SSC CHSL Tier 1 2021 Quantitative Aptitude Questions with Solutions

Explanation

To find the teacher's age, we can use the average deviation method:

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

Here, the initial number of students is 36, and their average age is 14 years. When the teacher is included, the average age rises by 1 year, making the new average 15 years.

Teacher's age = 15 + 36 × 1 = 51 years

Alternatively, this can be calculated using the total sum of ages:

Total age of 36 students = 36 × 14 = 504 years Total age of 37 people (including the teacher) = 37 × 15 = 555 years Teacher's age = 555 - 504 = 51 years

Explanation

In triangle ABC, since DE is parallel to BC, triangle ADE is similar to triangle ABC because ∠ADE = ∠ABC and ∠AED = ∠ACB.

The ratio of corresponding sides in similar triangles is equal: DE : BC = AD : AB

The ratio of AD to DB is given as 9 : 8. If AD is represented as 9x and DB as 8x, then the total length AB is: AB = AD + DB = 9x + 8x = 17x

Substituting these values to find the ratio of DE to BC: DE : BC = 9x : 17x = 9 : 17

Explanation

Manoj fetches 5 litres of water in 4 minutes, which means his fetching rate is 5/4 litres per minute. Swathi fetches 4 litres of water in 5 minutes, which gives her a fetching rate of 4/5 litres per minute.

Their combined fetching rate per minute when working together is the sum of their individual rates: 5/4 + 4/5 = (25 + 16) / 20 = 41/20 litres per minute.

The total time required to fetch 205 litres of water together is calculated by dividing the total volume by their combined rate: Time = 205 ÷ (41/20) = 205 × 20 / 41 = 5 × 20 = 100 minutes.

Explanation

A number is divisible by 36 if it is divisible by both 4 and 9, because 36 is the product of these two co-prime factors.

To test divisibility by 9, the sum of the digits of the number must be a multiple of 9. For the number 136216, the sum of its digits is:

1 + 3 + 6 + 2 + 1 + 6 = 19

Since 19 is not divisible by 9, the number 136216 is not divisible by 9. Consequently, it cannot be divisible by 36.

Explanation

Let r be the radius of the circle and O be the center. The perpendicular from the center O to any chord bisects the chord.

For the chord RS of length 24 cm, its half-length is 12 cm. Let its perpendicular distance from the center O be x cm. Since PQ is shorter than RS, it is further from the center. Thus, for the chord PQ of length 10 cm, its half-length is 5 cm and its perpendicular distance from the center O is x + 7 cm.

Applying the Pythagorean theorem to both right-angled triangles: r² = x² + 12² r² = (x + 7)² + 5²

Equating the two expressions: x² + 144 = (x + 7)² + 25 x² + 144 = x² + 14x + 49 + 25 144 = 14x + 74 14x = 70 x = 5 cm

Substituting x = 5 back into the equation for r²: r² = 5² + 12² r² = 25 + 144 = 169 r = √169 = 13 cm

Explanation

The total cost price of the mixture is the sum of the costs of the two individual quantities of rice.

Cost of the first variety of rice = 26 kg × £20/kg = £520 Cost of the second variety of rice = 30 kg × £36/kg = £1080 Total cost price = £520 + £1080 = £1600

The total weight of the mixture is 26 kg + 30 kg = 56 kg.

The total selling price is calculated by multiplying this total weight by the selling price per kg.

Total selling price = 56 kg × £30/kg = £1680

The profit made by the seller is the difference between the total selling price and the total cost price.

Profit = £1680 - £1600 = £80

The profit percentage is calculated using the formula: Profit Percentage = (Profit ÷ Cost Price) × 100 Profit Percentage = (80 ÷ 1600) × 100 = 5%

Explanation

According to the BODMAS rule, mathematical operations must be performed in the order of brackets, division, multiplication, addition, and subtraction. Here, the expression contains a division by 8 at the end.

