SSC CHSL Tier 1 2016 Quantitative Aptitude Questions with Solutions

Explanation

First, calculate the total distance jogged during the week by adding the distances for all seven days: Total distance = 4.5 + 0.5 + 1.5 + 2.5 + 4 + 4 + 3.5 = 20.5 km

The calorie burn rate per kilometer is: Rate = 400 calories / 5 km = 80 calories per km

To find the total calories burned in the week, multiply the total distance by the calorie burn rate: Total calories burned = 20.5 km × 80 calories per km = 1640 calories

Explanation

To find the percentage of Rent and Taxes in the total expenses, first calculate the sum of all yearly expenses:

Total Expenses = Raw Materials + Labour + Rent + Interest + Taxes Total Expenses = 7 + 6 + 5 + 5 + 3 = 26 lakhs

Next, find the combined expense of Rent and Taxes:

Rent and Taxes = Rent + Taxes Rent and Taxes = 5 + 3 = 8 lakhs

Now, calculate the percentage of Rent and Taxes relative to the Total Expenses using the formula:

Percentage = (Rent and Taxes / Total Expenses) × 100 Percentage = (8 / 26) × 100 ≈ 30.77%

Explanation

Since both the policeman and the thief start running at the same time and run until the policeman catches the thief, the time of travel is constant for both.

When time is constant, the distance traveled is directly proportional to speed: Distance ∝ Speed

Therefore, the ratio of the distance covered by the policeman (D_p) to the distance covered by the thief (D_t) is equal to the ratio of their respective speeds (V_p and V_t): D_p / D_t = V_p / V_t

Given: V_p = 9 km/h V_t = 5 km/h D_p = D_t + 400 (since the policeman starts 400 metres behind the thief)

Substituting these values into the ratio: (D_t + 400) / D_t = 9 / 5

Cross-multiplying to solve for D_t: 5 × (D_t + 400) = 9 × D_t 5 × D_t + 2000 = 9 × D_t 4 × D_t = 2000 D_t = 500 metres

Explanation

To find the possible values of x, the compound inequality is solved by breaking it into two separate inequalities.

First, solving the left inequality: 2x - 3(4 - 2x) < 4x - 5 2x - 12 + 6x < 4x - 5 8x - 12 < 4x - 5 4x < 7 x < 1.75

Second, solving the right inequality: 4x - 5 < 4x + 2x/3 -5 < 2x/3 -15 < 2x x > -7.5

Combining these two results gives the interval: -7.5 < x < 1.75

The value 0 lies within this interval because -7.5 < 0 < 1.75.

Explanation

We can express tan A and cot A in terms of sin A and cos A: tan A = sin A / cos A cot A = cos A / sin A

Substituting these into the given expression: tan A + cot A = (sin A / cos A) + (cos A / sin A)

To add these fractions, we find the common denominator: tan A + cot A = (sin²A + cos²A) / (sin A cos A)

Using the fundamental trigonometric identity, sin²A + cos²A = 1: tan A + cot A = 1 / (sin A cos A)

Now, substituting this back into the expression for x: x = 1 / (tan A + cot A) = 1 / (1 / (sin A cos A)) = sin A cos A

This is equivalent to cos A sin A.

Explanation

In an isosceles trapezium, the two non-parallel sides are equal in length, which makes the base angles equal. If ABCD is an isosceles trapezium with parallel bases AB and CD, then the consecutive angles sharing the base AB (Angle A and Angle B) are congruent. Likewise, the consecutive angles sharing the base CD (Angle C and Angle D) are also congruent. Since consecutive angles in a quadrilateral are those that share a common side, these two pairs of base angles constitute at least two pairs of congruent consecutive angles.

Explanation

Let the maximum marks of the examination be M.

The passing mark is 25% of M. Since the student secures 47 marks and fails by 43 marks, the passing mark is the sum of the marks obtained and the deficiency: Passing Marks = 47 + 43 = 90

We can set up the equation: 25% of M = 90 0.25 × M = 90 M = 90 / 0.25 M = 360

Explanation

In a rhombus, the diagonals are perpendicular bisectors of each other. Therefore, diagonal QS is the perpendicular bisector of diagonal PR.

