SSC CHSL Tier 1 2016 Quantitative Aptitude Questions with Solutions

Explanation

First, calculate the total distance jogged during the week by summing the distances for each day: Total distance = 3 + 2 + 2.5 + 5 + 1 + 2.5 + 4 = 20 km

Next, find the rate of calories burned per kilometer using the given relation: Calories burned per km = 400 calories / 5 km = 80 calories/km

Using this rate, calculate the total calories burned for the entire week's distance: Total calories burned = 20 km × 80 calories/km = 1600 calories

Explanation

To find the percentage of total expenses represented by Raw Materials and Taxes, we use the percentage formula:

Percentage = (Sum of target expenses / Total expenses) × 100

First, calculate the sum of Raw Materials and Taxes: 11 + 3 = 14

Next, calculate the total yearly expenses: 11 + 7 + 5 + 3 + 3 = 29

Now, substitute these values into the percentage formula: (14 ÷ 29) × 100 ≈ 48.28%

Explanation

A rhombus is defined as a quadrilateral with four equal sides. In geometry, line segments of equal length are congruent. Therefore, all four sides of a rhombus are congruent.

Explanation

Let the total work be 100 units.

The daily work efficiency of P is 100 / 50 = 2 units per day. The daily work efficiency of Q is 100 / 20 = 5 units per day.

When P and Q work together, their combined efficiency is 2 + 5 = 7 units per day.

The work to be completed is 70% of the total work, which is 70% of 100 = 70 units.

The number of days required for P and Q working together to complete 70 units is 70 / 7 = 10 days.

Explanation

Let the volume of pure milk purchased be 3 litres. At Rs 24 per litre, the total Cost Price (CP) is 3 × 24 = Rs 72.

Water added to the milk is 1/3 of the volume of milk, which is 1/3 × 3 = 1 litre. This brings the total volume of the mixture to 3 + 1 = 4 litres. Since water is assumed to be free, the CP of this 4-litre mixture remains Rs 72.

The mixture is sold at Rs 32 per litre. Therefore, the Selling Price (SP) of 4 litres of the mixture is 4 × 32 = Rs 128.

The gain made by the milkman is SP - CP = 128 - 72 = Rs 56.

The gain percentage is calculated as (Gain ÷ CP) × 100 = (56 ÷ 72) × 100 = (7 ÷ 9) × 100 = 77.78%.

Explanation

The total interest earned is the sum of the interest earned on both deposits by the end of the year.

The first deposit of Rs 7200 is made on 1st January and earns interest for two half-yearly periods at a rate of 15% per half year. Using the compound interest formula, the final amount for this deposit is: Amount₁ = 7200 × (1 + 0.15)² = 7200 × 1.3225 = Rs 9522 Interest₁ = 9522 - 7200 = Rs 2322

The second deposit of Rs 7200 is made on 1st July and earns interest for one half-yearly period: Amount₂ = 7200 × (1 + 0.15)¹ = 7200 × 1.15 = Rs 8280 Interest₂ = 8280 - 7200 = Rs 1080

Total interest gained by the end of the year is: Total Interest = Interest₁ + Interest₂ = 2322 + 1080 = Rs 3402

Explanation

The area of a sector of a circle is given by the formula:

Area = (θ/360°) × πr²

Here, the given parameters are: Area = 462 Radius (r) = 21 Using π = 22/7 and substituting these values into the formula:

462 = (θ/360°) × (22/7) × 21 × 21

Simplifying the terms on the right side: 462 = (θ/360°) × 22 × 3 × 21 462 = (θ/360°) × 1386

Solving for the central angle θ: θ = (462 × 360°) / 1386 θ = 360° / 3 θ = 120°

Explanation

To simplify the expression √[(1 - sinA)/(1 + sinA)], multiply both the numerator and the denominator inside the square root by (1 - sinA):

√[(1 - sinA)/(1 + sinA)] = √[((1 - sinA)(1 - sinA)) / ((1 + sinA)(1 - sinA))]

Using the algebraic identity (a - b)(a + b) = a² - b² in the denominator:

= √[(1 - sinA)² / (1 - sin²A)]

Using the fundamental trigonometric identity 1 - sin²A = cos²A:

= √[(1 - sinA)² / cos²A]

Taking the square root of both the numerator and the denominator:

= (1 - sinA) / cosA

Separating the terms:

= 1/cosA - sinA/cosA

Using the reciprocal and quotient identities, 1/cosA = secA and sinA/cosA = tanA:

= secA - tanA

Explanation

To simplify the given expression (4a² + 8b + 14c + 2)/2, we divide each term in the numerator by 2:

(4a² + 8b + 14c + 2)/2 = 4a²/2 + 8b/2 + 14c/2 + 2/2

Dividing each coefficient by 2 gives:

4a²/2 = 2a² 8b/2 = 4b 14c/2 = 7c 2/2 = 1

Combining these terms yields 2a² + 4b + 7c + 1.

