SSC CHSL Tier 1 2021 Quantitative Aptitude Questions with Solutions

Explanation

The given expression is in the form of (a² - b²) / (a + b), which simplifies to (a - b) using the algebraic identity. Substituting a = 17.46 and b = 4.46, we get 17.46 - 4.46 = 13.

Explanation

Let the salaries of X, Y, and Z be represented as 2, 3, and 5 units respectively.

To find by what percentage the salary of Z is more than that of X, the formula for percentage increase is used:

Percentage Increase = ((Z - X) / X) × 100

Substituting the respective values of Z and X:

Percentage Increase = ((5 - 2) / 2) × 100 Percentage Increase = (3 / 2) × 100 Percentage Increase = 1.5 × 100 = 150%

Explanation

Let the marked price of the item be M.

The part of the marked price paid in cash is 40% of M, which is 0.4M. Since a 24% discount is offered on this portion, the actual cash paid is: 0.4M × (1 - 0.24) = 0.304M

The remaining part of the marked price paid through a credit card is 60% of M, which is 0.6M. Since a 1.5% surcharge is charged on this portion, the amount paid through the credit card is: 0.6M × (1 + 0.015) = 0.609M

The total final payment is the sum of both components: Total Payment = 0.304M + 0.609M = 0.913M

Given that the total final payment is 6,391: 0.913M = 6391 M = 6391 / 0.913 M = 7000

Explanation

When two people run in the same direction on a circular track of length L, the time taken for them to meet for the first time at any point on the track is given by the formula:

t = L / (v₁ - v₂)

where v₁ and v₂ are their respective speeds, with v₁ > v₂.

Here, the length of the track L is 1200 m.

The speeds of Badal and Ali are 45 km/h and 27 km/h, respectively. Since they are running in the same direction, their relative speed is:

v_rel = 45 - 27 = 18 km/h

Converting the relative speed into meters per second (m/s):

v_rel = 18 × 5/18 = 5 m/s

Using the formula to calculate the meeting time:

t = 1200 / 5 = 240 seconds

Explanation

Let the total income of the man be I.

The man spends 15% of his income on house rent, leaving 85% of his income. Remaining income = 0.85 × I

He spends 60% of this remaining income on household expenses, which leaves 40% of the remaining income as savings. Savings = 0.40 × 0.85 × I = 0.34 × I

Given that his total savings are ₹52,500, we can set up the equation: 0.34 × I = 52500 I = 52500 / 0.34 I ≈ 154411.76

To round 154411.76 to the nearest tens, we examine the units place. Since the value 11.76 is closer to 10 than to 20, it rounds down to 154410.

Explanation

The volume of a cuboid is determined by the formula:

Volume = Length × Breadth × Height

By substituting the given dimensions:

Volume = 16 m × 12 m × 6 m = 1152 m³

Explanation

The perimeter of the triangle is 36 cm, and two of its sides are 17 cm and 9 cm.

The third side of the triangle is calculated as: 36 - (17 + 9) = 10 cm

Using Heron's formula to find the area of the triangle: s = perimeter / 2 = 36 / 2 = 18 cm

Area = √(s(s - a)(s - b)(s - c)) Area = √(18 × (18 - 17) × (18 - 9) × (18 - 10)) Area = √(18 × 1 × 9 × 8) Area = √(1296) Area = 36 cm²

Explanation

Copper production values from the table show a continuous and successive increase every year over the given period from 1990 to 1994: In 1990, the production was 209 tonnes. In 1991, the production increased to 212 tonnes. In 1992, the production increased to 215 tonnes. In 1993, the production increased to 226 tonnes. In 1994, the production increased to 228 tonnes.

This consecutive growth is represented by the inequality 209 < 212 < 215 < 226 < 228.

Explanation

Let M be Madhuri's income and S be Sushma's income. Since Madhuri spends 80% of her income, her savings are 100% - 80% = 20% of M. Since Sushma spends 95% of her income, her savings are 100% - 95% = 5% of S.