First, find the midpoint of PR, which lies on QS: Midpoint = ((4 + (-2))/2, (2 + 0)/2) = (1, 1)

Next, find the slope of diagonal PR: Slope of PR = (0 - 2) / (-2 - 4) = -2 / -6 = 1/3

Since diagonal QS is perpendicular to PR, its slope is the negative reciprocal of the slope of PR: Slope of QS = -1 / (1/3) = -3

Using the point-slope form of a linear equation, the equation of diagonal QS passing through (1, 1) with slope -3 is: y - 1 = -3(x - 1) y - 1 = -3x + 3 3x + y = 4

Explanation

By using the algebraic identity: (a - b)² = a² + b² - 2ab

We can rearrange the relation to solve for a² + b²: a² + b² = (a - b)² + 2ab

Substituting the given values of a - b = 11 and ab = 24 into the equation: a² + b² = 11² + 2 × 24 a² + b² = 121 + 48 a² + b² = 169

Explanation

The simple interest rate r can be found directly from the percentage increase in the principal over 8 years: Increase % = r × t 40% = r × 8 r = 5% per annum

The compound interest (CI) on a principal P for 2 years at rate r is given by: CI = P × ((1 + r/100)² - 1)

Substituting P = 30000 and r = 5 into the formula: CI = 30000 × ((1 + 5/100)² - 1) CI = 30000 × ((21/20)² - 1) CI = 30000 × (441/400 - 1) CI = 30000 × 41/400 CI = 75 × 41 CI = 3075

Explanation

The length of an arc of a circle is calculated using the formula L = (θ / 360°) × 2πr, where θ is the measure of the central angle in degrees and r is the radius of the circle.

By substituting the given arc length L = 11 cm, radius r = 14 cm, and using π ≈ 22/7:

11 = (θ / 360°) × 2 × (22/7) × 14 11 = (θ / 360°) × 2 × 22 × 2 11 = (θ / 360°) × 88

Now, solve for θ:

θ / 360° = 11 / 88 θ / 360° = 1/8 θ = 360° / 8 θ = 45°

Explanation

Discount percentage is calculated using the formula: Discount % = (Discount / Marked Price) × 100

Here, the Marked Price is ₹1200 and the Selling Price is ₹960.

Discount = Marked Price - Selling Price Discount = 1200 - 960 = 240

Substituting these values into the formula: Discount % = (240 / 1200) × 100 = 20%

Explanation

We expand each term in the expression using the standard algebraic identities (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b².

Expanding the first term: (x + 3)² = x² + 6x + 9

Expanding the second term: (x - 1)² = x² - 2x + 1

Adding these two expanded terms together: (x + 3)² + (x - 1)² = (x² + 6x + 9) + (x² - 2x + 1)

Combining the like terms: 2x² + 4x + 10

Factoring out the common multiplier 2: 2(x² + 2x + 5)

Explanation

The prime numbers lying between 58 and 68 are 59, 61, and 67.

The sum of these prime numbers is: 59 + 61 + 67 = 187

Explanation

The volume of sand remains constant when poured from the cylindrical vessel to form the right circular cone.

Volume of cylinder = Volume of cone

The formula for the volume of a cylinder is π × r₁² × h₁ and the formula for the volume of a cone is 1/3 × π × r₂² × h₂.

Equating the two volumes: π × r₁² × h₁ = 1/3 × π × r₂² × h₂

Canceling π from both sides: r₁² × h₁ = 1/3 × r₂² × h₂

Substituting the given values, where the radius of the cylinder r₁ = 4 cm, the height of the cylinder h₁ = 5 cm, and the radius of the cone r₂ = 6 cm: 4² × 5 = 1/3 × 6² × h₂ 16 × 5 = 12 × h₂ 80 = 12 × h₂ h₂ = 80/12 = 6.67 cm

Explanation

The relationship between Marked Price (MP), Cost Price (CP), Profit percentage (P), and Discount percentage (D) is given by the formula:

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

For the first scenario, where the discount is 20% and the profit is 28%:

MP/CP = (100 + 28) / (100 - 20) = 128 / 80 = 1.6

For the second scenario, where the discount is 14%, let the new profit percentage be P:

MP/CP = (100 + P) / (100 - 14)

Substituting the ratio MP/CP = 1.6 into the equation:

1.6 = (100 + P) / 86

100 + P = 1.6 × 86

100 + P = 137.6

P = 37.6%

Explanation

By the midpoint formula, the coordinates of the midpoint P(x, y) of a line segment joining A(x₁, y₁) and B(x₂, y₂) are given by:

x = (x₁ + x₂)/2 y = (y₁ + y₂)/2

Substituting the given coordinates of P(2, 1) and A(11, 5) into the formula:

2 = (11 + x₂)/2 4 = 11 + x₂ x₂ = -7

1 = (5 + y₂)/2 2 = 5 + y₂ y₂ = -3

The coordinates of point B are (-7, -3).

