SSC CHSL Tier 1 2022 Quantitative Aptitude Questions with Solutions

Explanation

The trigonometric function cotangent is the reciprocal of the tangent function, defined by the relation cot θ = 1 / tan θ.

For the given angle θ = 60°: cot 60° = 1 / tan 60°

Since the standard trigonometric value of tan 60° is √3, substituting this value yields: cot 60° = 1 / √3

Explanation

The total sum of ₹1,248 is divided in the ratio 2:3 between Ridhaan and Vihaan.

The total ratio parts equal 2 + 3 = 5.

Vihaan's share corresponds to 3 parts of the total 5 parts.

Vihaan's share = (3/5) × 1,248 Vihaan's share = 0.6 × 1,248 = 748.80

Explanation

The standard trigonometric values are tan(45°) = 1 and cos(30°) = √3/2.

This gives the system of linear equations: x + y = 45 x - y = 30

Adding these two equations: 2x = 75 x = 37.5

Subtracting the second equation from the first: 2y = 15 y = 7.5

This directly yields the values x = 37.5 and y = 7.5.

Explanation

The algebraic identity for the product of the sum and difference of two terms, also known as the difference of squares, is formulated as: (a + b)(a - b) = a² - b²

By mapping the given expression (x + 11)(x - 11) to this formula, we identify a = x and b = 11. Substituting these values into the identity gives: (x + 11)(x - 11) = x² - 11²

Calculating the square of 11: 11 × 11 = 121

Substituting this back into the equation results in the simplified expanded form: x² - 121

Explanation

According to Thales's theorem, the angle subtended by a diameter at any point on the circumference of a circle is a right angle. Since AC is the diameter of the circle and B is a point on the circumference, angle ABC is 90°.

In triangle ABC, the sum of all interior angles is 180°: angle BAC + angle ABC + angle BCA = 180°

Substituting the known values into the equation: 40° + 90° + angle BCA = 180° 130° + angle BCA = 180° angle BCA = 50°

Explanation

Let the original number of watermelons be N.

Since the fruit seller sells 45% of the watermelons, the percentage of watermelons remaining with him is: 100% - 45% = 55%

This remaining quantity is given as 495 watermelons. Using the percentage relation: 55% of N = 495 (55 / 100) × N = 495 (11 / 20) × N = 495 N = (495 × 20) / 11 N = 45 × 20 = 900

Explanation

The Selling Price (SP) after successive discounts can be calculated using the formula: SP = MP × (1 - d₁/100) × (1 - d₂/100)

Given: Marked Price (MP) = Rs. 1650 First discount (d₁) = 10% Second discount (d₂) = 20%

Substituting these values: SP = 1650 × (1 - 10/100) × (1 - 20/100) SP = 1650 × 0.9 × 0.8 SP = 1650 × 0.72 SP = 1188

Explanation

If x + 1/x = 2K, squaring both sides of the equation yields: (x + 1/x)² = (2K)² x² + 2 + 1/x² = 4K² x² + 1/x² = 4K² - 2

Squaring this result again to find the fourth power terms gives: (x² + 1/x²)² = (4K² - 2)² x⁴ + 2 + 1/x⁴ = 16K⁴ - 16K² + 4 x⁴ + 1/x⁴ = 16K⁴ - 16K² + 4 - 2 x⁴ + 1/x⁴ = 16K⁴ - 16K² + 2

Explanation

Correct Answer: D

The algebraic identity for the square of a trinomial is: (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

By comparing the given expression a² + 4b² + 9c² - 4ab + 12bc - 6ca with this identity, we can determine the terms x, y, and z: x² = a² which gives x = a y² = 4b² which gives y = -2b (since the term -4ab is negative) z² = 9c² which gives z = -3c (since the term -6ca is negative and 12bc is positive, meaning y and z must have the same sign)

Substituting x = a, y = -2b, and z = -3c into the identity: (a - 2b - 3c)² = a² + (-2b)² + (-3c)² + 2(a)(-2b) + 2(-2b)(-3c) + 2(-3c)(a) = a² + 4b² + 9c² - 4ab + 12bc - 6ca

Explanation

The two-digit odd numbers form an arithmetic progression (AP): 11, 13, 15, ..., 99.

Here, the first term a = 11, the last term l = 99, and the common difference d = 2.