Given that their savings are equal: 20% of M = 5% of S 0.20M = 0.05S 4M = S

The sum of their incomes is 10,000: M + S = 10,000

Substituting S = 4M into the sum: M + 4M = 10,000 5M = 10,000 M = 2,000

Sushma's income is: S = 4 × 2,000 = 8,000

Explanation

Using the work-rate relation: 1/T_together = 1/T_Priya + 1/T_Renu

Substituting the given values, where the combined time T_together is 12 hours and Priya's individual time T_Priya is 18 hours: 1/12 = 1/18 + 1/T_Renu

Solving for the rate of Renu: 1/T_Renu = 1/12 - 1/18

Using the common denominator of 36: 1/T_Renu = 3/36 - 2/36 = 1/36

Taking the reciprocal gives: T_Renu = 36 hours

Explanation

To find the total sales of cars of all four manufacturers (A, B, C, and D) over the entire six-year period from 2015 to 2020, we calculate the sum of the annual sales for each manufacturer.

Total sales of Manufacturer A = 44 + 48 + 47 + 50 + 52 + 51 = 292 thousand Total sales of Manufacturer B = 40 + 41 + 41 + 41 + 42 + 43 = 248 thousand Total sales of Manufacturer C = 36 + 38 + 40 + 42 + 44 + 50 = 250 thousand Total sales of Manufacturer D = 48 + 44 + 44 + 42 + 42 + 43 = 263 thousand

Summing the totals for all four manufacturers yields: 292 + 248 + 250 + 263 = 1053 thousand

Converting this value from thousands into units: 1053 × 1000 = 1053000

Explanation

Given that sec²θ = 4/3.

Since θ is an acute angle, taking the positive square root on both sides gives: sec θ = 2/√3

This implies that: cos θ = √3/2

For an acute angle, θ = 30°.

Now, substitute θ = 30° into the expression cosec (θ + 30°): cosec (θ + 30°) = cosec (30° + 30°) = cosec 60°

Since sin 60° = √3/2, the reciprocal is: cosec 60° = 2/√3

Explanation

By the factor theorem, substituting x = -2 and x = 2 into the polynomial yields the system of equations -8p + q = 2 and 8p + q = -10. Solving these equations simultaneously gives q = -4 and p = -3/4, which corresponds to option D.

Explanation

To find the total number of students eligible to pursue higher studies in B and C, we determine the number of students who scored at least 60% marks in each subject. Since the maximum marks for each subject is 100, at least 60% marks corresponds to scoring 60 marks and above.

From the table: The number of students who scored 60 and above in Subject B is 20. The number of students who scored 60 and above in Subject C is 26.

Thus, the total number of eligible students for higher studies in B and C combined is: 20 + 26 = 46

Explanation

The total surface area of a cube is given by the formula S = 6a², where a is the side length of the cube.

Substituting the given surface area S = 726 cm²: 6a² = 726 a² = 121 a = 11 cm

The volume of a cube is given by the formula V = a³.

Substituting the side length a = 11 cm: V = 11³ = 1331 cm³

Explanation

A number is divisible by 88 if it is divisible by both 8 and 11.

For divisibility by 8, the last three digits of the number 7P323Q, which are 23Q, must be divisible by 8. Since 232 is divisible by 8 (232 ÷ 8 = 29), the value of Q must be 2.

For divisibility by 11, the difference between the sum of the digits at even positions and the sum of the digits at odd positions must be 0 or a multiple of 11.

Sum of digits at odd positions = 2 + 2 + P = 4 + P Sum of digits at even positions = 3 + 3 + 7 = 13

Difference = 13 - (4 + P) = 9 - P

For 9 - P to be 0, the value of P must be 9.

This gives P = 9 and Q = 2.

Explanation

To find the combined ratio a:b:c, the common term b must be equated by finding the least common multiple (LCM) of its values in both ratios.

In the first ratio, a:b = 2:5, the value of b is 5. In the second ratio, b:c = 3:4, the value of b is 3.

The LCM of 5 and 3 is 15.

Multiplying the terms of the ratio a:b by 3: a:b = (2 × 3) : (5 × 3) = 6:15

Multiplying the terms of the ratio b:c by 5: b:c = (3 × 5) : (4 × 5) = 15:20

Combining these ratios yields: a:b:c = 6:15:20

Explanation

The length of the diagonal of a cuboid with length l, breadth b, and height h is calculated using the formula:

d = √(l² + b² + h²)

Substituting the given values: l = 13 m b = 7 m h = 3 m

We compute: d = √(13² + 7² + 3²) d = √(169 + 49 + 9) d = √227 m

Explanation

Let the total cost price of the sugar in the bag be C.

