π × r² × L

Canceling π from both sides: 4/3 × R³ = r² × L

Substitute the given values into the equation: 4/3 × 15³ = 1.5² × L 4/3 × 3375 = 2.25 × L 4 × 1125 = 2.25 × L 4500 = 2.25 × L L = 4500 / 2.25 L = 2000 cm

Explanation

Correct Answer: D

The net profit percentage resulting from a markup followed by a discount can be calculated directly using the successive percentage formula:

Net profit percentage = x + y + xy/100

In this case, the markup percentage is x = 25 and the discount percentage is y = -12. Substituting these values into the formula:

Net profit percentage = 25 - 12 + (25 × (-12)) / 100 Net profit percentage = 13 - 300/100 Net profit percentage = 13 - 3 = 10%

Explanation

Dividing the given equation b² - 4b - 1 = 0 by b on both sides gives: b - 4 - 1/b = 0 b - 1/b = 4

Squaring both sides of this equation: (b - 1/b)² = 4² b² + 1/b² - 2 = 16 b² + 1/b² = 18

The expression to evaluate can be rearranged and grouped as: (b² + 1/b²) + 3(b - 1/b)

Substituting the values of (b² + 1/b²) and (b - 1/b) into this expression: 18 + 3(4) = 18 + 12 = 30

Explanation

The respondents till the age of 30 years include those in the Less than 20 years category and the From 21 years to 30 years category.

Total number of respondents till the age of 30 years = 36 + 34 = 70

Number of respondents in this age range who indicated Dandiya as their favourite style of dance = 7 + 8 = 15

The percentage of these respondents is calculated as: Percentage = (15 / 70) × 100 = 21.4285...% ≈ 21.43%

Explanation

The relationship between the Selling Price (SP), Marked Price (MP), and Discount Percentage is given by the formula:

SP = MP × (100 - Discount%) / 100

Substituting the given values, SP = 1755 and Discount% = 35, into the formula:

1755 = MP × (100 - 35) / 100

1755 = MP × 65 / 100

MP = 1755 × 100 / 65

MP = 27 × 100

MP = 2700

Explanation

Let n be the number of persons in the group.

The net increase in the total age of the group is the difference between the age of the incoming person and the outgoing person: 66 - 24 = 42 years

The relation between the change in total age and the change in average age is: Net increase in total age = Increase in average age × Number of persons

Substituting the given values: 42 = 6 × n n = 7

Explanation

Let the cost price of the article for A be CP.

A sells the article to B at a 10% profit. The cost price for B is: CP × (1 + 10/100) = 1.1 × CP

B sells the article to C at a 25% profit. The cost price for C is: 1.1 × CP × (1 + 25/100) = 1.1 × 1.25 × CP

Since C pays ₹6,875: 1.1 × 1.25 × CP = 6875

Converting decimals to fractions: (11/10) × (5/4) × CP = 6875 (55/40) × CP = 6875 (11/8) × CP = 6875

Solving for CP: CP = (6875 × 8) / 11 CP = 625 × 8 = 5000

Explanation

The present value (PV) under compound interest is calculated using the formula:

PV = A / (1 + r)ⁿ

Here, A is the amount due (₹90,774), r is the annual interest rate (23% or 0.23), and n is the time period (2 years).

Substituting the given values into the formula:

PV = 90774 / (1 + 0.23)²

PV = 90774 / (1.23)²

PV = 90774 / 1.5129

PV = 60000

Explanation

According to the BODMAS rule, calculations must be performed in order of brackets from innermost to outermost, followed by subtraction.

First, solve the innermost parenthesis: 28 - 24 = 4

Next, add this result within the curly braces: 40.22 + 4 = 44.22

Now, perform the subtraction within the square brackets: 86.23 - 44.22 = 42.01

Finally, complete the outer subtraction: 178.01 - 42.01 = 136

Explanation

The formula for the depreciated value A of an asset after n years, given its initial cost P and an annual depreciation rate R, is:

A = P × (1 - R/100)ⁿ

Here, the initial cost P is ₹10,00,000, the depreciation rate R is 10% per annum, and the time period n is 3 years. Substituting these values into the formula:

A = 10,00,000 × (1 - 10/100)³ A = 10,00,000 × (0.9)³ A = 10,00,000 × 0.729 A = 7,29,000

This calculation directly yields the depreciated value of the residential flat after 3 years.