First, solve the innermost parentheses: 5 - 3 = 2

Next, solve the nested brackets: 2 - 2 × 2 + 5 = 2 - 4 + 5 = 3

Now, solve the outer square brackets: 2 + 3 × 3 - 10 = 2 + 9 - 10 = 1

Finally, substitute these values back into the main expression and perform division followed by subtraction: 52 - 5 × 1 ÷ 8 = 52 - 5 ÷ 8 52 - 0.625 = 51.375

Explanation

The distance d covered when a journey is made at two different speeds with a known difference in time is given by the relation:

d = (v₁ × v₂) ÷ (v₁ - v₂) × Δt

Where v₁ is the initial speed of 60 km/h, v₂ is the slower speed of 45 km/h, and Δt is the time delay of 20 minutes.

First, convert the time delay from minutes to hours: Δt = 20/60 hours = 1/3 hours

Substituting the values into the formula: d = (60 × 45) ÷ (60 - 45) × 1/3 d = 2700 ÷ 15 × 1/3 d = 180 × 1/3 d = 60 km

Explanation

Let the radius of the solid metallic sphere be R and the radius of the base of the cone be r.

The surface area of a sphere is given by: Surface Area = 4πR²

Substituting the given values: 4 × (22/7) × R² = 616 R² = (616 × 7) / 88 R² = 49 R = 7 cm

When the sphere is melted and recast into a cone, their volumes are equal. Using the volume formulas: Volume of sphere = Volume of cone (4/3)πR³ = (1/3)πr²h

Substituting R = 7 cm and height h = 28 cm: 4 × 7³ = r² × 28 4 × 7 × 7 × 7 = r² × 28 28 × 7 × 7 = 28 × r² r² = 49 r = 7 cm

The diameter of the base of the cone is: Diameter = 2r = 2 × 7 = 14 cm

Explanation

The area of a square is given by the formula: Area = side²

We are given the area of the square as 4x² - 12x + 9. We can write this expression as a perfect square by using the algebraic identity: (a - b)² = a² - 2ab + b²

Comparing the given expression with the identity: a² = 4x², which gives a = 2x b² = 9, which gives b = 3 -2ab = -2 × 2x × 3 = -12x

Substituting these values into the identity: 4x² - 12x + 9 = (2x - 3)²

Since Area = side², we have: side² = (2x - 3)² side = 2x - 3

Explanation

The volume V of a sphere of radius r is given by the formula:

V = 4/3 π r³

Given that the volume is 4851 cm³ and π = 22/7, we can substitute these values into the formula:

4851 = 4/3 × 22/7 × r³

4851 = 88/21 × r³

Rearranging the terms to solve for r³:

r³ = (4851 × 21) / 88

By dividing both 4851 and 88 by their common factor of 11, we get:

r³ = (441 × 21) / 8

Since 441 is the square of 21 (21²), the expression can be simplified as:

r³ = (21² × 21) / 2³

r³ = 21³ / 2³

r³ = (21/2)³

Taking the cube root on both sides:

r = 21/2

r = 10.5 cm

Explanation

The algebraic identity for the difference of two cubes is: a³ - b³ = (a - b)³ + 3ab(a - b)

Substituting the given values a - b = 3 and a³ - b³ = 999 into the formula: 999 = 3³ + 3ab(3) 999 = 27 + 9ab 9ab = 972 ab = 108

To find the value of a + b, use the relation: (a + b)² = (a - b)² + 4ab

Substituting the known values: (a + b)² = 3² + 4 × 108 (a + b)² = 9 + 432 (a + b)² = 441 a + b = 21

Now, apply the difference of squares formula: a² - b² = (a - b)(a + b)

Substituting the values of a - b and a + b: a² - b² = 3 × 21 = 63

Explanation

By the rule of alligation, the ratio of the quantities of wheat sold at 10% gain to that sold at 25% gain is: (25 - 15) : (15 - 10) = 10 : 5 = 2 : 1

The sum of the ratios is 2 + 1 = 3 parts, which represents the total quantity of 120 kg of wheat.