The first half of the sugar represents ½ of the total cost price, C. The profit from this portion sold at 20% profit is: ½ × C × 20% = 0.10C

The next quarter of the sugar represents ¼ of the total cost price, C. The profit from this portion sold at 16% profit is: ¼ × C × 16% = 0.04C

The remaining portion of the sugar is 1 - ½ - ¼ = ¼ of the total quantity. The profit from this remaining portion sold at 24% profit is: ¼ × C × 24% = 0.06C

The total profit obtained is the sum of these three profits: Total Profit = 0.10C + 0.04C + 0.06C = 0.20C

We are given that the total profit obtained is 90. Therefore, we can set up the equation: 0.20C = 90 C = 90 / 0.20 C = 450

Explanation

The length of a direct common tangent to two circles touching each other externally is given by the formula:

L = 2 × √(R₁ × R₂)

where R₁ and R₂ are the radii of the two circles.

Substituting the given values of R₁ = 28 cm and R₂ = 18 cm:

L = 2 × √(28 × 18)

L = 2 × √504

Since the square root of 504 is approximately 22.45:

L ≈ 2 × 22.45 = 44.90 cm

Explanation

Let the initial volume of the mixture be V₁ = 300 ml with a milk concentration of C₁ = 75%. Let the volume of the final mixture be V₂ with a milk concentration of C₂ = 45%.

Since only water is added to the mixture, the absolute quantity of milk remains constant throughout the process. Using the conservation of milk quantity:

V₁ × C₁ = V₂ × C₂

Substituting the given values:

300 × 75% = V₂ × 45%

V₂ = (300 × 75) / 45

V₂ = 22500 / 45 = 500 ml

The volume of water that must be added is the difference between the final and initial volume of the mixture:

Water added = V₂ - V₁ = 500 - 300 = 200 ml

Explanation

The effective discount for two successive discounts of d₁% and d₂% is given by the formula: Effective Discount = d₁ + d₂ - (d₁ × d₂)/100

Substituting d₁ = 25 and d₂ = 20: Effective Discount = 25 + 20 - (25 × 20)/100 = 45 - 5 = 40%

The selling price is calculated by reducing the marked price by this effective discount: Selling Price = Marked Price × (100 - Effective Discount)% Selling Price = 1200 × (100 - 40)/100 = 1200 × 0.60 = 720

Explanation

Using the weighted average formula: Average score = (n₁ × A₁ + n₂ × A₂) ÷ (n₁ + n₂)

For the first group of n₁ = 20 students, the average score is A₁ = 75. For the remaining n₂ = 30 - 20 = 10 students, the average score is A₂ = 87.

Substituting the given values into the formula: Average score = (20 × 75 + 10 × 87) ÷ 30 Average score = (1500 + 870) ÷ 30 Average score = 2370 ÷ 30 Average score = 79

Explanation

By evaluating the equation from left to right using the BODMAS rules, the left-hand side simplifies to p/6 and the right-hand side simplifies to 1. Equating the two sides gives p/6 = 1, which yields p = 6.

Explanation

The compound interest amount formula is:

A = P × (1 + R/100)ⁿ

Where P is the principal amount, R is the annual rate of interest, and n is the number of years.

Given: P = ₹6,000 R = 10% n = 2 years

Substituting these values into the formula:

A = 6000 × (1 + 10/100)² A = 6000 × (1.1)² A = 6000 × 1.21 = 7260

Explanation

The relationship between the marked price, selling price, and discount percentage is given by the formula:

Marked Price = Selling Price ÷ (1 - Discount Rate)

Substituting the given values into the formula:

Marked Price = 453.60 ÷ (1 - 0.19) Marked Price = 453.60 ÷ 0.81 Marked Price = 45360 ÷ 81 Marked Price = 560

Explanation

Kumar's total monthly salary is ₹ 30,000.