The number of terms n in an AP is given by the formula: l = a + (n - 1)d

Substituting the values: 99 = 11 + (n - 1) × 2 88 = (n - 1) × 2 44 = n - 1 n = 45

The sum S of an AP is given by the formula: S = (n / 2) × (a + l)

Substituting the values: S = (45 / 2) × (11 + 99) S = (45 / 2) × 110 S = 45 × 55 S = 2475

Explanation

Let the original fraction be x/y.

When the numerator x is increased by 140%, the new numerator becomes x + 1.40x = 2.40x.

When the denominator y is decreased by 20%, the new denominator becomes y - 0.20y = 0.80y.

The value of the resulting fraction is given as 12/7: 2.40x / 0.80y = 12/7

Simplifying the ratio of the coefficients on the left side: 3 × (x/y) = 12/7

Dividing both sides by 3 gives: x/y = 4/7

Explanation

The Simple Interest (SI) earned is the difference between the final amount and the principal sum invested: SI = Amount - Principal SI = 6000 - 3000 = 3000

The formula for simple interest is: SI = (P × R × T) / 100

Here, the principal (P) is 3000. Since the annual rate of interest (R) and the time period in years (T) are equal, let R = T = x.

Substituting these values into the formula: 3000 = (3000 × x × x) / 100 3000 = 3000 × x² / 100 1 = x² / 100 x² = 100 x = 10

The annual rate of interest is 10%.

Explanation

The profit percentage is 33.33%, which corresponds to 1/3 in fractional terms.

Using the relation between selling price (SP) and cost price (CP): SP = CP × (1 + Profit Fraction)

Substituting the first selling price of Rs. 960: 960 = CP × (1 + 1/3) 960 = CP × 4/3 CP = 960 × 3/4 = 720

To find the new selling price for a 20% profit, we use the same formula with CP = 720 and a profit fraction of 20% or 0.2: New SP = 720 × (1 + 0.2) New SP = 720 × 1.2 = 864

Explanation

The single equivalent discount percentage for two successive discounts of d₁ = 20% and d₂ = 10% is calculated using the formula: Effective Discount % = d₁ + d₂ - (d₁ × d₂)/100

Substituting the values: Effective Discount % = 20 + 10 - (20 × 10)/100 = 28%

Given that this total discount is Rs.252, the Marked Price (MP) can be determined as: 28% of MP = 252 MP = (252 × 100) / 28 = Rs.900

The Selling Price (SP) of the book is: SP = MP - Discount = 900 - 252 = Rs.648

Given the Cost Price (CP) is Rs.600, the profit earned by Vikram is: Profit = SP - CP = 648 - 600 = Rs.48

Explanation

Using the standard algebraic identity: (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

By substituting the given values of (a + b + c) = 7 and (ab + bc + ca) = 12 into the equation: 7² = a² + b² + c² + 2(12) 49 = a² + b² + c² + 24

Rearranging the terms to solve for the required expression: a² + b² + c² = 49 - 24 a² + b² + c² = 25

Explanation

Since MN is parallel to BC, triangle MAN is similar to triangle ABC.

The ratio of the corresponding sides is: AN/AC = AN / (AN + NC) = 4 / (4 + 5) = 4/9

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides: Area(triangle MAN) / Area(triangle ABC) = (AN/AC)² = (4/9)² = 16/81

Let Area(triangle MAN) = 16x and Area(triangle ABC) = 81x.

The area of the quadrilateral MBCN is the difference between the areas of the two triangles: Area(quadrilateral MBCN) = Area(triangle ABC) - Area(triangle MAN) 130 = 81x - 16x 130 = 65x x = 2

Therefore, the area of triangle MAN is: Area(triangle MAN) = 16x = 16 × 2 = 32 cm²

Explanation

The algebraic identity relating the sum of three terms, their squares, and their pairwise products is: (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Substituting the given values, a + b + c = 0 and ab + bc + ca = -11, into the identity gives: 0² = a² + b² + c² + 2(-11) 0 = a² + b² + c² - 22 a² + b² + c² = 22

Explanation

The area of a triangle is calculated using the formula:

Area = ½ × base × altitude

Substituting the given values of base = 12 cm and altitude = 8 cm into the formula:

Area = ½ × 12 cm × 8 cm Area = 6 cm × 8 cm Area = 48 cm²

Explanation

In any triangle XYZ with incentre I, the angle subtended by the side YZ at the incentre is related to the opposite vertex angle ∠YXZ by the standard formula: ∠YIZ = 90° + ½ ∠YXZ

Substitute the given value ∠YIZ = 115° into this relation: 115° = 90° + ½ ∠YXZ

Subtract 90° from both sides of the equation: 25° = ½ ∠YXZ

Multiply both sides by 2: ∠YXZ = 50°

This calculation yields the vertex angle ∠YXZ as 50°.