Explanation

To find the average annual percentage increase, first calculate the total percentage increase over the decade (10 years) and then divide it by the number of years.

Total population increase = 2,62,500 - 1,75,000 = 87,500

Total percentage increase over 10 years = (Total population increase / Original population) × 100 Total percentage increase = (87,500 / 1,75,000) × 100 = 50%

Average annual percentage increase = Total percentage increase / Number of years Average annual percentage increase = 50% / 10 = 5%

Explanation

The surface area of a sphere is given by the formula: Surface Area = 4πr²

where r is the radius of the sphere.

Given that the diameter of the sphere is 21 cm, the radius is: r = 21/2 cm

Substituting the values into the formula with π = 22/7: Surface Area = 4 × (22/7) × (21/2)² Surface Area = 4 × (22/7) × (441/4) Surface Area = 22 × 63 Surface Area = 1386 cm²

Explanation

Since the distance traveled is constant, the speed of the train is inversely proportional to the time taken.

The ratio of the time taken in the two scenarios is T₁ : T₂ = 6 : 9 = 2 : 3.

Therefore, the ratio of the corresponding speeds is S₁ : S₂ = 3 : 2.

The difference in speed is 3 - 2 = 1 unit, which corresponds to the given speed reduction of 13 km/h.

This means 1 unit = 13 km/h.

The original speed S₁ = 3 × 13 = 39 km/h.

The distance between the two stations is original speed × original time = 39 km/h × 6 hours = 234 km.

Explanation

Let the number of black tablet covers be B and the number of white tablet covers be W. The ratio of black to white tablet covers is given as B:W = 5:9.

Given that the number of white tablet covers W is 450, we can set up the proportion:

B = W × (5/9)

Substituting W = 450 into the equation:

B = 450 × 5/9

B = 50 × 5

B = 250

Explanation

Using the algebraic identity for the sum of cubes: a³ + b³ = (a + b)(a² - ab + b²)

Let a = 777 and b = 423. The first part of the expression can be written as: (a³ + b³) / (a² - ab + b²) = a + b

Substituting the values of a and b: 777 + 423 = 1200

Now, evaluate the second part of the expression: 77 - 47 = 30

Dividing the simplified first part by the second part: 1200 ÷ 30 = 40

Explanation

Correct Answer: D

Using the algebraic identity (a + b)² = a² + b² + 2ab, let a = tan θ and b = cot θ.

Since tan θ and cot θ are reciprocals of each other, their product is 1: tan θ × cot θ = 1

Squaring both sides of the given equation tan θ + cot θ = 4 yields: (tan θ + cot θ)² = 4² tan²θ + cot²θ + 2(tan θ)(cot θ) = 16

Substituting tan θ × cot θ = 1 into the equation gives: tan²θ + cot²θ + 2(1) = 16 tan²θ + cot²θ = 16 - 2 tan²θ + cot²θ = 14

Explanation

The formula for the total amount accumulated under compounding is A = P(1 + r)ⁿ, where P is the principal amount, r is the interest rate per conversion period, and n is the number of conversion periods.

When interest is compounded half-yearly, the annual interest rate is halved and the number of compounding periods is doubled.

Given: Principal P = 40,000 Annual interest rate = 20%, so the half-yearly rate r = 20% / 2 = 10% = 0.1 Time = 2 years 6 months = 2.5 years, which gives the number of half-yearly periods n = 2.5 × 2 = 5

Substituting these values into the formula: A = 40,000 × (1 + 0.1)⁵ A = 40,000 × (1.1)⁵ A = 40,000 × 1.61051 A = 64,420.40

The compound interest (CI) is the difference between the accumulated amount and the principal: CI = A - P CI = 64,420.40 - 40,000 CI = 24,420.40

Explanation

The given equation is 8x³ + 27y³ + 64z³ = 72xyz.

This can be rewritten in the standard algebraic form: (2x)³ + (3y)³ + (4z)³ = 3 × (2x) × (3y) × (4z)

Using the algebraic identity, if a³ + b³ + c³ = 3abc, then a + b + c = 0 or a = b = c.

By comparing the terms, we have a = 2x, b = 3y, and c = 4z.