First, the expenditure on food and rent is 25% of the salary: Food and rent expenditure = 25% of 30,000 = ₹ 7,500

The remaining amount after food and rent is: 30,000 - 7,500 = ₹ 22,500

Next, the expenditure on education is 20% of this remaining amount: Education expenditure = 20% of 22,500 = ₹ 4,500

The income tax paid is 5% of the total salary: Income tax = 5% of 30,000 = ₹ 1,500

Now, we calculate the total of these three deductions: Total deductions = 7,500 + 4,500 + 1,500 = ₹ 13,500

The amount left with Kumar after these three deductions is: 30,000 - 13,500 = ₹ 16,500

From this balance, Kumar saves ₹ 8,000. The amount available with him after his savings is: 16,500 - 8,000 = ₹ 8,500

Explanation

Using the algebraic identity for the sum of cubes: x³ + y³ = (x + y)(x² - xy + y²)

Substituting the given values: 416 = 8(x² - xy + y²) x² - xy + y² = 52

We also know that: (x + y)² = x² + 2xy + y² 8² = x² + 2xy + y² x² + 2xy + y² = 64

Subtracting the first simplified equation from this result: (x² + 2xy + y²) - (x² - xy + y²) = 64 - 52 3xy = 12 xy = 4

Now, we find the value of x² + y²: x² + y² = (x + y)² - 2xy x² + y² = 64 - 2(4) x² + y² = 56

To find x⁴ + y⁴, we square the expression for x² + y²: (x² + y²)² = 56² x⁴ + 2(xy)² + y⁴ = 3136 x⁴ + y⁴ = 3136 - 2(4²) x⁴ + y⁴ = 3136 - 32 = 3104

Explanation

The given expression is of the form of the standard algebraic identity:

(a - b)³ = a³ - 3a²b + 3ab² - b³

By comparing the terms, we can identify a = 32 and b = 12. Substituting these values into the identity:

(32 - 12)³ = 20³

Evaluating this power:

20³ = 20 × 20 × 20 = 8000

Explanation

When a vehicle covers equal distances at two different speeds, u and v, the average speed for the entire journey is calculated using the harmonic mean formula:

Average Speed = 2uv / (u + v)

Given: Speed to the mark (u) = 15 km/h Speed back to the starting point (v) = 10 km/h

Substituting these values into the formula:

Average Speed = (2 × 15 × 10) / (15 + 10) Average Speed = 300 / 25 Average Speed = 12 km/h

Explanation

Let the woman's total income be I.

According to the problem, her expenditure is 25% of her income, which is given as 1,250.

We can set up the relation: 25% of I = 1,250

By converting the percentage into a fraction: (25/100) × I = 1,250 I / 4 = 1,250

Solving for I: I = 1,250 × 4 I = 5,000

Explanation

Average Speed formula for three equal distances covered at speeds v₁, v₂, and v₃ is:

Average Speed = 3 / (1/v₁ + 1/v₂ + 1/v₃)

Given: v₁ = 40 km/h v₂ = 60 km/h v₃ = 72 km/h

Since the cities A, B, and C form an equilateral triangle, the distance between any two of them is equal. Let this distance be d. To make calculations simpler, we can assume d to be the lowest common multiple of the three speeds 40, 60, and 72, which is 360 km.

Time taken to travel from A to B = 360 / 40 = 9 hours Time taken to travel from B to C = 360 / 60 = 6 hours Time taken to travel from C to A = 360 / 72 = 5 hours

Total distance traveled = 360 + 360 + 360 = 1080 km Total time taken = 9 + 6 + 5 = 20 hours

Average Speed = Total Distance / Total Time Average Speed = 1080 / 20 = 54 km/h

Explanation

Let the side of the equilateral triangle be a. The perimeter of an equilateral triangle is given by the formula: Perimeter = 3a

Given that the perimeter is 75 cm: 3a = 75 a = 25 cm

The area of an equilateral triangle is given by the formula: Area = (√3 / 4) × a²

Substituting the value of the side length a = 25 cm: Area = (√3 / 4) × 25² Area = 625√3 / 4 cm²

Explanation

Given the relation 2z = x + y, we can rewrite it as: x - z = z - y

This also means: y - z = -(x - z)

We need to find the value of the expression: x/(x - z) + y/(y - z)

Substituting y - z = -(x - z) into the second term gives: x/(x - z) + y/(-(x - z)) = x/(x - z) - y/(x - z) = (x - y)/(x - z)

From the given equation 2z = x + y, we can express y as: y = 2z - x

Substituting this value of y into the numerator: (x - (2z - x))/(x - z) = (2x - 2z)/(x - z) = 2(x - z)/(x - z) = 2

Explanation

The net profit or loss percent when an item is marked up by x% and then a discount of y% is offered can be calculated using the successive percentage change formula:

Net change = x - y - xy/100

Substituting the given markup of x = 30 and discount of y = 20:

Net profit percent = 30 - 20 - (30 × 20)/100 Net profit percent = 10 - 600/100 Net profit percent = 10 - 6 = 4%

Since the net change is positive, the shopkeeper makes a profit of 4%.