Explanation

Complementary angles are two angles whose sum is 90°. For any angle θ, its complementary angle is 90° - θ.

Using the trigonometric co-function identities, the tangent of the complementary angle is defined by the relation:

tan(90° - θ) = cot(θ)

This identity shows that the tangent of the complementary of an angle is equal to the cotangent (cot) of that angle.

Explanation

Correct Answer: D

According to the BODMAS rule, operations must be performed in the order of Brackets, Of, Division, Multiplication, Addition, and Subtraction.

The given expression is: 15 - 3 of 12 ÷ 2 + 3 of 2 ÷ 2

First, evaluate the "of" operations, which have higher priority than division: 3 of 12 = 3 × 12 = 36 3 of 2 = 3 × 2 = 6

Substitute these values back into the expression: 15 - 36 ÷ 2 + 6 ÷ 2

Next, perform the division operations: 36 ÷ 2 = 18 6 ÷ 2 = 3

Substitute these values: 15 - 18 + 3

Finally, perform the subtraction and addition from left to right: 15 - 18 + 3 = -3 + 3 = 0

Explanation

Let the first number be x and the second number be y.

According to the given condition: 45% of x = 6/5 of y

Convert the percentage to a fraction and set up the equation: 45/100 × x = 6/5 × y 9/20 × x = 6/5 × y

Rearranging the terms to find the ratio x : y: x/y = (6/5) × (20/9) x/y = (6 × 20) / (5 × 9) x/y = 120/45 x/y = 8/3

Thus, the ratio between the two numbers is 8:3.

Explanation

The circumference of a circle is given by the formula C = 2πr, where r is the radius. Rearranging this gives r = C / 2π.

For the smaller circle with circumference C₁ = 264 m: r₁ = 264 ÷ (2 × 22/7) = (264 × 7) / 44 = 42 m

For the larger circle with circumference C₂ = 308 m: r₂ = 308 ÷ (2 × 22/7) = (308 × 7) / 44 = 49 m

The area of a circle is given by A = πr². The difference between the area of the larger circle and the smaller circle can be calculated using the algebraic identity a² - b² = (a - b)(a + b):

Difference in Area = πr₂² - πr₁² = π(r₂² - r₁²) Difference in Area = π(r₂ - r₁)(r₂ + r₁) Difference in Area = (22/7) × (49 - 42) × (49 + 42) Difference in Area = (22/7) × 7 × 91 Difference in Area = 22 × 91 = 2002 m²

Explanation

Using the complementary angle identity cot(90° - θ) = tan θ, cot 70° can be written as: cot 70° = cot(90° - 20°) = tan 20°

Substituting this into the given expression: 3/5 (sec² 20° - cot² 70°) = 3/5 (sec² 20° - tan² 20°)

Using the fundamental trigonometric identity sec² θ - tan² θ = 1: 3/5 (1) = 3/5

Explanation

Let the distance covered each way be d km.

Using the formula Time = Distance / Speed, the time taken for the onward journey is d/60 hours, and the time taken for the return journey is d/30 hours.

Since the return journey takes 1 hour longer, we set up the equation:

d/30 - d/60 = 1

To solve for d, multiply the entire equation by the common denominator, 60:

2d - d = 60

d = 60 km

Explanation

The circumference C of a circle is given by the formula C = 2πr, where r is the radius. Substituting the given circumference of 22 cm and using π ≈ 22/7:

22 = 2 × (22/7) × r r = 7/2 = 3.5 cm

The area A of a circle is calculated using the formula A = πr². Substituting the obtained radius:

A = (22/7) × (7/2)² A = (22/7) × (49/4) A = 77/2 = 38.5 cm²

Explanation

Let the total marks of the first three students be T₃. T₃ = 3 × 55 = 165

When two students, A and B, are added, the number of students becomes 5, and the new average is 55 - 5 = 50. Let the total marks of all five students be T₅. T₅ = 5 × 50 = 250

The sum of the marks scored by A and B is the difference between the two total scores: A + B = 250 - 165 = 85

We are given that B scores 15 marks more than A: B = A + 15

Substituting this into the sum equation: A + (A + 15) = 85 2A + 15 = 85 2A = 70 A = 35

Explanation

The time taken to complete a work is directly proportional to the quantity of work done.