Explanation

Expanding the algebraic expression (x + 9)(6 - 4x) yields:

(x + 9)(6 - 4x) = 6x - 4x² + 54 - 36x = -4x² - 30x + 54

In this expanded quadratic polynomial, the term containing x² is -4x². Therefore, the coefficient of x² is -4.

Explanation

According to the divisibility rule of 9, a number is completely divisible by 9 if the sum of its individual digits is divisible by 9.

Let the missing digit in the number 247₆79 be x.

Summing the digits of the number: 2 + 4 + 7 + x + 6 + 7 + 9 = 35 + x

For the number to be divisible by 9, the expression 35 + x must be a multiple of 9. The smallest multiple of 9 that is greater than or equal to 35 is 36.

By setting the sum equal to 36: 35 + x = 36 x = 36 - 35 x = 1

Explanation

Let the two natural numbers be x and y.

The problem states that the sum of the squares of the two numbers is 52: x² + y² = 52

For the values 4 and 6, the calculation yields: 4² + 6² = 16 + 36 = 52

This matches the given sum.

Explanation

The given expression is cot(5π/3), where n represents the mathematical constant π.

The angle 5π/3 lies in the fourth quadrant (300°), where the cotangent function is negative.

We can rewrite the angle as: 5π/3 = 2π - π/3

Applying the trigonometric identity cot(2π - θ) = -cot(θ): cot(5π/3) = cot(2π - π/3) = -cot(π/3)

Since cot(π/3) = 1/I3, we substitute this value to get: -cot(π/3) = -1/√3

Explanation

The triple-angle identity for the sine function is derived using the sum of angles formula, sin(α + β) = sin α cos β + cos α sin β.

By setting α = 2A and β = A: sin(2A + A) = sin(2A)cos(A) + cos(2A)sin(A)

Using the double-angle formulas sin(2A) = 2sin(A)cos(A) and cos(2A) = 1 - 2sin²(A), the expression becomes: sin(3A) = (2sin(A)cos(A))cos(A) + (1 - 2sin²(A))sin(A) sin(3A) = 2sin(A)cos²(A) + sin(A) - 2sin³(A)

Since cos²(A) = 1 - sin²(A), we substitute this relation: sin(3A) = 2sin(A)(1 - sin²(A)) + sin(A) - 2sin³(A) sin(3A) = 2sin(A) - 2sin³(A) + sin(A) - 2sin³(A) sin(3A) = 3sin(A) - 4sin³(A)

Explanation

To solve the system of equations, divide both equations by xy, assuming x and y are not equal to 0:

7/y + 6/x = 5 10/y - 4/x = 4

Let u = 1/y and v = 1/x. This transforms the equations into a linear system:

7u + 6v = 5 10u - 4v = 4

Dividing the second equation by 2 gives:

5u - 2v = 2 2v = 5u - 2 v = (5u - 2)/2

Substitute this expression for v into the first equation:

7u + 6((5u - 2)/2) = 5 7u + 3(5u - 2) = 5 7u + 15u - 6 = 5 22u = 11 u = ½

Since u = 1/y, we find y = 2.

Substituting u = ½ back to find v:

v = (5(½) - 2)/2 = (2.5 - 2)/2 = 0.5/2 = ¼

Since v = 1/x, we find x = 4.

Explanation

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

SP = MP × (1 - Discount / 100)

Substituting the given values into the formula:

728 = MP × (1 - 9 / 100) 728 = MP × 0.91 MP = 728 ÷ 0.91 MP = 800

Explanation

Correct Answer: D

Volume of a canal with a trapezoidal cross-section is given by the formula: Volume = Area of cross-section × Length of the canal

The cross-section is an isosceles trapezium. The area of a trapezium is calculated as: Area = ½ × (a + b) × h where a is the bottom width, b is the top width, and h is the depth of the canal.

