SSC CHSL Tier 1 2016 Quantitative Aptitude Questions with Solutions

Explanation

The expression can be simplified by substituting tan² A = sec² A - 1 = (sec A - 1)(sec A + 1), which reduces the expression to (sec A + 1) / (sec A - 1). Converting sec A to 1/cos A and simplifying the fraction yields (1 + cos A) / (1 - cos A).

Explanation

Let the cost price of the toaster be T and the cost price of the washing machine be W.

The total cost price of both items is: T + W = 10500

The toaster is sold at a 22% profit, so its selling price is: 1.22 × T

The washing machine is sold at a 12% loss, so its selling price is: (1 - 0.12) × W = 0.88 × W

Given that the selling prices of both items are equal: 1.22 × T = 0.88 × W 122 × T = 88 × W T / W = 88 / 122 = 44 / 61

The cost price of the toaster and the washing machine are in the ratio 44 : 61.

The sum of the ratio parts is 44 + 61 = 105.

Since the toaster has the smaller ratio term, it is the cheaper item. Its cost price is: (44 / 105) × 10500 = 44 × 100 = Rs 4400

Explanation

The percentage increase required to restore a price to its original value after a reduction of r% is given by the formula:

Percentage Increase = (r / (100 - r)) × 100 %

Substituting r = 24 into the formula:

Percentage Increase = (24 / (100 - 24)) × 100 % = (24 / 76) × 100 % = (6 / 19) × 100 % = 600 / 19 % ≈ 31.58%

Explanation

To find the average bonus in rupees, we first calculate the total bonus paid to all employees and divide it by the total number of employees.

Total number of employees = 2 + 12 + 1 = 15

Total bonus for managers: Each manager receives 50% of ₹48,00,000, which is ₹24,00,000. For 2 managers, total bonus = 2 × ₹24,00,000 = ₹48,00,000

Total bonus for executives: Each executive receives 30% of ₹8,00,000, which is ₹2,40,000. For 12 executives, total bonus = 12 × ₹2,40,000 = ₹28,80,000

Total bonus for trainees: The trainee receives 10% of ₹4,00,000, which is ₹40,000. For 1 trainee, total bonus = 1 × ₹40,000 = ₹40,000

Sum of all bonuses = ₹48,00,000 + ₹28,80,000 + ₹40,000 = ₹77,20,000

Average bonus = Total bonus ÷ Total number of employees Average bonus = ₹77,20,000 ÷ 15 = ₹5,14,666.67 ≈ ₹5,14,667

Explanation

The total exports from the three companies together for the year 2011 is calculated as: 1000 + 4000 + 3000 = 8000 lakh rupees.

The total exports from the three companies together for the year 2014 is calculated as: 4000 + 2000 + 2000 = 8000 lakh rupees.

Both 2011 and 2014 have equal total exports of 8000 lakh rupees.

Explanation

To find the total profit or loss of the company over the last five years, we sum the values given in the table for each year:

Total Profit or Loss = (-5) + 15 + 25 + (-5) + 25

Total Profit or Loss = 55

A positive sum of 55 indicates that the company made a net profit of Rs 55 crores.

Explanation

To find the percentage of cotton exports out of the total exports, first calculate the sum of all exports from the given table:

Total exports = 750 + 950 + 775 + 525 + 700 = 3700 million USThe value of cotton exports is 775 million US.

The percentage is calculated as:

Cotton percentage = (Cotton exports / Total exports) × 100 Cotton percentage = (775 / 3700) × 100 Cotton percentage = 775 / 37 ≈ 20.95%

Explanation

Let the marks obtained by the two students be x and y, where x is the higher score.

Based on the first condition, the difference between their marks is 21: x - y = 21

Based on the second condition, the higher score is 80% of the sum of both scores: x = 0.8(x + y)

Expanding and simplifying this equation: x = 0.8x + 0.8y 0.2x = 0.8y x = 4y

Substituting x = 4y into the first equation: 4y - y = 21 3y = 21 y = 7

Using this value to find x: x = 4 × 7 = 28

The marks obtained by the two students are 28 and 7.

Explanation

Pannalal completes 1/3 of the work in 20 days. Therefore, the time taken by Pannalal to complete the entire work alone is 20 × 3 = 60 days.