Explanation

Let the original number of selected and unselected candidates be 4x and x respectively. Thus, the total number of candidates who applied is 5x.

According to the given conditions, if 90 less had applied and 20 less were selected: New total candidates applied = 5x - 90 New selected candidates = 4x - 20

The new ratio of selected to unselected candidates is 5:1. This means the ratio of selected candidates to the total candidates applied is 5:6.

We can set up the equation: (4x - 20) / (5x - 90) = 5/6

By cross-multiplying: 6 × (4x - 20) = 5 × (5x - 90) 24x - 120 = 25x - 450 25x - 24x = 450 - 120 x = 330

The original number of candidates who applied is 5x = 5 × 330 = 1650.

Explanation

For any sequence of n consecutive odd integers, the highest integer can be found directly from the average using the standard formula:

Highest integer = Average + (n - 1)

Given that the number of terms n is 25 and the average is 55, we substitute these values into the formula:

Highest integer = 55 + (25 - 1) Highest integer = 55 + 24 Highest integer = 79

This relationship holds because consecutive odd integers form an arithmetic progression with a common difference of 2. Since there are 25 terms, the average of 55 corresponds exactly to the middle term, which is the 13th term. To find the 25th (highest) term, we add the common difference of 2 a total of 12 times to the middle term:

Highest term = 55 + 12 × 2 = 55 + 24 = 79

Explanation

Let the original two-digit number be represented as 10x + y, where x is the tens digit and y is the units digit.

According to the first condition, the product of the digits is 24: x × y = 24

According to the second condition, adding 45 to the number reverses its digits: 10x + y + 45 = 10y + x 9y - 9x = 45 y - x = 5 y = x + 5

Substituting y into the product equation: x × (x + 5) = 24 x² + 5x - 24 = 0 (x + 8)(x - 3) = 0

Since x represents a digit, it must be a positive integer, which gives x = 3.

Using x = 3 to find y: y = 3 + 5 = 8

This gives the tens digit as 3 and the units digit as 8, which forms the original number 38.

Explanation

We can write the angle 11π/6 as 2π - π/6.

Using the trigonometric identity sin(2π - θ) = -sin(θ), we get: sin(11π/6) = sin(2π - π/6) = -sin(π/6)

Since the standard value of sin(π/6) is ½, we substitute this to find: sin(11π/6) = -½

Explanation

Sister's rate of baking = 50 cakes / 25 hours = 2 cakes per hour.

Combined rate of Sister and Mummy = 75 cakes / 15 hours = 5 cakes per hour.

Mummy's individual rate of baking = Combined rate - Sister's rate = 5 - 2 = 3 cakes per hour.

Number of cakes Mummy can bake in 15 hours = Mummy's rate × 15 hours = 3 × 15 = 45 cakes.

Explanation

The trigonometric sum-to-product identity for the difference of two sines is expressed as:

sin C - sin D = 2 cos[(C + D)/2] sin[(C - D)/2]

By substituting this identity directly into the given equation x = sin C - sin D, we obtain:

x = 2 cos[(C + D)/2] sin[(C - D)/2]

Explanation

The total number of students who chose Engineering is the sum of the boys and girls in that field, which is 40 + 40 = 80.

Among these 80 students, the number of girls is 40.

The percentage of students who chose Engineering who are girls is calculated as:

(Number of girls in Engineering / Total students in Engineering) × 100 = (40 / 80) × 100 = 50%

Explanation

The cumulative production values represent the total number of cars manufactured from January up to that specific month. To find the number of cars manufactured specifically in the months of April and May, we subtract the cumulative production at the end of March from the cumulative production at the end of May.