Substituting the given values: a = 3 m b = 5 m h = 2 m

Area = ½ × (3 + 5) × 2 Area = ½ × 8 × 2 Area = 8 m²

Using the length of the canal, l = 110 m, the maximum capacity is: Volume = Area of cross-section × Length of the canal Volume = 8 m² × 110 m Volume = 880 m³

Explanation

Let the third number be 100.

The first number is 30% lesser than the third number: First number = 100 - 30 = 70

The second number is 37% lesser than the third number: Second number = 100 - 37 = 63

To make the second number equal to the first number, it must be increased by: Increase = 70 - 63 = 7

The required percentage enhancement relative to the second number is: Percentage enhancement = (Increase ÷ Second number) × 100 Percentage enhancement = (7 ÷ 63) × 100 = 1/9 × 100 = 11.11%

Explanation

Let the distance between City A and City B be d km. Since the time taken by a vehicle is given by the formula Time = Distance / Speed, the time taken by the slower car is d/24 hours and the faster car is d/32 hours.

Given that the difference in time is 2.5 hours, the relation is: d/24 - d/32 = 2.5

Finding the common denominator of 96: 4d/96 - 3d/96 = 2.5 d/96 = 2.5 d = 96 × 2.5 d = 240 km

Explanation

Let the present ages of Rangana and Sayed be 7x and 5x respectively.

After 11 years, the ratio of their ages will be 4:3. This relationship is expressed as:

(7x + 11) / (5x + 11) = 4/3

By cross-multiplying to solve for x:

3 × (7x + 11) = 4 × (5x + 11)

21x + 33 = 20x + 44

x = 11

Rangana's present age is 7x. Substituting x = 11:

7 × 11 = 77

Explanation

The total number of machines purchased is 10. The number of Machine-A is 2, the number of Machine-B is 3, and the remaining are Machine-C, which is 10 - (2 + 3) = 5.

The total cost of all 10 machines is: Total Cost = (2 × 95000) + (3 × 60000) + (5 × 50000) Total Cost = 190000 + 180000 + 250000 Total Cost = 620000

The average cost of the machines is: Average Cost = Total Cost ÷ Total number of machines Average Cost = 620000 ÷ 10 = 62000

Explanation

The intercept form of the equation of a straight line is x/a + y/b = 1, where a is the x-intercept and b is the y-intercept.

In this problem, the line cuts the x-axis at (-3,0) and the y-axis at (0,6), which gives the intercepts a = -3 and b = 6.

Substituting these values into the intercept form equation: x/-3 + y/6 = 1

To clear the fractions, multiply the entire equation by 6: -2x + y = 6

Rearranging the equation to solve for y: y = 2x + 6

Explanation

When a point (x, y) is reflected in the y-axis, its x-coordinate changes sign, while its y-coordinate remains the same. Therefore, the reflection of Q(a, b) in the y-axis gives Q1(-a, b).

When a point (x, y) is reflected in the x-axis, its y-coordinate changes sign, while its x-coordinate remains the same. Therefore, the reflection of Q1(-a, b) in the x-axis gives the coordinates (-a, -b).

According to the problem, this final point is (-6, 2). By equating the coordinates: -a = -6, which gives a = 6 -b = 2, which gives b = -2

The coordinates of the original point Q(a, b) are (6, -2).

Explanation

To find the overall ratio of boys to girls, we calculate the total number of boys and the total number of girls across all divisions and standards.

The total number of boys is the sum of boys in all categories: 25 + 30 + 30 + 20 + 40 + 30 = 175

The total number of girls is the sum of girls in all categories: 40 + 40 + 20 + 30 + 20 + 20 = 170

The ratio of total boys to total girls is 175 : 170. Dividing both terms by 5 yields the simplified ratio of 35 : 34.

Explanation

To find the number of students who scored marks 20 or more but less than 40, we subtract the number of students who scored 40 and above from the number of students who scored 20 and above.

Students scoring 20 and above = 60 Students scoring 40 and above = 30

Number of students scoring 20 or more but less than 40 = 60 - 30 = 30

Explanation

GDP at the beginning of 2013 is equivalent to the GDP at the end of 2012. The GDP at the end of 2012 is calculated by applying the growth rate of the year 2012 to the GDP at the end of 2011.