Time taken for 100% of the work = 40 days

To find the time taken for 20% of the work, multiply the total days by the required percentage:

Required days = 40 × 20% Required days = 40 × (20 / 100) Required days = 40 × 0.2 Required days = 8 days

Explanation

Using the algebraic identity for the square of a binomial: (p + 1/p)² = p² + 1/p² + 2

Given that p² + 1/p² = 14, substituting this value gives: (p + 1/p)² = 14 + 2 = 16 p + 1/p = 4

Now, using the algebraic identity for the sum of cubes: p³ + 1/p³ = (p + 1/p)³ - 3(p + 1/p)

Substituting p + 1/p = 4 into this relation: p³ + 1/p³ = 4³ - 3 × 4 = 64 - 12 = 52

Explanation

By Thales's Theorem (Basic Proportionality Theorem) in triangle STU, since the line XY is parallel to TU, it divides the sides ST and SU proportionally: SX/XT = SY/UY

Substituting the given values into the ratio: 2/5 = SY/20

Solving for SY: SY = (2 × 20) / 5 = 8 cm

The total length of side SU is the sum of SY and UY: SU = SY + UY = 8 + 20 = 28 cm

Explanation

The circumference of the base of a right circular cone is given by 2πr, where r is the radius of the base.

2πr = 88 2 × (22/7) × r = 88 r = 14 cm

The slant height l of the cone is calculated using the relation l = √(r² + h²), where h is the height of the cone.

l = √(14² + 28²) l = √(196 + 784) l = √980 l = 14√5 cm

The curved surface area of a cone is given by the formula πrl.

Curved surface area = (22/7) × 14 × 14√5 Curved surface area = 44 × 14√5 Curved surface area = 616√5 cm²

Explanation

When two congruent circles of radius r intersect each other such that each passes through the center of the other, the distance between their centers is equal to the radius r.

The line segment joining the centers and the common chord bisect each other at right angles. This forms two right-angled triangles sharing the common chord as their height.

Using the Pythagorean theorem in one of these triangles, the half-length of the common chord is given by √(r² - (r/2)²) = (r√3)/2.

Therefore, the total length of the common chord is twice this value: Length of common chord = r√3

Substituting the given radius r = 6 cm into the formula: Length of common chord = 6√3 cm

Explanation

The length of a direct common tangent (L) between two circles with radii R and r, and distance between their centres d, is given by the formula:

L = √(d² - (R - r)²)

Substituting the given values: L = 30 cm, R = 20 cm, and r = 4 cm:

30 = √(d² - (20 - 4)²) 30 = √(d² - 16²)

Squaring both sides:

900 = d² - 256 d² = 900 + 256 d² = 1156 d = √1156 = 34 cm

Explanation

According to the divisibility rule for 11, a number is divisible by 11 if the difference between the sum of the digits at the odd positions and the sum of the digits at the even positions is either 0 or a multiple of 11.

For the four-digit number 6m61, we identify the digits at each position: Sum of digits at odd positions (first and third from the right) = 1 + m Sum of digits at even positions (second and fourth from the right) = 6 + 6 = 12

The difference between these two sums is: 12 - (1 + m) = 11 - m

For 6m61 to be divisible by 11, this difference (11 - m) must be a multiple of 11. Since m is a single-digit integer from 0 to 9, the only possible value that satisfies this condition is m = 0, which gives a difference of 11.

Explanation

Using the weighted average formula for profit percentage:

Overall Profit % = (n₁ × P₁ + n₂ × P₂) / (n₁ + n₂)

Here, the first quantity n₁ is 40 pens sold at a loss of 20% (P₁ = -20), the second quantity n₂ is the remaining 40 pens sold at a profit of P₂%, and the overall profit is 20% on the total of 80 pens.