Cumulative production up to March = 1630 Cumulative production up to May = 2670

Cars manufactured in April and May = Cumulative production of May - Cumulative production of March Cars manufactured in April and May = 2670 - 1630 = 1040

Alternatively, calculating the individual production for each month: Production in April = Cumulative production of April - Cumulative production of March = 1970 - 1630 = 340 Production in May = Cumulative production of May - Cumulative production of April = 2670 - 1970 = 700 Total production in April and May = 340 + 700 = 1040

Explanation

First, we find the total distance jogged during the week by adding the distances for each day: Total distance = 2.5 + 4 + 2.5 + 3.5 + 0.5 + 2.5 + 1.5 = 17 km

Next, we calculate the calorie burn rate per kilometer. Since jogging 5 km burns 400 calories, the rate is: Calorie burn rate = 400 ÷ 5 = 80 calories per km

To find the total calories burned in the given week, we multiply the total distance by the calorie burn rate: Total calories burned = 17 × 80 = 1360 calories

Explanation

The total expenses of all items are calculated by summing up the yearly expenses for each category: Total Expenses = 12 + 6 + 3 + 4 + 3 = 28 lakhs

The combined expense of Raw Materials and Interest is: Raw Materials + Interest = 12 + 4 = 16 lakhs

The percentage of this combined expense relative to the total expenses is: Percentage = (16 / 28) × 100 = 57.14%

Explanation

The original fare and the new fare are in the ratio 1:2. This means that if the original fare is represented as 1 unit, the new fare is represented as 2 units.

The original fare is given as Rs. 175. Therefore, 1 unit corresponds to Rs. 175.

The increase in the fare is the difference between the new fare and the original fare: Increase in fare = 2 units - 1 unit = 1 unit

Since 1 unit is equal to Rs. 175, the increase in the fare is Rs. 175.

Explanation

By the division algorithm, the relationship between the dividend, divisor, quotient, and remainder is given by the formula:

Dividend = (Divisor × Quotient) + Remainder

Substituting the given values:

Divisor = 47 Quotient = 75 Remainder = 18

Dividend = (47 × 75) + 18 Dividend = 3525 + 18 Dividend = 3543

Explanation

To find the sum of the two algebraic expressions, we first expand each term individually.

Expanding the first expression: 2xy(3x + 4y - 5z) = 6x²y + 8xy² - 10xyz

Expanding the second expression: 5yz(2x - 3y) = 10xyz - 15y²z

Now, we add the two expanded expressions: (6x²y + 8xy² - 10xyz) + (10xyz - 15y²z)

Combining the like terms, the -10xyz and 10xyz terms cancel each other out: 6x²y + 8xy² - 15y²z

Explanation

The total surface area of a cuboid is calculated using the formula:

Total Surface Area = 2(lb + bh + hl)

In this formula, l, b, and h represent the length, breadth, and height of the cuboid respectively. Substituting the given dimensions, l = 10 cm, b = 6 cm, and h = 4 cm:

Total Surface Area = 2 × (10 × 6 + 6 × 4 + 4 × 10) Total Surface Area = 2 × (60 + 24 + 40) Total Surface Area = 2 × 124 Total Surface Area = 248 sq cm

Explanation

A rhombus has four equal sides of length 12 cm. The adjacent angles of a rhombus are supplementary, which means if one angle is 120°, the adjacent angle is 180° - 120° = 60°.

The diagonals of a rhombus bisect each other perpendicularly and also bisect the interior angles. This divides the rhombus into four congruent right-angled triangles.

The diagonal opposite to the larger angle is the longer diagonal. The angle of 120° is bisected into two 60° angles, while the adjacent angle of 60° is bisected into two 30° angles.

In each of the resulting right-angled triangles, the hypotenuse is the side of the rhombus (12 cm), the angle opposite to half of the longer diagonal is 60°, and the angle opposite to half of the shorter diagonal is 30°.

Using the sine ratio for the 60° angle: sin(60°) = (half of longer diagonal) / side √3/2 = (half of longer diagonal) / 12 half of longer diagonal = 12 × (√3/2) = 6√3 cm

Multiplying by 2 gives the full length of the longer diagonal: longer diagonal = 2 × 6√3 = 12√3 cm

Explanation

Under simple interest, the percentage increase in the amount over 5 years is 40%. The annual simple interest rate (R) is: R = 40% / 5 = 8% per annum

Alternatively, using the simple interest formula where SI is 0.40P: SI = (P × R × T) / 100 0.40P = (P × R × 5) / 100 R = 8%

To find the compound interest (CI) on Rs. 25000 for 3 years at 8% per annum, we use the formula: CI = P × ((1 + R/100)³ - 1)

Substituting the values: CI = 25000 × ((1 + 8/100)³ - 1) CI = 25000 × ((1.08)³ - 1) CI = 25000 × (1.259712 - 1) CI = 25000 × 0.259712 CI = 6492.8