Using the relation: GDP at the end of 2012 = GDP at the end of 2011 × (1 + Growth rate of 2012 / 100)

Substituting the given values: GDP at the end of 2011 = 3 trillion GDP growth rate for the year 2012 = -6%

GDP at the beginning of 2013 = 3 × (1 - 6/100) GDP at the beginning of 2013 = 3 × 0.94 = 2.82 trillion

Explanation

The sum of the marks scored by the student across all five subjects is:

45 + 65 + 30 + 45 + 35 = 220

The average of these marks is calculated by dividing the total sum by the number of subjects:

Average = 220 / 5 = 44

Since five points are to be deducted from this average due to poor attendance, the net average marks scored is:

44 - 5 = 39

Explanation

Let the present ages of Ramita and Satyajit be 9x and 7x, where x is a common multiplier.

According to the problem, after 9 years, the ratio of their ages becomes 5:4. We can express this relationship as:

(9x + 9) / (7x + 9) = 5/4

Cross-multiplying the terms gives:

4 × (9x + 9) = 5 × (7x + 9)

36x + 36 = 35x + 45

Subtracting 35x and 36 from both sides yields:

x = 9

To find Ramita's present age, substitute the value of x back into her present age representation:

9x = 9 × 9 = 81 years.

Explanation

Using the fundamental trigonometric identities: sec² A - tan² A = 1 cosec² A - cot² A = 1

These identities can be written in factored form as: (sec A - tan A)(sec A + tan A) = 1 → sec A - tan A = 1 / (sec A + tan A) (cosec A - cot A)(cosec A + cot A) = 1 → cosec A + cot A = 1 / (cosec A - cot A)

Substituting these expressions into the given term: (sec A - tan A) / (cosec A + cot A) = [1 / (sec A + tan A)] / [1 / (cosec A - cot A)]

Simplifying the fraction: = (cosec A - cot A) / (sec A + tan A)

Explanation

In a kite ABCD with diagonal AC as the axis of symmetry, AC bisects the angles at vertices A and C. Therefore, ∠BAC = m∠A / 2 = 45° and ∠BCA = m∠C / 2 = 30°.

In triangle ABC, the sum of interior angles is 180°, which gives ∠ABC = 180° - 45° - 30° = 105°.

By applying the Law of Sines in triangle ABC: AC / sin(∠ABC) = AB / sin(∠BCA) AC / sin(105°) = 6 / sin(30°)

Since sin(30°) = ½, we have: AC / sin(105°) = 12 AC = 12 × sin(105°)

Using the sum formula for sine, we find sin(105°): sin(105°) = sin(60° + 45°) sin(105°) = sin(60°)cos(45°) + cos(60°)sin(45°) sin(105°) = (√3/2)(1/√2) + (½)(1/√2) sin(105°) = (√3 + 1) / (2√2)

Substituting this value back into the equation for AC: AC = 12 × (√3 + 1) / (2√2) AC = 6(√3 + 1) / √2 AC = 3√2(√3 + 1) AC = 3(√2 + √6) cm

Explanation

The total weight of wheat is 9 quintals. Since 1 quintal is equal to 100 kg, the total weight of the wheat is 900 kg.

Using the rule of alligation, the ratio of the quantities sold at 10% profit and 20% profit can be determined directly:

Ratio = (20 - 14) : (14 - 10) = 6 : 4 = 3 : 2

This means the wheat is divided in the ratio of 3 : 2. The part sold at 20% profit corresponds to the ratio value of 2.

The quantity of wheat sold at 20% profit is calculated as: (2 / (3 + 2)) × 900 kg = 2/5 × 900 kg = 360 kg

Explanation

Let the two consecutive natural numbers be x and x + 1.

The sum of their squares is represented by the equation: x² + (x + 1)² = 25

Expanding and simplifying the equation: x² + x² + 2x + 1 = 25 2x² + 2x - 24 = 0 x² + x - 12 = 0

Factoring this quadratic equation: (x + 4)(x - 3) = 0

Since x must be a natural number, the negative solution x = -4 is discarded, giving x = 3. The consecutive natural numbers are therefore 3 and 4.

Explanation

The total number of machines purchased by the factory is 7. Since there are 2 of Machine-A and 4 of Machine-B, the remaining number of Machine-C is 7 - (2 + 4) = 1.

The total cost of these machines is calculated by summing the products of the quantity and price of each machine type: Total cost = (2 × 56000) + (4 × 45000) + (1 × 30000) Total cost = 112000 + 180000 + 30000 Total cost = 322000

To find the average cost, the total cost is divided by the total number of machines: Average cost = 322000 / 7 Average cost = 46000

Explanation

In the polynomial expression 6x³ + 4x² + 2x + 3, the coefficient of a term is the numerical factor that multiplies the variable. In this expression, the term containing x² is 4x². Therefore, the coefficient of x² is 4.