Explanation

Let the time spent traveling by bike be t₁ hours and by car be t₂ hours.

The total travel time is 10 hours: t₁ + t₂ = 10

The total distance covered is 200 km, with speeds of 15 km/h by bike and 25 km/h by car: 15t₁ + 25t₂ = 200

Multiplying the first equation by 15 gives: 15t₁ + 15t₂ = 150

Subtracting this from the distance equation: 10t₂ = 50 t₂ = 5 hours

Substituting t₂ back into the time equation: t₁ = 10 - 5 = 5 hours

The distances covered by bike and car are: Distance by bike = 15 × 5 = 75 km Distance by car = 25 × 5 = 125 km

The ratio of the distances covered by bike and car is: 75 : 125 = 3 : 5

Explanation

Since P varies directly as Q, the ratio of P to Q remains constant. This relationship can be expressed using the direct variation formula:

P₁/Q₁ = P₂/Q₂

Given that P₁ = 227 when Q₁ = 232, we can substitute these values along with Q₂ = 116 to find the new value of P (P₂):

227/232 = P₂/116

Solving for P₂:

P₂ = 227 × 116 / 232

P₂ = 227/2

P₂ = 113.5

Explanation

Using the algebraic identity for the square of a binomial: (x - y)² = x² + y² - 2xy

We can rearrange this formula to solve for x² + y²: x² + y² = (x - y)² + 2xy

Substitute the given values x - y = 25 and xy = 78 into the equation: x² + y² = 25² + 2 × 78 x² + y² = 625 + 156 x² + y² = 781

Explanation

The side of the cube is a = 6∛4 cm.

The volume of a cube is given by the formula: V = a³

Substituting the value of the side length: V = (6∛4)³ = 216 × 4 = 864 cm³

Let the height of the recast cuboid be h cm. Since the volume remains conserved during melting and recasting, the volume of the cuboid is equal to the volume of the cube: l × b × h = 864 12 × 9 × h = 864 108h = 864 h = 8 cm

The length of the longest diagonal of the cuboid is given by the formula: d = √(l² + b² + h²)

Substituting the dimensions: d = √(12² + 9² + 8²) d = √(144 + 81 + 64) d = √289 d = 17 cm

Explanation

Meenal has a start of 500 m in a 1200 m race, which means she only needs to cover a distance of 1200 m - 500 m = 700 m to complete the race.

The ratio of the speeds of Meenal and Nitu is 5:7. Let the speed of Meenal be 5v and the speed of Nitu be 7v.

The time taken by Meenal to complete her required 700 m is: Time = 700 / 5v = 140/v

During this same time, the distance covered by Nitu is: Distance = Speed × Time = 7v × (140/v) = 980 m

Since Nitu has only covered 980 m of the total 1200 m race by the time Meenal crosses the finish line, Meenal wins the race. The distance by which Meenal wins is: 1200 m - 980 m = 220 m

Explanation

Revenue is the product of tax and consumption. When two quantities are multiplied, the net percentage change in their product is given by the successive percentage change formula:

Net percentage change = a + b + (a × b)/100

Here, the tax diminishes by 14%, so a = -14. The consumption increases by 10%, so b = 10.

Substituting these values into the formula:

Net percentage change = -14 + 10 + (-14 × 10)/100 Net percentage change = -4 - 1.4 Net percentage change = -5.4%

The negative sign indicates a decrease of 5.4%.

Explanation

The total surface area of a solid hemisphere is given by the formula:

Total Surface Area = 3πr²

Given that the radius r = 4.2 cm and π = 22/7, we substitute these values into the formula:

Total Surface Area = 3 × (22 / 7) × 4.2 × 4.2

Simplifying the calculation:

Total Surface Area = 3 × 22 × 0.6 × 4.2

Total Surface Area = 66 × 2.52

Total Surface Area = 166.32 cm²

Explanation

Let Ranita's income be R and Bhaskar's income be B.