The remaining part of the work is 1 - 1/3 = 2/3. Saiprasad completes this 2/3 of the work in 10 days. Therefore, the time taken by Saiprasad to complete the entire work alone is 10 × 3/2 = 15 days.

Using the work formula for two people working together, the combined time taken by both to complete the work is (P × S) / (P + S), where P and S are their individual completion times. Substituting the values gives (60 × 15) / (60 + 15) = 900 / 75 = 12 days.

Explanation

To find the value of x, simplify the given linear equation by removing the parentheses and combining like terms:

(7x - 13) - (12x + 3) = 14

7x - 13 - 12x - 3 = 14

Group the terms containing x and the constant terms:

(7x - 12x) - (13 + 3) = 14

-5x - 16 = 14

Add 16 to both sides of the equation to isolate the term with x:

-5x = 14 + 16

-5x = 30

Divide both sides by -5:

x = 30 ÷ -5

x = -6

Explanation

Chutki's rate of baking is 30 cakes / 15 hours = 2 cakes per hour.

Chutki and Badki's combined rate of baking is 90 cakes / 30 hours = 3 cakes per hour.

Subtracting Chutki's rate from their combined rate gives Badki's rate of baking: 3 cakes per hour - 2 cakes per hour = 1 cake per hour.

In 10 hours, Badki can bake: 1 cake per hour × 10 hours = 10 cakes.

Explanation

The given equation is 3x² = 10² - 5².

First, calculate the terms on the right side of the equation: 10² = 100 5² = 25

Subtracting these values gives: 100 - 25 = 75

Now substitute this back into the equation: 3x² = 75

Divide both sides by 3 to isolate x²: x² = 75 / 3 x² = 25

Taking the square root of both sides gives: x = √25 x = 5

Explanation

Let Hariraj's salary be represented as H.

According to the given conditions, Giridhar's salary (G) is 5/3 of Hariraj's salary, which is written as G = (5/3)H.

Shaunak's salary (S) is 2/3 of Hariraj's salary, which is written as S = (2/3)H.

The ratio of Giridhar's salary to Shaunak's salary (G : S) is:

G : S = (5/3)H : (2/3)H

By canceling the common term H and the denominator 3, the ratio simplifies directly to:

G : S = 5 : 2

Explanation

The sum of the values of a set of observations is equal to the product of their number and their average.

Total revenue of all 9 years = 9 × 65 = 585 lakhs

Total revenue of the first 5 years = 5 × 60 = 300 lakhs

Total revenue of the last 5 years = 5 × 72 = 360 lakhs

The 5th year is included in both the first 5 years and the last 5 years. Therefore, adding the sum of the first 5 years and the last 5 years counts the 5th year twice.

Revenue of the 5th year = (Total of first 5 years + Total of last 5 years) - Total of 9 years Revenue of the 5th year = (300 + 360) - 585 = 660 - 585 = 75 lakhs

Explanation

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 0 or a multiple of 11.

Let the missing digit be x. The number is 347x547.

Sum of digits at odd positions starting from the rightmost digit: 7 + 5 + 7 + 3 = 22

Sum of digits at even positions: 4 + x + 4 = 8 + x

Difference = 22 - (8 + x) = 14 - x

For the number to be exactly divisible by 11, this difference must be equal to 11: 14 - x = 11 x = 3

Explanation

Let the cost price of the machine be CP.

When the machine is sold for Rs 57 lakhs at a loss: Loss = CP - 57

When the machine is sold for Rs 67 lakhs at a gain: Gain = 67 - CP

According to the given condition, the gain is 7 times the former loss: Gain = 7 × Loss 67 - CP = 7 × (CP - 57) 67 - CP = 7CP - 399 8CP = 466 CP = 58.25

Therefore, the cost price of the machine is Rs 58.25 lakhs.

Explanation

Solving the first inequality: 7 + 4x > 3 + 3x Subtracting 3x and 7 from both sides: x > -4

Solving the second inequality: 3x - 2 < 5 - x Adding x and 2 to both sides: 4x < 7 x < 1.75

Combining both inequalities, the range for x is: -4 < x < 1.75

Since 1 lies within this range, x can take the value of 1.