Substituting these values into the formula:

20 = (40 × (-20) + 40 × P₂) / 80

20 = (-800 + 40 × P₂) / 80

1600 = -800 + 40 × P₂

2400 = 40 × P₂

P₂ = 60%

The profit percentage on the remaining 40 pens is 60%.

Explanation

Using the fundamental trigonometric identity sec² β - tan² β = 1, we can factor the expression as (sec β + tan β)(sec β - tan β) = 1.

Substituting the given value of sec β + tan β = 2 into this equation: 2(sec β - tan β) = 1 sec β - tan β = ½

By subtracting this equation from the given equation sec β + tan β = 2, we get: 2 tan β = 2 - ½ 2 tan β = 3/2 tan β = 3/4

Since cot β is the reciprocal of tan β, we find: cot β = 1/tan β = 4/3

Explanation

The trigonometric ratio sec A is defined as the ratio of the hypotenuse to the base of a right-angled triangle.

sec A = hypotenuse/base = 9/4

This gives the hypotenuse as 9 and the base as 4.

Using the Pythagorean theorem: hypotenuse² = base² + perpendicular² 9² = 4² + perpendicular² 81 = 16 + perpendicular² perpendicular² = 81 - 16 = 65 perpendicular = √65

The trigonometric ratio cot A is defined as the ratio of the base to the perpendicular: cot A = base/perpendicular = 4/√65

Explanation

In triangle PQR, N is the midpoint of QR because PN is the median. Therefore, QN = NR = ½ QR.

Given that PN = QN, we have PN = QN = NR. This means that the distance from N to all three vertices P, Q, and R is equal. Thus, N is the circumcenter of triangle PQR, and the circumcircle passes through P, Q, and R with QR as the diameter.

An angle subtended by a diameter at any point on the circle is a right angle. Since QR is the diameter, the angle ∠QPR is 90°.

Explanation

In any triangle, the angle formed by the angle bisectors at the incentre is related to the opposite vertex angle by the standard relation: ∠OLP = 90° + ½ ∠ONP

We are given the relation: ∠OLP + ∠ONP = 195°

Substituting the formula for ∠OLP into this relation: (90° + ½ ∠ONP) + ∠ONP = 195° 90° + 3/2 ∠ONP = 195° 3/2 ∠ONP = 105° ∠ONP = 70°

Substituting ∠ONP = 70° back into the relation for ∠OLP: ∠OLP = 90° + ½ × 70° = 125°

Explanation

Using the algebraic identity for the square of a trinomial: (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Substituting the given values, a + b + c = 0 and a² + b² + c² = 40, into the formula: 0² = 40 + 2(ab + bc + ca)

This simplifies to: 0 = 40 + 2(ab + bc + ca) 2(ab + bc + ca) = -40 ab + bc + ca = -20

Explanation

Let the number be x. The sum of the number and its reciprocal is given as: x + 1/x = 4

Squaring both sides of this equation: (x + 1/x)² = 4²

Using the algebraic expansion formula (a + b)² = a² + 2ab + b²: x² + 2 × x × 1/x + 1/x² = 16 x² + 2 + 1/x² = 16

Subtracting 2 from both sides yields the sum of their squares: x² + 1/x² = 16 - 2 x² + 1/x² = 14

Explanation

Revenue is the product of price and sales volume. When there are successive percentage changes in the factors of a product, the net percentage change in the product can be calculated using the successive percentage formula:

Net Percentage Change = x + y + (x × y)/100

Here, x represents the percentage change in price, which is -30 (since it decreases), and y represents the percentage change in sales, which is +40 (since it increases).

Substituting these values into the formula:

Net Percentage Change = -30 + 40 + ((-30 × 40) / 100) Net Percentage Change = 10 - (1200 / 100) Net Percentage Change = 10 - 12 Net Percentage Change = -2%

The negative sign indicates a decrease. Therefore, there is a 2% decrease in revenue.

Explanation

Let the present ages of Rustam, Preetam, and Geetam be R, P, and G respectively.

Based on the given average ages, we can write the sum equations: R + P = 2 × 30 = 60 P + G = 2 × 20 = 40 R + G = 2 × 26 = 52

Adding these three equations: 2(R + P + G) = 60 + 40 + 52 = 152 R + P + G = 76

To find the age of each individual: G = (R + P + G) - (R + P) = 76 - 60 = 16 years R = (R + P + G) - (P + G) = 76 - 40 = 36 years P = (R + P + G) - (R + G) = 76 - 52 = 24 years

The youngest among them is Geetam, who is currently 16 years old.