Explanation

The distance covered during the first part of the journey is calculated using the formula: Distance = Speed × Time

Suresh rides for 5 hours at a speed of 50 km/hr, so: Distance covered = 50 km/hr × 5 hours = 250 km

The remaining distance of the total 410 km journey is: Remaining Distance = 410 km - 250 km = 160 km

Since the remaining journey takes 4 hours, the speed for this part is: Speed = Remaining Distance / Remaining Time = 160 km / 4 hours = 40 km/hr

Explanation

The area of a circle is directly proportional to the square of its radius, represented by the formula A = πr². When the radius increases by 25%, the change in area can be calculated using the successive percentage change formula:

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

Since the radius is squared in the area formula, the 25% increase is applied twice (x = 25 and y = 25):

Net Percentage Change = 25 + 25 + (25 × 25)/100 Net Percentage Change = 50 + 625/100 Net Percentage Change = 50 + 6.25 = 56.25%

Explanation

The relationship between selling price, cost price, and loss or gain percentage is given by the formula:

Cost Price = Selling Price / (1 - Loss Rate)

Initially, the selling price is ₹1,260 with a loss of 8%, meaning the loss rate is 0.08.

Cost Price = 1260 / (1 - 0.08) = 1260 / 0.92

When the selling price is changed to ₹1,386, the ratio of the new selling price to the cost price determines the profit or loss:

Ratio = New Selling Price / Cost Price Ratio = 1386 / (1260 / 0.92) Ratio = (1386 / 1260) × 0.92 Ratio = 1.1 × 0.92 = 1.012

A ratio of 1.012 means the new selling price is 101.2% of the cost price. This corresponds to a gain of:

(1.012 - 1) × 100 = 1.2% gain

Explanation

To find the value of x, we multiply both the numerator and the denominator of the given expression by (1 - sinA):

x = (1 - sinA) / (1 + sinA)

x = ((1 - sinA) × (1 - sinA)) / ((1 + sinA) × (1 - sinA))

x = (1 - sinA)² / (1 - sin²A)

Using the trigonometric identity 1 - sin²A = cos²A, we can rewrite the denominator:

x = (1 - sinA)² / cos²A

Taking the square as a common power for the entire fraction:

x = ((1 - sinA) / cosA)²

By separating the terms inside the parentheses:

x = (1/cosA - sinA/cosA)²

Applying the reciprocal identity secA = 1/cosA and the quotient identity tanA = sinA/cosA:

x = (secA - tanA)²

Explanation

Two angles are complementary if their sum is 90°. Let the measure of the required angle be x. Its complementary angle is 90° - x.

According to the given condition, the angle is thrice its complementary angle: x = 3(90° - x)

Solving the equation: x = 270° - 3x 4x = 270° x = 270°/4 x = 67.5°

Explanation

The area of an equilateral triangle with side length a is given by the formula:

Area = (√3 / 4) × a²

Substituting the given area of 36√3 square centimeters into the formula:

36√3 = (√3 / 4) × a²

Dividing both sides by √3:

36 = ¼ × a²

Multiplying both sides by 4:

a² = 144

Taking the square root:

a = 12 cm

Explanation

Using the standard trigonometric values for angles in radians, where the superscript c denotes circular measure:

cos(π/4) = 1/√2 tan(π/4) = 1

Substituting these values into the given equation:

x = cos(π/4) - tan(π/4) x = 1/√2 - 1

Taking the common denominator √2:

x = (1 - √2)/√2

Explanation

Using the fundamental trigonometric identity relating secant and tangent: sec²A - tan²A = 1

By rearranging this equation to isolate tan²A, we get: tan²A = sec²A - 1

Taking the square root on both sides: tan A = √(sec²A - 1)

Substituting tan A = x directly into the equation yields: x = √(sec²A - 1)

Explanation

Discount percentage is calculated using the formula:

Discount % = (Marked Price - Selling Price) / Marked Price × 100

Substituting the given values into the formula:

Discount % = (1500 - 1250) / 1500 × 100 Discount % = 250 / 1500 × 100 Discount % = 1/6 × 100 Discount % = 16.67%

Explanation

The angle θ between two lines with slopes m₁ and m₂ is given by the formula:

tan θ = |(m₂ - m₁) / (1 + m₁ m₂)|

Substituting the given slopes m₁ = 1 and m₂ = √3 into the formula:

tan θ = (√3 - 1) / (1 + 1 × √3) = (√3 - 1) / (√3 + 1)

Multiplying the numerator and the denominator by √3 - 1 to rationalize the denominator:

tan θ = (√3 - 1)² / (3 - 1) = (3 + 1 - 2√3) / 2 = (4 - 2√3) / 2 = 2 - √3

Since tan 15° = 2 - √3, the acute angle θ between the two lines is 15°.