Applying the condition a + b + c = 0 gives: 2x + 3y + 4z = 0

Rearranging the terms, we get: 2x + 3y = -4z

Explanation

To find the most favourite drink of the people in winter, we look at the values in the Winter row of the table:

Drink A: 25 Drink B: 32 Drink C: 40 Drink D: 50

Comparing these values, Drink D has the highest number of purchases with 50, making it the most favourite drink during the winter season. This corresponds to option C.

Explanation

Let the distance driven on Monday be M km.

The distance driven on Tuesday is 12.5% less than Monday. Since 12.5% is equivalent to the fraction 1/8, the distance driven on Tuesday is: Tuesday = M × (1 - 1/8) = (7/8)M

The distance driven on Wednesday is 20% more than Tuesday. Since 20% is equivalent to the fraction 1/5, the distance driven on Wednesday is: Wednesday = Tuesday × (1 + 1/5) = Tuesday × (6/5)

Substituting the expression for Tuesday into the Wednesday equation: Wednesday = (7/8)M × (6/5) = (21/20)M

Given that Sonam drives 336 km on Wednesday, we set up the equation: (21/20)M = 336 M = 336 × (20/21) M = 16 × 20 = 320

Explanation

For two successive discounts of a% and b%, the single equivalent discount is calculated using the formula:

Equivalent Discount = a + b - ab/100

Applying this formula to each scheme:

For Scheme (i), the equivalent discount is 20 + 12 - (20 × 12)/100 = 32 - 2.4 = 29.6%

For Scheme (ii), the equivalent discount is 25 + 5 - (25 × 5)/100 = 30 - 1.25 = 28.75%

For Scheme (iii), the equivalent discount is 30 + 3 - (30 × 3)/100 = 33 - 0.9 = 32.1%

A customer always benefits from the highest discount. Since 32.1% is the highest discount among the three options, Scheme (iii) is the best scheme for the customer.

Explanation

To find the profit percentage, first calculate the cost price and selling price per unit.

Cost Price of 1 dozen toys = ₹375 Since 1 dozen contains 12 toys, the Cost Price of 1 toy = 375 ÷ 12 = ₹31.25

The Selling Price of 1 toy is given as ₹33.

Profit per toy = Selling Price - Cost Price = 33 - 31.25 = ₹1.75

Profit percentage = (Profit ÷ Cost Price) × 100 Profit percentage = (1.75 ÷ 31.25) × 100 = 5.6%

Explanation

The depreciated value A of an asset after n years, with a present value P and an annual depreciation rate R, is given by the formula:

A = P × (1 - R/100)ⁿ

Substituting the given values, P = 35000, R = 10, and n = 2:

A = 35000 × (1 - 10/100)² A = 35000 × (9/10)² A = 35000 × 81/100 A = 350 × 81 A = 28350

Explanation

The expression can be simplified using the algebraic identity: a³ - b³ = (a - b)(a² + ab + b²)

Letting a = 5.4 and b = 0.4, we have: b³ = (0.4)³ = 0.064 ab = 5.4 × 0.4 = 2.16 b² = (0.4)² = 0.16

Substituting these values into the algebraic relation: [(5.4)³ - 0.064] ÷ [(5.4)² + 2.16 + 0.16] = [(5.4)³ - (0.4)³] ÷ [(5.4)² + (5.4 × 0.4) + (0.4)²]

This simplifies directly to: a - b = 5.4 - 0.4 = 5

Explanation

Let the initial total volume of the mixture in the beaker be V litres. The initial ratio of liquid X to liquid Y is 5:3, which means liquid X is 5/8 of the total mixture and liquid Y is 3/8 of the total mixture.

When 6 litres of the mixture is drawn off, the remaining volume of the mixture is V - 6 litres. In this remaining mixture, the ratio of X to Y remains 5:3.

Therefore, the remaining quantity of X is (5/8) × (V - 6) and the remaining quantity of Y is (3/8) × (V - 6).

When 6 litres of liquid Y is added to the mixture, the new quantity of Y becomes (3/8) × (V - 6) + 6.

The new ratio of X to Y is given as 5:7. Setting up the equation:

[(5/8) × (V - 6)] / [(3/8) × (V - 6) + 6] = 5/7

Dividing the numerator of both sides by 5:

[(1/8) × (V - 6)] / [(3/8) × (V - 6) + 6] = 1/7

Cross-multiplying to solve for V:

(7/8) × (V - 6) = (3/8) × (V - 6) + 6

(4/8) × (V - 6) = 6

½ × (V - 6) = 6

V - 6 = 12

V = 18 litres

Thus, the initial total volume of the mixture was 18 litres.