Explanation

The effective discount percentage when free items are offered on a purchase is calculated using the relation:

Discount Percentage = (Number of free items / Total number of items) × 100

In this transaction, the number of free pairs of trousers is 2, and the customer receives a total of 5 pairs of trousers (3 purchased + 2 free).

Substituting these values:

Discount Percentage = (2 / 5) × 100 = 40%

This percentage remains the same regardless of the individual price of each trouser, as the discount on each of the 5 trousers is uniformly 40% of its marked price.

Explanation

For three terms a, b, and c to be in arithmetic progression, the middle term must be the arithmetic mean of the other two terms, which is represented by the formula:

2b = a + c

Substituting the given terms a = 3x + p, b = x - 10, and c = -x + 16 into the formula gives:

2(x - 10) = (3x + p) + (-x + 16)

Expanding both sides of the equation:

2x - 20 = 2x + p + 16

Subtracting 2x from both sides simplifies the equation to:

-20 = p + 16

Solving for p:

p = -20 - 16 p = -36

Explanation

By the section formula, if a point P divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂) internally in the ratio m:n, the coordinates of P are given by:

P_x = (mx₂ + nx₁) / (m + n) P_y = (my₂ + ny₁) / (m + n)

Here, the points are A(x, 0) and B(0, y), the ratio is m:n = 1:3, and the dividing point is P(3, -2).

Substituting the values into the formula for the x-coordinate:

3 = (1 × 0 + 3 × x) / (1 + 3) 3 = 3x / 4 12 = 3x x = 4

Substituting the values into the formula for the y-coordinate:

-2 = (1 × y + 3 × 0) / (1 + 3) -2 = y / 4 y = -8

Explanation

The slope-intercept form of the equation of a line is: y = mx + c

Here, the slope m is 1/4 and the y-intercept c is -3.

Substituting these values into the formula: y = (1/4)x - 3

Multiplying the entire equation by 4 to clear the fraction: 4y = x - 12

Rearranging the terms to standard form: x - 4y = 12

Explanation

When two objects move in the same direction, the ratio of the distances they travel in the same time is equal to the ratio of their speeds.

Distance traveled by policeman / Distance traveled by thief = Speed of policeman / Speed of thief

Let the distance run by the thief before being overtaken be d metres. The policeman has to cover the initial gap of 250 metres in addition to this distance, so the distance traveled by the policeman is d + 250 metres.

Substituting these into the ratio:

(d + 250) / d = 7 / 5

By cross-multiplying, we get:

5 × (d + 250) = 7d

5d + 1250 = 7d

2d = 1250

d = 625 metres

Explanation

In triangle ABC, since DE is parallel to BC, the corresponding angles are equal, making triangle ADE similar to triangle ABC by Angle-Angle similarity.

For similar triangles, the ratio of corresponding sides is equal: AD / AB = DE / BC

The length of AB is the sum of AD and DB: AB = AD + DB = 8 + 6 = 14 cm

Substituting the given values into the similarity ratio: 8 / 14 = 7.2 / BC

Simplifying the ratio: 4 / 7 = 7.2 / BC

Solving for BC: BC = (7.2 × 7) / 4 BC = 1.8 × 7 BC = 12.6 cm

Explanation

Using the trigonometric identity sec(-θ) = sec(θ), we have: sec(-7π/4) = sec(7π/4)

We can express the angle 7π/4 as 2π - π/4: sec(7π/4) = sec(2π - π/4)

Using the identity sec(2π - θ) = sec(θ), we get: sec(2π - π/4) = sec(π/4)

Since cos(π/4) = 1/√2, the reciprocal is: sec(π/4) = 1 / cos(π/4) = √2

This gives the value of x as √2.

Explanation

Since the sum of angles in a triangle is 180°, a triangle with angles measuring 30° and 60° must have its third angle measuring 90° (180° - 30° - 60° = 90°). This is a standard 30°-60°-90° right-angled triangle.

In any 30°-60°-90° triangle, the lengths of the sides opposite to these angles are always in the ratio of 1 : √3 : 2.

Let the side opposite to the 30° angle be x. We are given: x = 9√3 cm

The side opposite to the 60° angle is given by x√3. Substituting the value of x: x√3 = (9√3) × √3 = 9 × 3 = 27 cm

Explanation

Let the number be x.