The quantity of wheat sold at 10% gain corresponds to 2 parts of the total 3 parts: Quantity = (2/3) × 120 = 80 kg.

Explanation

Let the time taken by B to complete the work alone be t days.

The time taken by A to complete half of the work is one-sixth of the time taken by B, which is t/6 days.

Therefore, the time taken by A to complete the entire work is 2 × (t/6) = t/3 days.

Since efficiency is inversely proportional to the time taken, the ratio of the efficiency of A to B is (3/t) : (1/t) = 3 : 1. Let the efficiency of A be 3 units per day and B be 1 unit per day.

Working together, their combined efficiency is 3 + 1 = 4 units per day.

Given that they complete the work together in 16 days, the total work is 16 × 4 = 64 units.

The time taken by B to complete the work alone is the total work divided by B's efficiency, which is 64 / 1 = 64 days.

Explanation

The volume V of a cuboidal box with length l, breadth b, and height h is given by the formula: V = lbh

The areas of three adjacent faces are given as: lb = 729 cm² bh = 529 cm² hl = 289 cm²

Multiplying these three equations yields: (lb) × (bh) × (hl) = l²b²h² = (lbh)² = V²

Therefore, the volume V can be calculated as: V = √(729 × 529 × 289) V = √729 × √529 × √289

Since 27² = 729, 23² = 529, and 17² = 289, the square roots are: V = 27 × 23 × 17 V = 621 × 17 V = 10557 cm³

Explanation

According to the divisibility rule for 3, a number is divisible by 3 if and only if the sum of its individual digits is divisible by 3.

For the number 7865001, the sum of the digits is calculated as: 7 + 8 + 6 + 5 + 0 + 0 + 1 = 27

Since the sum, 27, is a multiple of 3 (27 ÷ 3 = 9), the number 7865001 is divisible by 3.

Explanation

For any positive real numbers, the product of their square roots can be combined under a single square root using the property √x × √y × √z = √(x × y × z).

Applying this to the given expression: √(a⁻¹b) × √(b⁻¹c) × √(c⁻¹a) = √(a⁻¹b × b⁻¹c × c⁻¹a)

By using the laws of exponents, we can simplify the product inside the radical: a⁻¹b × b⁻¹c × c⁻¹a = (b/a) × (c/b) × (a/c)

Combining the fractions: (b × c × a) / (a × b × c) = 1

Taking the square root of this simplified term: √1 = 1

Explanation

Cost price of 1000 grams of rice = ₹32 Cost price of 900 grams of rice = (32 / 1000) × 900 = ₹28.8

Since the dealer sells 900 grams while charging for 1000 grams, the selling price for this quantity is the selling price of 1 kg: Selling price of this quantity = ₹40

Actual Profit = Selling Price - Cost Price Actual Profit = 40 - 28.8 = ₹11.2

Actual Profit Percentage = (Actual Profit / Cost Price) × 100 Actual Profit Percentage = (11.2 / 28.8) × 100 Actual Profit Percentage = (7 / 18) × 100 = 38.88% ≈ 38.9%

Explanation

By finding a common denominator for the terms, we simplify the expression as follows:

x²/yz + y²/zx + z²/xy = (x³ + y³ + z³) / xyz

According to the standard algebraic identity: x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)

Given that x + y + z = 0, the entire right-hand side of the identity becomes zero, which simplifies the equation to: x³ + y³ + z³ = 3xyz

Substituting this relationship back into our simplified expression yields: 3xyz / xyz = 3

Explanation

To simplify the expression, we apply the BODMAS rule, starting from the innermost grouping symbol, which is the vinculum (bar) over n + p.