Explanation

Parimal completes 1/4 of the job in 10 days. Therefore, Parimal alone can complete the entire job in 10 × 4 = 40 days, which means Parimal's 1-day work rate is 1/40.

The remaining part of the job is 1 - 1/4 = 3/4. Salim completes this remaining 3/4 of the job in 20 days. Thus, Salim alone can complete the entire job in 20 × 4/3 = 80/3 days, giving Salim a 1-day work rate of 3/80.

When working together, their combined 1-day work rate is the sum of their individual rates: 1/40 + 3/80 = 2/80 + 3/80 = 5/80 = 1/16.

Since they complete 1/16 of the job in one day, working together they will complete the entire job in 16 days.

Explanation

To find the values x can take, we solve the two inequalities separately and then find their intersection.

First inequality: 4x - 7 < x - 2 Subtracting x from both sides and adding 7 to both sides: 3x < 5 x < 5/3

Second inequality: 5x + 2/3 ≥ 3x + 1 Subtracting 3x and 2/3 from both sides: 2x ≥ 1 - 2/3 2x ≥ 1/3 Dividing both sides by 2: x ≥ 1/6

Combining the two solutions, we obtain the range for x: 1/6 ≤ x < 5/3

Since 5/3 is approximately 1.67 and 1/6 is approximately 0.17, the integer value 1 lies within this interval.

Explanation

Let the present ages of the brother and sister be x and 21 - x.

Five years ago, their ages were x - 5 and (21 - x) - 5, which simplifies to 16 - x.

According to the question, the product of their ages five years ago was 28: (x - 5)(16 - x) = 28

Expanding the terms: 16x - x² - 80 + 5x = 28 -x² + 21x - 80 = 28 x² - 21x + 108 = 0

Solving this quadratic equation by factoring: x² - 12x - 9x + 108 = 0 x(x - 12) - 9(x - 12) = 0 (x - 9)(x - 12) = 0

Thus, x = 9 or x = 12.

If x = 9, then the other age is 21 - 9 = 12. If x = 12, then the other age is 21 - 12 = 9. Therefore, their present ages are 9 and 12.

Explanation

To find the solution set of the given system of linear equations, we can use the elimination method. The two equations are:

(1) 4x - 3y = 47 (2) 3x + y = 32

Multiply equation (2) by 3 to align the coefficients of y:

9x + 3y = 96

Now, add this equation to equation (1) to eliminate y:

(4x - 3y) + (9x + 3y) = 47 + 96 13x = 143 x = 11

Substitute x = 11 back into equation (2) to solve for y:

3(11) + y = 32 33 + y = 32 y = -1

The solution set is (11, -1).

Explanation

The total number of boys in the class is the difference between the total students and the number of girls: 55 - 34 = 21 boys

Using the weighted average formula, the total weight of the class is the sum of the total weight of the girls and the total weight of the boys: Total weight of the class = 55 × 55.2 = 3036 kg Total weight of the girls = 34 × 51 = 1734 kg

The total weight of the boys is the difference between the total class weight and the total weight of the girls: 3036 - 1734 = 1302 kg

The average weight of the boys is the total weight of the boys divided by the number of boys: 1302 ÷ 21 = 62 kg

Explanation

To find the pair of years with equal total exports, we calculate the sum of exports for all three companies for the years 2013 and 2014.

For the year 2013: Total exports = 5000 + 2000 + 4000 = 11000 lakh rupees

For the year 2014: Total exports = 5000 + 5000 + 1000 = 11000 lakh rupees

Both 2013 and 2014 have equal total exports of 11000 lakh rupees.

Explanation

The total profit or loss of the company over the last five years is calculated by finding the algebraic sum of the profits and losses for each year from 2011 to 2015.

Total Profit/Loss = 25 + (-20) + 20 + 10 + 10 = 45

Since the resulting sum is positive, it represents a net profit of Rs 45 crores.