According to the problem, when the number is increased by 26, it becomes 113% of itself. This can be represented by the algebraic equation: x + 26 = 1.13x

Subtracting x from both sides gives: 0.13x = 26

Solving for x: x = 26 / 0.13 x = 2600 / 13 x = 200

Explanation

Let r be the radius of the base and h be the height of the cylinder.

The circumference of the base is given by the formula 2πr. 2πr = 44 2 × (22/7) × r = 44 r = 7 cm

The volume of a cylinder is given by the formula: Volume = πr²h

Substituting the volume of 2310 cubic cm and the radius of 7 cm: (22/7) × 7² × h = 2310 154 × h = 2310 h = 15 cm

The curved surface area of the cylinder is given by the formula: Curved Surface Area = 2πrh

Using the known base circumference (2πr = 44 cm) and height (h = 15 cm): Curved Surface Area = 44 × 15 = 660 sq cm

Explanation

The amount A accrued under compound interest after n interest periods is given by the formula:

A = P × (1 + R)ⁿ

where P is the principal, R is the interest rate per period, and n is the number of interest periods.

Here, the interest rate per half year R is 5% or 0.05.

The first deposit of ₹3200 is made on 1st January, which earns interest for 2 half-years (n = 2) until the end of the year. The accrued amount for this deposit is:

A₁ = 3200 × (1 + 0.05)² A₁ = 3200 × 1.1025 = ₹3528

The second deposit of ₹3200 is made on 1st July, which earns interest for 1 half-year (n = 1) until the end of the year. The accrued amount for this deposit is:

A₂ = 3200 × (1 + 0.05)¹ A₂ = 3200 × 1.05 = ₹3360

The total amount accumulated at the end of the year is:

Total Amount = A₁ + A₂ = 3528 + 3360 = ₹6888

The total principal deposited during the year is:

Total Principal = 3200 + 3200 = ₹6400

The interest gained by the customer is the difference between the total accumulated amount and the total principal deposited:

Interest Gained = 6888 - 6400 = ₹488

Explanation

Total collection is the product of the price of the entry ticket and the number of visitors.

Let the initial price of the ticket be 11x and the new price be 16x. Let the initial number of visitors be 19y and the new number of visitors be 9y.

Initial collection = 11x × 19y = 209xy New collection = 16x × 9y = 144xy

Comparing the initial collection to the new collection, the ratio is 209xy:144xy, which simplifies to 209:144. Since the value changes from 209 to 144, the total collection has decreased in the ratio 209:144.

Explanation

Using the trigonometric identity cos(π + θ) = -cos(θ), the expression cos(4π/3) can be written as cos(π + π/3) = -cos(π/3). Since cos(π/3) is equal to ½, substituting this value yields -½.

Explanation

The standard trigonometric identity for tan 3A is: tan 3A = (3tanA - tan³A) / (1 - 3tan²A)

By multiplying both sides of the equation by (1 - 3tan²A), we get: tan 3A (1 - 3tan²A) = 3tanA - tan³A

Rearranging the terms to isolate tan³A on one side gives: tan³A = 3tanA - tan 3A (1 - 3tan²A)

Explanation

To simplify the expression sin A / (1 + cos A), we multiply both the numerator and the denominator by (1 - cos A):

(sin A (1 - cos A)) / ((1 + cos A)(1 - cos A))

Using the identity (a - b)(a + b) = a² - b², the denominator becomes:

(1 + cos A)(1 - cos A) = 1 - cos²A

Using the trigonometric identity sin²A + cos²A = 1, we can substitute 1 - cos²A with sin²A in the denominator:

(sin A (1 - cos A)) / sin²A

Canceling sin A from both the numerator and denominator yields:

(1 - cos A) / sin A

Splitting this into two separate fractions gives:

1/sin A - cos A/sin A

Since 1/sin A = cosec A and cos A/sin A = cot A, the expression simplifies to:

cosec A - cot A

Explanation

The total number of students who chose Engineering is the sum of the boys and girls in that stream: Total Engineering students = 80 + 40 = 120

The percentage of these students who are girls is: Percentage = (Number of girls who chose Engineering / Total Engineering students) × 100 Percentage = (40 / 120) × 100 = 33.33%

Explanation

The table provides the cumulative production of cars for each month. To find the total number of cars manufactured in the months of April and May, we subtract the cumulative production up to the end of March from the cumulative production up to the end of May.