Explanation

Let the efficiency of Balaraj be 1 unit per day. Since Azhar is 4 times as good a workman as Balaraj, the efficiency of Azhar is 4 units per day.

The ratio of the efficiency of Azhar to Balaraj is 4 : 1. Since the time taken to complete a job is inversely proportional to efficiency, the ratio of the time taken by Azhar to Balaraj is 1 : 4.

Let the time taken by Azhar be x days and that by Balaraj be 4x days. The difference in the time taken is 4x - x = 3x days.

Given that this difference is 45 days: 3x = 45 x = 15

Thus, Azhar takes 15 days and Balaraj takes 60 days to complete the job individually.

The total work is efficiency multiplied by time, which is 4 × 15 = 60 units.

When working together, their combined efficiency is 4 + 1 = 5 units per day.

The time taken by both of them working together is: Total work / Combined efficiency = 60 / 5 = 12 days.

Explanation

The slope m₁ of the line 2x - 3y = 11 is: m₁ = -A₁/B₁ = -2/(-3) = 2/3

The slope m₂ of the line 3x + ky = -4 is: m₂ = -A₂/B₂ = -3/k

Two lines are perpendicular if the product of their slopes is -1: m₁ × m₂ = -1

Substituting the values of m₁ and m₂: (2/3) × (-3/k) = -1 -6/3k = -1 -2/k = -1 k = 2

Explanation

Dividing the algebraic expression 8a²b²c² by 4a² involves dividing the numerical coefficients and the literal coefficients separately:

(8a²b²c²) ÷ (4a²) = (8 ÷ 4) × (a² ÷ a²) × b² × c²

Since 8 ÷ 4 = 2 and a² ÷ a² = 1, this simplifies directly to:

2 × 1 × b² × c² = 2b²c²

Explanation

When a point P(a, b) is reflected in the origin, both of its coordinates change sign, yielding P1(-a, -b).

When the point P1(-a, -b) is subsequently reflected in the Y-axis, the sign of its x-coordinate is reversed while its y-coordinate remains unchanged. This yields the coordinates (a, -b).

Equating (a, -b) to the given final coordinates (4, -3): a = 4 -b = -3, which gives b = 3

Thus, the coordinates of the original point P(a, b) are (4, 3).

Explanation

The student obtained 45 marks and failed by 45 marks, which means the passing marks required are: 45 + 45 = 90 marks

Since the passing marks correspond to 25% of the maximum marks, we can set up the relation: 25% of Maximum Marks = 90

To find the maximum marks, we calculate: Maximum Marks = 90 × 100 / 25 = 90 × 4 = 360 marks

Explanation

Let the time spent traveling by rail be t hours. Since the man spends 10 hours more on the steamer, the time spent traveling by steamer is t + 10 hours.

Using the relation Distance = Speed × Time, the equation for the total distance covered is:

65t + 25(t + 10) = 430

Expanding and simplifying the equation:

65t + 25t + 250 = 430

90t = 430 - 250

90t = 180

t = 2 hours

Thus, the time spent traveling by steamer is 2 + 10 = 12 hours.

The distance covered by steamer is:

25 km/hr × 12 hours = 300 km

Explanation

The largest 5-digit number is 99999. Dividing 99999 by 89, we find the remainder:

99999 ÷ 89 = 1123 with a remainder of 52

Subtracting this remainder from 99999 gives the largest 5-digit number that is exactly divisible by 89:

99999 - 52 = 99947

This can be verified by multiplying 89 by 1123, which equals 99947.

Explanation

Using the fundamental trigonometric identity: 1 + tan²A = sec²A

Taking the square root gives: √(1 + tan²A) = secA

Substituting this into the given expression: √(1 + tan²A) / tanA = secA / tanA

Expressing secA and tanA in terms of sine and cosine: secA = 1/cosA tanA = sinA/cosA

Dividing the two terms: (1/cosA) / (sinA/cosA) = 1/sinA = cosecA

Explanation

For any principal, the simple interest is equal for each year. Thus, the simple interest for the first year is: SI₁ = 2800 / 2 = Rs 1400

The difference between the compound interest and the simple interest for two years represents the interest earned on the first year's simple interest during the second year: Difference = CI - SI = 2996 - 2800 = Rs 196

The rate of interest R is given by the formula: R = (Difference / SI₁) × 100 % R = (196 / 1400) × 100 = 14%

Explanation

The volume of a swimming pool with a uniformly sloping floor can be calculated using the formula for the volume of a prism with a trapezoidal cross-section:

Volume = Area of trapezoidal cross-section × Breadth

The parallel sides of the trapezoidal cross-section represent the depths at the two ends, which are 1 m and 3 m, and the distance between them is the length of the pool, which is 20 m.