First, resolve the term under the vinculum: n - (n + p) = n - n - p = -p

Substitute this back into the expression: 2[8p + 5{n - 2(-p) + 4p}]

Next, simplify the terms inside the curly brackets: n - 2(-p) + 4p = n + 2p + 4p = n + 6p

Now, substitute this result back and expand the terms inside the square brackets: 8p + 5(n + 6p) = 8p + 5n + 30p = 38p + 5n

Finally, multiply the entire expression by the outer factor 2: 2(38p + 5n) = 76p + 10n

Explanation

To find the number of students using a bicycle, we use the ratio of transport modes, which is given as 6:3:1 for school bus, bike, and bicycle respectively.

The sum of the ratio terms is: 6 + 3 + 1 = 10

Since the total strength of the school is 1200, the value of one part of the ratio is: 1200 ÷ 10 = 120

The proportion of students using a bicycle is 1 part of the total. Therefore, the number of students who use a bicycle is: 1 × 120 = 120

Explanation

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side. For three side lengths ordered such that a ≤ b ≤ c, the relation a + b > c must be satisfied. For the side lengths 18, 23, and 41, the sum of the two smaller sides is 18 + 23 = 41. Since 41 is equal to the third side 41 and not strictly greater than it, these lengths violate the triangle inequality and cannot form a triangle.

Explanation

The expression is evaluated using the BODMAS rule, which stands for Brackets, Of, Division, Multiplication, Addition, and Subtraction.

First, simplify the terms inside the innermost brackets: 18 - 6 = 12 1 + 2 = 3

Next, evaluate the multiplication within the square brackets: -2 × 3 = -6

Now, substitute these values back into the square brackets to simplify further: 12 + (-6) = 6

Substituting this value back into the original expression gives: 1800 ÷ 10[6]

According to the order of operations where brackets and their implicit multiplication are solved first, simplify the term 10[6]: 10 × 6 = 60

Finally, perform the division: 1800 ÷ 60 = 30

Explanation

The weighted average formula relates the averages and counts of the two groups to the overall average:

Total score of the class = (Number of boys × Average of boys) + (Number of girls × Average of girls)

The total number of students in the class is 26 boys + 24 girls = 50 students.

Using the given average of 85 for the entire class, the total score of the class is: 50 × 85 = 4250

The total score of the boys is: 26 × 82 = 2132

Subtracting the boys' total score from the class total score gives the total score of the girls: 4250 - 2132 = 2118

To find the average score of the girls, divide their total score by the number of girls: 2118 ÷ 24 = 88.25

Explanation

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

MP / CP = (100 + P) / (100 - D)

where P is the profit percentage and D is the discount percentage.

Substituting CP = 85, P = 20, and D = 15 into the formula:

MP / 85 = (100 + 20) / (100 - 15)

MP / 85 = 120 / 85

MP = 120

Explanation

The volume of a cylinder is calculated using the formula: V = π r² h

Given: Radius of the base, r = 5 cm Height of the cylinder, h = 24 cm Value of π = 3.14

Substituting these values into the formula: V = 3.14 × 5² × 24 V = 3.14 × 25 × 24 V = 3.14 × 600 V = 1884 cm³

Explanation

Using the trigonometric double-angle identity, we have: sin 2θ = 2 sin θ cos θ

This can be rewritten as: sin θ cos θ = ½ sin 2θ

Substituting θ = 15° into the given expression: 100(sin 15° cos 15°) = 100 × ½ sin(2 × 15°) = 50 sin 30°

Since sin 30° = ½, we substitute this value to get: 50 × ½ = 25

Explanation

The perimeter of an isosceles triangle is given by the formula: Perimeter = 2x + y

where x is the length of each of the two equal sides, and y is the length of the unequal side.

Substituting the given values, we get: 80 = 2x + 20

Subtracting 20 from both sides: 2x = 60

Dividing by 2 gives: x = 30 cm

Explanation

Let the original number be x.

When a number is increased by 25%, it becomes 1.25x or 5/4 of x. When this new value is decreased by 10%, it becomes 90% of its value, which can be represented as 9/10 of the increased number.