Cumulative production up to May = 1800 Cumulative production up to March = 840

Cars manufactured in April and May = Cumulative production up to May - Cumulative production up to March Cars manufactured in April and May = 1800 - 840 = 960

Alternatively, this can be calculated by finding the individual production for each month: Production in April = Cumulative production of April - Cumulative production of March = 1510 - 840 = 670 Production in May = Cumulative production of May - Cumulative production of April = 1800 - 1510 = 290 Total production in April and May = 670 + 290 = 960

Explanation

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

Let the missing digit in the number 275₄76 be x.

Sum of digits at odd positions from left = 2 + 5 + 4 + 6 = 17 Sum of digits at even positions from left = 7 + x + 7 = 14 + x

The difference between these two sums must be 0: 17 - (14 + x) = 0 3 - x = 0 x = 3

Explanation

The total distance jogged in the week is the sum of the daily distances, which equals 20.5 km. Since 400 calories are burned for every 5 km, the rate is 80 calories per km, resulting in a total of 1640 calories burned (20.5 km multiplied by 80).

Explanation

First, calculate the total yearly expenses by summing the individual expenses:

Total expenses = 12 + 8 + 5 + 3 + 1 = 29

The percentage share of Labour alone is:

(8 ÷ 29) × 100 ≈ 27.59%

This calculation directly yields the percentage of 27.59%.

Explanation

Using the standard half-angle trigonometric identities, we know that:

1 - cosA = 2 sin²(A/2)

sinA = 2 sin(A/2) cos(A/2)

By dividing the expression for 1 - cosA by the expression for sinA, we get:

(1 - cosA) / sinA = 2 sin²(A/2) / (2 sin(A/2) cos(A/2))

Simplifying this by cancelling out 2 sin(A/2) from both the numerator and the denominator yields:

(1 - cosA) / sinA = sin(A/2) / cos(A/2) = tan(A/2)

Given that x = tan(A/2), substituting this relation gives:

x = (1 - cosA)/sinA

Explanation

Using basic trigonometric definitions, secA = 1/cosA and tanA = sinA/cosA.

Substituting these into the given expression:

x = (secA - tanA)² x = (1/cosA - sinA/cosA)² x = ((1 - sinA)/cosA)² x = (1 - sinA)² / cos²A

Using the fundamental identity cos²A = 1 - sin²A:

x = (1 - sinA)² / (1 - sin²A)

Factoring the denominator as a difference of squares, (1 - sin²A) = (1 - sinA)(1 + sinA):

x = (1 - sinA)² / ((1 - sinA)(1 + sinA))

Canceling the common term (1 - sinA) from the numerator and denominator:

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

Explanation

When a solid object is melted and recast into another shape, its volume remains the same.

The volume of a cylinder is given by the formula: V = π × r² × h₁

The volume of a cone is given by the formula: V = ⅓ × π × r² × h₂

Since the radius of both the cylinder and the cone is the same, we equate their volumes: π × r² × h₁ = ⅓ × π × r² × h₂

Canceling out π and r² from both sides gives: h₁ = ⅓ × h₂ h₂ = 3 × h₁

Given that the height of the cylinder (h₁) is 8 cm: h₂ = 3 × 8 = 24 cm

Explanation

In triangle ABC, since PQ is parallel to BC, triangle APQ is similar to triangle ABC.

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides: Area(Δ APQ) / Area(Δ ABC) = (AP / AB)²

Since AP : PB = 2 : 3, the total length AB is AP + PB = 2 + 3 = 5 units. Thus, the ratio AP / AB is 2/5.