According to the first condition: 0.40 × R = 0.56 × B R / B = 56 / 40 = 7 / 5

We can represent Ranita's income as 7x and Bhaskar's income as 5x.

Using the second condition, when Ranita's income is increased by ₹800 and Bhaskar's income is increased by ₹2,000, the ratio of their incomes becomes 4 : 3: (7x + 800) / (5x + 2000) = 4 / 3

By cross-multiplying: 3 × (7x + 800) = 4 × (5x + 2000) 21x + 2400 = 20x + 8000 21x - 20x = 8000 - 2400 x = 5600

The combined actual income of Ranita and Bhaskar is: 7x + 5x = 12x 12 × 5600 = 67,200

Explanation

The average age of the family is calculated using the weighted average formula:

Weighted Average = (n₁A₁ + n₂A₂ + n₃A₃) / (n₁ + n₂ + n₃)

Here, n₁, n₂, and n₃ represent the number of members in each group, and A₁, A₂, and A₃ represent their respective average ages: Grandparents: n₁ = 2, A₁ = 67 Parents: n₂ = 2, A₂ = 35 Grandchildren: n₃ = 3, A₃ = 6

Substituting these values into the formula:

Average Age = (2 × 67 + 2 × 35 + 3 × 6) / (2 + 2 + 3) Average Age = (134 + 70 + 18) / 7 Average Age = 222 / 7 Average Age = 31 5/7 years

Explanation

The weight of the new person when replacing an existing person can be directly calculated using the relation:

Weight of new person = Weight of replaced person + (Total number of persons × Increase in average weight)

Substituting the given values into the formula: Weight of replaced person = 72 kg Total number of persons = 18 Increase in average weight = 2.5 kg

Weight of new person = 72 + (18 × 2.5) Weight of new person = 72 + 45 = 117 kg

Explanation

The total work is constant and is given by the product of the number of people and the number of days:

M₁ × D₁ = M₂ × D₂

Substituting the given values:

15 × 5 = 25 × D₂

75 = 25 × D₂

D₂ = 75 ÷ 25 = 3

Explanation

The total surface area of a closed cylinder is calculated as the sum of its curved surface area and the areas of its two circular bases.

Total Surface Area = Curved Surface Area + 2 × Base Area

Substituting the given values into the formula:

Total Surface Area = 225 + 2 × 169 Total Surface Area = 225 + 338 Total Surface Area = 563 cm²

Explanation

Following the BODMAS rule, simplify the expression from the innermost bracket to the outer ones.

First, simplify the innermost parenthesis: 2 + 2/3 = 8/3

Next, evaluate the terms inside the curly braces: 2 + 2 ÷ (8/3) = 2 + 2 × 3/8 = 2 + 3/4 = 11/4

Now, evaluate the terms inside the square brackets: 2 + 2 ÷ (11/4) = 2 + 2 × 4/11 = 2 + 8/11 = 30/11

Finally, compute the entire expression: 4 ÷ (30/11) = 4 × 11/30 = 44/30 = 22/15

Explanation

Given the condition ab + bc + ca = 0, we can express -bc as: -bc = ab + ca

Adding a² to both sides gives: a² - bc = a² + ab + ca = a(a + b + c)

Similarly, we can rewrite the other denominators in the expression: b² - ca = b² + ab + bc = b(a + b + c) c² - ab = c² + bc + ca = c(a + b + c)

Substituting these simplified denominators back into the given expression: 1/(a² - bc) + 1/(b² - ca) + 1/(c² - ab) = 1/(a(a + b + c)) + 1/(b(a + b + c)) + 1/(c(a + b + c))

Taking the common term 1/(a + b + c) out: = (1 / (a + b + c)) × (1/a + 1/b + 1/c) = (1 / (a + b + c)) × ((bc + ca + ab) / abc)

Since we are given that ab + bc + ca = 0, the expression becomes: = (1 / (a + b + c)) × (0 / abc) = 0

Explanation

From the given table, the number of GATE exams attempted by Dinesh is 20.

The number of times Rajesh took the exam is 30% less than the number of times Dinesh took it: Rajesh's attempts = 20 - 30% of 20 = 20 - (30/100 × 20) = 20 - 6 = 14

According to the table, the number of exams cleared by Rajesh is 5.

The percentage of times Rajesh cleared the exam out of his total attempts is: Success percentage = (5 / 14) × 100% ≈ 35.71%