Setting up the equation for the final result of 72: x × (5/4) × (9/10) = 72

Simplifying the equation: x × 45/40 = 72 x × 9/8 = 72 x = (72 × 8) / 9 x = 8 × 8 x = 64

Explanation

The given table presents the cumulative frequency of marks obtained by a group of students. The category "Less than 50" represents the cumulative count of all students who scored below 50. Since this is the highest upper limit provided in the cumulative distribution, it encompasses every student in the group. Therefore, the corresponding frequency for "Less than 50", which is 10, is the total number of students in the group.

Explanation

Using the formula for compound interest, the amount after n years is given by: Aₙ = P(1 + R/100)ⁿ

where P is the principal sum and R is the yearly rate of interest.

The amount at the end of 3 years (A₃) is £2,000, and the amount at the end of 4 years (A₄) is £2,400.

Taking the ratio of the amount in the fourth year to that in the third year: A₄ / A₃ = [P(1 + R/100)⁴] / [P(1 + R/100)³] A₄ / A₃ = 1 + R/100

Substituting the given amounts: 2400 / 2000 = 1 + R/100 1.2 = 1 + R/100 R/100 = 0.2 R = 20%

Explanation

The downstream speed (D) of the boat is the sum of the speed of the boat in still water and the speed of the river: D = 22 + 8 = 30 km/h

The upstream speed (U) of the boat is the difference between the speed of the boat in still water and the speed of the river: U = 22 - 8 = 14 km/h

Let the distance to be covered be d km. The time taken to cover the distance upstream is d/14 hours, and the time taken downstream is d/30 hours.

According to the question, the upstream time is 4 hours more than the downstream time: d/14 - d/30 = 4

Taking the least common multiple of 14 and 30, which is 210, we get: (15d - 7d) / 210 = 4 8d / 210 = 4 8d = 840 d = 105 km

Explanation

The children whose age is below 11 years but above 8 years are those who are either 9 or 10 years old.

From the given table, the number of children corresponding to these age groups is: For age 9 years: 15 children For age 10 years: 42 children

To find the total number of children in this range, we add the number of children in both categories: 15 + 42 = 57

Explanation

Let k = x + 1/x = -3√2.

The value of x⁵ + 1/x⁵ can be determined using standard algebraic identities: x² + 1/x² = (x + 1/x)² - 2 x³ + 1/x³ = (x + 1/x)³ - 3(x + 1/x) x⁵ + 1/x⁵ = (x² + 1/x²)(x³ + 1/x³) - (x + 1/x)

Substituting the value of k into the first two equations: x² + 1/x² = (-3√2)² - 2 = 18 - 2 = 16 x³ + 1/x³ = (-3√2)³ - 3(-3√2) = -54√2 + 9√2 = -45√2

Substituting these results into the relation for x⁵ + 1/x⁵: x⁵ + 1/x⁵ = 16 × (-45√2) - (-3√2) x⁵ + 1/x⁵ = -720√2 + 3√2 = -717√2

Explanation

Let the total work be represented as 1 unit.

The combined hourly work rate of Ram and Shawan is 1/5 of the job per hour, and Ram's individual work rate is 1/6 of the job per hour.

The work rate of Shawan alone is the difference between the combined rate and Ram's rate: 1/5 - 1/6 = (6 - 5) / 30 = 1/30

Since Shawan completes 1/30 of the job per hour, Shawan alone requires 30 hours to complete the entire job.

Explanation

The discount percentage for schemes of the form Buy A, get B free is calculated using the formula: Discount % = (B / (A + B)) × 100

For Scheme c (Buy 5, get 4 free), the discount percentage is: (4 / (5 + 4)) × 100 = (4/9) × 100 = 44.44%

Evaluating the other schemes to find the maximum: Scheme a offers two successive discounts of 22% and 25%, resulting in a net discount of 22 + 25 - (22 × 25)/100 = 41.5%. Scheme b offers a discount of (2 / (3 + 2)) × 100 = 40%. Scheme d offers a discount of (3 / (4 + 3)) × 100 = 42.86%.