Substituting the values: Area(Δ APQ) / Area(Δ ABC) = (2/5)² = 4/25

Given that Area(Δ APQ) = 8 sq cm: 8 / Area(Δ ABC) = 4/25 Area(Δ ABC) = 8 × 25 / 4 = 50 sq cm

The area of the trapezium PQCB is the difference between the area of triangle ABC and the area of triangle APQ: Area(PQCB) = Area(Δ ABC) - Area(Δ APQ) = 50 - 8 = 42 sq cm

Explanation

The midpoint of the segment joining (2, -5) and (0, 7) is: ((2 + 0)/2, (-5 + 7)/2) = (1, 1)

The slope of the line segment joining these two points is: m = (7 - (-5)) / (0 - 2) = 12 / -2 = -6

The slope of the perpendicular bisector is the negative reciprocal of this slope: m_perp = -1 / -6 = 1/6

Using the point-slope form with the midpoint (1, 1) and slope 1/6, the equation of the perpendicular bisector is: y - 1 = (1/6)(x - 1) 6(y - 1) = x - 1 6y - 6 = x - 1 x - 6y = -5

Explanation

Let the cost price of the machine be CP lakhs.

The loss when sold at Rs 45 lakhs is CP - 45, and the gain when sold at Rs 55 lakhs is 55 - CP.

Using the given relation: Gain = 9 × Loss 55 - CP = 9 × (CP - 45) 55 - CP = 9CP - 405 10CP = 460 CP = 46 lakhs

Explanation

The measure of each interior angle of a regular polygon with n sides is given by the formula:

Interior Angle = (n - 2) × 180° / n

A regular decagon has 10 sides. Substituting n = 10 into the formula:

Interior Angle = (10 - 2) × 180° / 10 Interior Angle = 8 × 18° Interior Angle = 144°

Explanation

Let the efficiency of Mansukh be 1 unit per hour. Since Mansukh can complete the work in 10 hours, the total work is 10 units.

Jayanti is 50% more efficient than Mansukh, so Jayanti's efficiency is 1.5 units per hour.

Their combined efficiency is 1 + 1.5 = 2.5 units per hour.

The time taken by both of them together to finish the work is: Time = Total work ÷ Combined efficiency Time = 10 ÷ 2.5 = 4 hours.

Explanation

In compound interest, the amount at the end of the third year is the amount at the end of the second year plus the interest earned on it during the third year. This relation is expressed by the formula:

A₃ = A₂ × (1 + R/100)

Substituting the given values:

28098.56 = 25088 × (1 + R/100)

1 + R/100 = 28098.56 / 25088

R/100 = (28098.56 - 25088) / 25088

R/100 = 3010.56 / 25088

R = 301056 / 25088

R = 12

Explanation

To find the value of x for which the two expressions are equal, set them equal to each other:

19 - 5x = 19x + 5

Rearrange the terms to group the variable terms on one side and the constant terms on the other:

19 - 5 = 19x + 5x

14 = 24x

Divide both sides by 24 to solve for x:

x = 14/24

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, 2:

x = 7/12

Explanation

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

Given that C = 88 cm, we can find the radius: 2 × (22/7) × r = 88 r = (88 × 7) / 44 r = 14 cm

The area of a circle is given by the formula Area = πr².

Substituting the value of r: Area = (22/7) × 14 × 14 Area = 22 × 2 × 14 Area = 616 sq cm

Explanation

The mean of marks of the combined divisions is calculated using the weighted mean formula:

Weighted Mean = (n₁x₁ + n₂x₂ + n₃x₃) / (n₁ + n₂ + n₃)

Given: n₁ = 45, x₁ = 69 n₂ = 65, x₂ = 65 n₃ = 50, x₃ = 63

To simplify the calculation, we can divide the student counts by their greatest common divisor, which is 5. This gives scaled weights: w₁ = 9 w₂ = 13 w₃ = 10

The total scaled weight is: W = 9 + 13 + 10 = 32

Now, compute the weighted sum of the marks: Weighted Sum = (9 × 69) + (13 × 65) + (10 × 63) Weighted Sum = 621 + 845 + 630 = 2096

Dividing this sum by the total scaled weight gives the combined mean: Combined Mean = 2096 / 32 = 65.5

Explanation

Since the expression (6a - 5b)/(a + 2b) is homogeneous of degree 1 in both the numerator and the denominator, we can directly substitute a = 5 and b = 8.

Substituting these values into the expression: (6(5) - 5(8)) / (5 + 2(8)) = (30 - 40) / (5 + 16) = -10 / 21