After 5 years, Geetam's age will be: 16 + 5 = 21 years.

Explanation

Loss percentage is calculated using the formula: Loss % = ((CP - SP)/CP) × 100

Given the selling prices SP₁ = 210 and SP₂ = 420, the respective loss percentages are: L1 = ((CP - 210)/CP) × 100 L2 = ((CP - 420)/CP) × 100

We are given that L1 - L2 = 7. Substituting these expressions: (((CP - 210)/CP) × 100) - (((CP - 420)/CP) × 100) = 7

Factoring out 100/CP: (100/CP) × (CP - 210 - CP + 420) = 7 (100/CP) × 210 = 7 21000 / CP = 7 CP = 21000 / 7 CP = 3000

Explanation

Using the work rate relation:

1/P + 1/Q = 1/T

where P is the time taken by P alone, Q is the time taken by Q alone (25 days), and T is the combined time (20 days).

Substituting the values:

1/P + 1/25 = 1/20

1/P = 1/20 - 1/25

Taking the common denominator of 100:

1/P = (5 - 4) / 100 = 1/100

P = 100 days

Alternatively, using the LCM method:

Let the total work be the LCM of 20 and 25, which is 100 units.

Combined efficiency of P and Q = 100 / 20 = 5 units per day.

Efficiency of Q = 100 / 25 = 4 units per day.

Efficiency of P = 5 - 4 = 1 unit per day.

Days required by P alone = 100 / 1 = 100 days.

Explanation

Given the trigonometric equation sec x + cos x = 5/2, we can substitute sec x = 1/cos x.

Let cos x = t. The equation becomes: 1/t + t = 5/2

Multiplying both sides by 2t yields: 2 + 2t² = 5t 2t² - 5t + 2 = 0

Factoring this quadratic equation: (2t - 1)(t - 2) = 0

This gives two possible values for t: t = ½ or t = 2

Since x lies between 0° and 90°, the value of cos x must lie in the interval (0, 1). Thus, t = 2 is discarded, leaving: cos x = ½

Using the fundamental trigonometric identity sin²x + cos²x = 1, we solve for sin²x: sin²x = 1 - cos²x sin²x = 1 - (½)² sin²x = 1 - ¼ sin²x = ¾

Explanation

Correct Answer: D

To find the arrival time, first convert the speed of the train from meters per second to kilometers per hour using the conversion factor 18/5:

Speed = 20 × 18/5 = 72 km/h

Next, calculate the travel time using the distance-speed-time relation:

Travel Time = Distance / Speed = 720 / 72 = 10 hours

The total time for the journey is the sum of the active travel time and the stoppage duration:

Total Time = 10 hours + 1 hour 30 minutes = 11 hours 30 minutes

Adding 11 hours 30 minutes to the departure time of 6:00 am gives an arrival time of 5:30 pm at Q.

Explanation

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

Given: Principal (P) = Rs. 18000 Annual rate = 20% per annum Half-yearly rate (r) = 20% ÷ 2 = 10% Time = 1 year, which gives n = 2 half-yearly periods

Using the compound interest formula: Amount (A) = P × (1 + r/100)ⁿ A = 18000 × (1 + 10/100)² A = 18000 × (1.1)² A = 18000 × 1.21 A = Rs. 21780

Compound Interest = Amount - Principal Compound Interest = 21780 - 18000 = Rs. 3780

Explanation

The marked price of the article is Rs.13,000.

If a discount of 10% is offered on this marked price, the selling price becomes: Selling Price = Marked Price × (100 - Discount %)/100 Selling Price = 13,000 × 90/100 = Rs.11,700

At this selling price, a profit of 30% is earned. Using the cost price formula: Cost Price = Selling Price / (1 + Profit %/100) Cost Price = 11,700 / 1.30 = Rs.9,000

Explanation

The sum of the angles of a triangle is always 180°. Let the three angles of the triangle be 2x, 2x, and 5x.

Setting up the equation for the sum of the angles: 2x + 2x + 5x = 180° 9x = 180° x = 20°

The largest angle is represented by the largest part of the ratio, which is 5x. Largest angle = 5 × 20° = 100°