Comparing these values, the discount of 44.44% in Scheme c is the highest.

Explanation

Let the total number of votes cast in the election be V. Since there are only two candidates and all votes are valid, the percentage of votes obtained by the winning candidate is the remaining share of the total votes, which is 100% - 20% = 80%.

The difference between the votes of the winner and the loser is given as 600. Expressing this difference as a percentage of the total votes:

Winner share - Loser share = 80% - 20% = 60%

This 60% of the total votes corresponds to the margin of 600 votes. Therefore, the relation is:

60% of V = 600

(60/100) × V = 600

V = 600 × 100 ÷ 60

V = 1000

Explanation

The given numbers 11, 21, 31, 41, 51, and 61 form an arithmetic progression with a first term of 11 and a last term of 61.

For any arithmetic progression, the average is the mean of the first and the last term.

Average = (First term + Last term) / 2

Substituting the values:

Average = (11 + 61) / 2 = 72 / 2 = 36

Explanation

Using the work equivalence formula: (M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

where M represents the number of workers, D represents the number of days, and W represents the amount of work (number of walls).

Substituting the given values into the formula: (20 × 36) / 24 = (30 × D₂) / 20

720 / 24 = 1.5 × D₂

30 = 1.5 × D₂

D₂ = 20

Explanation

Following the order of operations (BODMAS), we first simplify the numerator of the main fraction:

N = (27/14) ÷ (24/7 of 63/28) - 9/4

First, evaluate the of operation: 24/7 of 63/28 = (24/7) × (63/28) = 54/7

Next, perform the division: (27/14) ÷ (54/7) = (27/14) × (7/54) = 1/4

Thus, the numerator becomes: N = 1/4 - 9/4 = -8/4 = -2

Next, simplify the denominator of the main fraction:

D = (35/8) ÷ (15/4 of 7/48) + 5/16

First, evaluate the of operation: 15/4 of 7/48 = (15/4) × (7/48) = 35/64

Next, perform the division: (35/8) ÷ (35/64) = (35/8) × (64/35) = 8

Thus, the denominator becomes: D = 8 + 5/16 = 133/16

Now, divide the numerator by the denominator:

N/D = -2 / (133/16) = -32/133

Finally, divide this result by 196/95:

(-32/133) ÷ (196/95) = (-32/133) × (95/196)

Using prime factorization to simplify: 95 = 5 × 19 and 133 = 7 × 19, so 95/133 = 5/7 32 = 4 × 8 and 196 = 4 × 49, so 32/196 = 8/49

Multiplying these simplified fractions: (8 × 5) / (7 × 49) = -40/343

Explanation

Let x = tan θ. The given equation is: x + 1/x = 2

Using the algebraic identity (x + 1/x)² = x² + 1/x² + 2: 2² = x² + 1/x² + 2 4 = x² + 1/x² + 2 x² + 1/x² = 4 - 2 = 2

Alternatively, the equation x + 1/x = 2 yields x = 1. Substituting this value directly gives: 1² + 1/1² = 2

Explanation

The production trend shows a continuous year-on-year increase from 2001-02 to 2008-09, with the sole exception of the year 2005-06. In the preceding year 2004-05, the production was 890 tonnes, which declined sharply to 516 tonnes in 2005-06. This represents a drop of 374 tonnes, making 2005-06 the only year in the given period to register a decrease in production before the rising trend resumed in the subsequent years.

Explanation

Since the sum of squares of real numbers is always non-negative, the equation (a - 1)² + (b + 2)² + (c - 1)² = 0 can only hold true if each individual squared term is equal to zero.