The initial quantity of liquid X was:

(5/8) × 18 = 90/8 = 11.25 litres

Explanation

To find the largest six-digit number exactly divisible by 81, start with the largest possible six-digit number, which is 999999. Dividing 999999 by 81 yields a quotient of 12345 and a remainder.

999999 ÷ 81 = 12345 with a remainder of 54

Subtracting this remainder from 999999 gives the largest six-digit number that is perfectly divisible by 81:

999999 - 54 = 999945

Explanation

Let the total volume of the mixture be 10 units. Initial volume of Water = 3 units Initial volume of Medicine = 7 units

Let x be the fraction of the mixture that is replaced with water. When x fraction of the mixture is removed, the remaining fraction of the mixture is (1 - x). Since we only add back water, the final volume of medicine depends solely on this remaining fraction: Final Medicine = Initial Medicine × (1 - x) Final Medicine = 7 × (1 - x)

In the final 1:1 mixture of 10 units, both water and medicine must be equal, meaning each must be 5 units. 7 × (1 - x) = 5 1 - x = 5/7 x = 1 - 5/7 x = 2/7

Explanation

Let the time taken by B to complete the work be x days. Since A is 3 times as fast as B, the time taken by A is x/3 days.

The difference in time taken by B and A to complete the work is 32 days: x - x/3 = 32 2x/3 = 32 x = 48 days

Thus, B takes 48 days and A takes 16 days to complete the work individually.

Working together, the time taken by A and B to complete the work is: Time = (A × B) / (A + B) Time = (16 × 48) / (16 + 48) Time = 768 / 64 = 12 days

Explanation

From the given equation, we have: 1.5x = 0.04y

We can find the ratio of x to y as: x/y = 0.04/1.5 = 4/150 = 2/75

Thus, we can let x = 2 and y = 75.

Substituting these values into the expression: (y - x)/(y + x) = (75 - 2)/(75 + 2) = 73/77

Explanation

The radius r of the cylinder base is half of the diameter, which is 20/2 = 10 cm.

The height h of the cylinder is two times the radius of its base, which gives h = 2 × 10 = 20 cm.

The volume V of a cylinder is given by the formula V = πr²h.

Substituting the values into the formula: V = π × 10² × 20 V = π × 100 × 20 V = 2000π cm³

Explanation

Using the algebraic identity for the difference of two squares: a² - b² = (a - b)(a + b)

Substituting a = 82 and b = 18: 82² - 18² = (82 - 18) × (82 + 18) 82² - 18² = 64 × 100 = 6400

Taking the power of 0.5 is equivalent to finding the square root: (6400)⁰.⁵ = √6400 = 80

Explanation

Using the work rate formula, the individual rate of work and the combined rate of work are related by:

1/A + 1/B = 1/Combined

Here, A can complete the work in 15 days, and A and B together can complete it in 9 days. Substituting these values into the equation:

1/15 + 1/B = 1/9

Rearranging the equation to solve for the rate of B:

1/B = 1/9 - 1/15

The least common multiple of 9 and 15 is 45. Converting the fractions to have a common denominator:

1/B = 5/45 - 3/45 1/B = 2/45

Taking the reciprocal to find the number of days B needs to complete the work alone:

B = 45/2 = 22.5 days

Explanation

The discount percentage is calculated using the formula:

Discount % = (Free Items / Total Items Received) × 100

Here, the number of free items is 6, and the number of paid items is 24.

Total items received = 24 + 6 = 30

Substituting these values into the formula:

Discount % = (6 / 30) × 100 = (1 / 5) × 100 = 20%

Explanation

To find the student with the lowest aggregate marks, we calculate the sum of marks obtained by each student in all four subjects:

Aggregate marks of P = 65 + 75 + 72 + 58 = 270 Aggregate marks of Q = 73 + 67 + 78 + 52 = 270 Aggregate marks of R = 71 + 59 + 55 + 65 = 250 Aggregate marks of S = 57 + 73 + 58 + 71 = 259

Comparing these totals, R has the lowest aggregate score of 250 marks.