Area of trapezoidal cross-section = ½ × (sum of parallel sides) × distance between them Area = ½ × (1 + 3) × 20 = 40 m²

Multiplying this cross-sectional area by the breadth of the pool (10 m) gives the total volume of water needed to completely fill the pool:

Volume = 40 × 10 = 400 cubic metres

Explanation

The secant function is the reciprocal of the cosine function, defined as sec θ = 1 / cos θ.

To find sec 4π/3, the angle is expressed in terms of a reference angle in the first quadrant. Since 4π/3 lies in the third quadrant, it can be rewritten as π + π/3.

Using the trigonometric identity cos(π + x) = -cos x, we have: cos(4π/3) = cos(π + π/3) = -cos(π/3)

Since the value of cos(π/3) is ½: cos(4π/3) = -½

Taking the reciprocal to find the secant value: sec(4π/3) = 1 / (-½) = -2

Explanation

The area of a sector of a circle is given by the formula: Area = (θ / 360°) × π × r²

where θ is the central angle, r is the radius of the circle, and π is approximately 22/7.

Substituting the given values into the formula: 30.8 = (72 / 360) × (22 / 7) × r²

Simplifying the fraction 72/360 to 1/5: 30.8 = (1 / 5) × (22 / 7) × r² 30.8 = (22 / 35) × r²

Rearranging the equation to solve for r²: r² = (30.8 × 35) / 22 r² = 1.4 × 35 r² = 49

Taking the square root of both sides gives: r = 7 cm

Explanation

To solve the system of equations, we first divide both equations by xy:

2/y + 6/x = 3

10/y - 3/x = 4

Let u = 1/y and v = 1/x. This transforms the system into linear equations:

2u + 6v = 3

10u - 3v = 4

Multiplying the second equation by 2 yields:

20u - 6v = 8

Adding this equation to 2u + 6v = 3 eliminates v:

22u = 11

u = 11/22 = ½

Since u = 1/y = ½, we find y = 2.

Substituting u = ½ back into 2u + 6v = 3:

2(½) + 6v = 3

1 + 6v = 3

6v = 2

v = 2/6 = ⅓

Since v = 1/x = ⅓, we find x = 3.

Explanation

Let the list price of the item be MP and the cost price be CP.

In the first case, a discount of 10% on the list price is offered, which means the selling price SP₁ is: SP₁ = 0.9 × MP

The merchant makes a loss of 25%, meaning: SP₁ = 0.75 × CP

Equating the two expressions for SP₁: 0.9 × MP = 0.75 × CP CP = (0.9 / 0.75) × MP = 1.2 × MP

In the second case, a discount of 20% on the list price is offered, so the new selling price SP₂ is: SP₂ = 0.8 × MP

To find the profit or loss percentage, we calculate the ratio of the new selling price to the cost price: SP₂ / CP = (0.8 × MP) / (1.2 × MP) = 0.8 / 1.2 = 2/3

Since the selling price is less than the cost price, the merchant incurs a loss. The loss percentage is: Loss % = (1 - SP₂ / CP) × 100 Loss % = (1 - 2/3) × 100 = (1/3) × 100 = 33.33%

Explanation

The percentage of students who chose Engineering who are girls is calculated by dividing the number of girls in Engineering by the total number of students in Engineering, and then multiplying by 100.

Total number of students who chose Engineering = 90 + 30 = 120

Number of girls who chose Engineering = 30

Required percentage = (30 ÷ 120) × 100 = ¼ × 100 = 25%

Explanation

To find the number of cars manufactured in the months of April and May, we calculate the difference between the cumulative production at the end of May and the cumulative production at the end of March.

Cumulative production till May = 2330 Cumulative production till March = 1210

Total production in April and May = Cumulative production till May - Cumulative production till March Total production in April and May = 2330 - 1210 = 1120