Equating each term to zero: a - 1 = 0 → a = 1 b + 2 = 0 → b = -2 c - 1 = 0 → c = 1

Substituting these values into the expression: a² + b² + c² = 1² + (-2)² + 1² = 1 + 4 + 1 = 6

Explanation

The arithmetic mean of a grouped frequency distribution is calculated using the formula:

Mean = ∑(f × x) ÷ ∑f

where x represents the number of major meals and f represents the frequency of students.

We calculate the sum of the products of each meal count and its corresponding frequency:

∑(f × x) = (1 × 3) + (2 × 2) + (3 × 2) + (4 × 5) + (5 × 5) + (6 × 4) + (7 × 6) + (8 × 3) + (9 × 5) + (10 × 3) + (11 × 1)

∑(f × x) = 3 + 4 + 6 + 20 + 25 + 24 + 42 + 24 + 45 + 30 + 11 = 234

The total number of students, which is the sum of the frequencies, is ∑f = 39.

Substituting these values into the formula yields:

Mean = 234 ÷ 39 = 6

Explanation

The given algebraic expression matches the standard algebraic identity: (a + b)² = a² + 2ab + b²

By comparing the given expression with this formula, we can identify: a = 2.19 b = 3.81

Substituting these values into the identity allows us to simplify the calculation significantly: (2.19 + 3.81)² = (6.00)² (6.00)² = 36

Explanation

Let the marked price of the article be M.

The selling price after two successive discounts of 20% and 30% is calculated as: Selling Price = M × (1 - 0.20) × (1 - 0.30) 840 = M × 0.80 × 0.70 840 = M × 0.56 M = 840 ÷ 0.56 M = 1500

The total discount offered is the difference between the marked price and the selling price: Discount = Marked Price - Selling Price Discount = 1500 - 840 = 660

Explanation

The net percentage gain when an item is marked up by x% and then a discount of y% is offered is given by the successive percentage formula:

Net Gain% = x - y - (x × y) / 100

Here, the markup percentage x = 12% and the discount percentage y = 8%. Substituting these values:

Net Gain% = 12 - 8 - (12 × 8) / 100 Net Gain% = 4 - 96 / 100 Net Gain% = 4 - 0.96 Net Gain% = 3.04%

Alternatively, if the cost price of the mobile phone is ₹100, the marked price is 12% higher, which is ₹112. When an 8% discount is given on this marked price, the selling price is calculated as:

Selling Price = 112 × (100 - 8) / 100 Selling Price = 112 × 0.92 Selling Price = ₹103.04

The gain on a cost price of ₹100 is ₹3.04, representing a gain of 3.04%.

Explanation

The formula for the total surface area of a right circular cone is given by πr(r + l), where r is the radius of the base and l is the slant height of the cone.

Given that the diameter of the base is 10 cm, the radius r is 10/2 = 5 cm. The slant height l is 16 cm.

Substituting these values into the formula: Total surface area = (22/7) × 5 × (5 + 16) Total surface area = (22/7) × 5 × 21 Total surface area = 22 × 5 × 3 Total surface area = 330 cm²

Explanation

The formula for the difference (D) between compound interest and simple interest on a principal sum (P) at a rate of interest (R%) for 3 years is:

D = P × (R/100)² × (300 + R)/100

Given: D = 93 R = 10%

Substituting these values into the formula:

93 = P × (10/100)² × (300 + 10)/100

93 = P × (1/10)² × 310/100

93 = P × (1/100) × 31/10

93 = P × 31/1000

P = (93 × 1000) / 31

P = 3 × 1000

P = 3000

Explanation

The total number of members in the cricket team is 11, consisting of 10 players and 1 captain.

The total score of all 11 members is calculated as: Total score = Average score × Total number of members Total score = 32 × 11 = 352

The sum of the scores of the 10 players is: 22 + 11 + 5 + 34 + 21 + 32 + 0 + 28 + 9 + 53 = 215

To find the score of the captain, subtract the sum of the players' scores from the total score of the team: Score of the captain = 352 - 215 = 137