SSC CHSL Tier 1 2016 Quantitative Aptitude Questions with Solutions

Explanation

The percent profit of the company was the least in the year 2014, when it was 10%.

The relation between Revenue, Expenditure, and Profit % is given by the formula: Profit % = (Revenue - Expenditure) / Expenditure × 100

Substituting the given values of Expenditure as Rs 325 crore and Profit % as 10% into the formula: 10 = (Revenue - 325) / 325 × 100 0.1 = (Revenue - 325) / 325 Revenue - 325 = 32.5 Revenue = 325 + 32.5 = 357.5 crore

Explanation

The average number of children per house is calculated using the weighted mean formula:

Average = ∑(f × x) / ∑ f

where x represents the number of children and f represents the number of houses.

First, calculate the total number of houses (∑ f): ∑ f = 3 + 9 + 18 + 3 = 33

Next, calculate the total number of children (∑(f × x)): ∑(f × x) = (0 × 3) + (1 × 9) + (2 × 18) + (3 × 3) ∑(f × x) = 0 + 9 + 36 + 9 = 54

Now, divide the total number of children by the total number of houses: Average = 54 / 33 ≈ 1.636

Rounding to two decimal places, the average number of children per house is 1.64.

Explanation

Total shares issued by the company is six lakh, which is 6,00,000 shares.

According to the table, Dhiraj initially holds a 30% share in the company.

The number of shares initially held by Dhiraj is calculated as: 30% of 6,00,000 = (30/100) × 6,00,000 = 1,80,000 shares

If Dhiraj buys 15,000 shares from Basu, his total shares will increase by 15,000.

Dhiraj's new total share count is: 1,80,000 + 15,000 = 1,95,000 shares

Explanation

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

11x + 7 = 17x - 1

Rearrange the equation to group the terms with x on one side and the constant terms on the other side. Subtract 11x from both sides of the equation:

7 = 6x - 1

Next, add 1 to both sides to isolate the term with x:

8 = 6x

Now, solve for x by dividing both sides by 6:

x = 8/6

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

x = 4/3

Explanation

Let the cost price of the watch for the wholesaler be CP.

The successive transactions from the wholesaler to the retailer, and then to the customer, can be represented by the formula: Customer Price = CP × (1 + Wholesaler Gain%) × (1 - Retailer Loss%)

Substituting the given values: 2499 = CP × (1 + 36/100) × (1 - 25/100) 2499 = CP × 1.36 × 0.75

Expressing the decimals as fractions simplifies the calculation: 2499 = CP × 136/100 × 3/4 2499 = CP × 34/100 × 3 2499 = CP × 102/100 CP = (2499 × 100) / 102 CP = 2450

Explanation

To find the percentage error easily, let the number be the least common multiple of the denominators 11 and 13, which is 143.

The correct value after multiplying by 13/11 is: 143 × 13/11 = 169

The incorrect value obtained by multiplying by 11/13 is: 143 × 11/13 = 121

The absolute error in the calculation is: 169 - 121 = 48

The percentage error is calculated relative to the correct value: Percentage Error = (Error / Correct Value) × 100 Percentage Error = (48 / 169) × 100 ≈ 28.4%

Explanation

To solve the expression 5 × [-0.6(2.8 + 1.2)] of 0.3, apply the standard order of operations.

First, calculate the sum inside the innermost parentheses: 2.8 + 1.2 = 4

Next, evaluate the terms inside the square bracket: -0.6 × 4 = -2.4

Substitute this result back into the main expression: 5 × [-2.4] of 0.3

The word "of" represents multiplication. Evaluate the multiplication from left to right: 5 × -2.4 = -12

Finally, multiply this value by 0.3: -12 × 0.3 = -3.6

Explanation

Using the given ratio (x + y)/(x - y) = 5/2, we cross-multiply to find the relationship between x and y:

2(x + y) = 5(x - y) 2x + 2y = 5x - 5y 3x = 7y x/y = 7/3

This gives x = 7 and y = 3 when substituted into a homogeneous expression. Substituting these values into the given expression:

(4x + 5y)/(x - 4y) = (4(7) + 5(3)) / (7 - 4(3)) (4x + 5y)/(x - 4y) = (28 + 15) / (7 - 12) (4x + 5y)/(x - 4y) = 43 / -5 (4x + 5y)/(x - 4y) = -43/5

Explanation

The rate of work of P is 1/25 of the project per day, and the rate of work of Q is 1/50 of the project per day.

When P and Q work together, their combined rate of work per day is: Combined rate = 1/25 + 1/50 = 2/50 + 1/50 = 3/50 of the project per day.

To complete 18% of the project, they need to complete a fraction of 18/100 of the total work. The time required is: Time = (Required fraction of work) / (Combined rate per day) Time = (18/100) / (3/50) = (18/100) × (50/3) = (18 ÷ 3) × (50 ÷ 100) = 6 × ½ = 3 days.

Explanation

The total number of students in the class is 56, out of which 21 are girls. Therefore, the number of boys in the class is: 56 - 21 = 35

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 Class = (Number of Girls × Average Weight of Girls) + (Number of Boys × Average Weight of Boys)

Substituting the given values: 56 × 62.875 = 21 × 56 + 35 × Average Weight of Boys

To simplify the calculation, divide the entire equation by 7: 8 × 62.875 = 3 × 56 + 5 × Average Weight of Boys

Recognizing that 62.875 can be written as 62 + 7/8 makes the multiplication straightforward: 8 × (62 + 7/8) = 168 + 5 × Average Weight of Boys 496 + 7 = 168 + 5 × Average Weight of Boys 503 = 168 + 5 × Average Weight of Boys 5 × Average Weight of Boys = 503 - 168 5 × Average Weight of Boys = 335 Average Weight of Boys = 335 / 5 = 67 kg

Explanation

To convert speed from kilometers per hour to meters per second, the speed is multiplied by the conversion factor 5/18.

Speed in m/s = 1296 × 5/18

First, divide 1296 by 18: 1296 ÷ 18 = 72

Next, multiply the result by 5: 72 × 5 = 360 m/s

The missile travels 360 meters in one second.

Explanation

Let the number of 1-rupee, 50-paise, and 10-paise coins be 4x, 2x, and 5x respectively.

To find the total value, we convert each denomination into rupees: The value of 1-rupee coins is 4x × 1 = 4x rupees The value of 50-paise coins is 2x × 0.5 = x rupees The value of 10-paise coins is 5x × 0.1 = 0.5x rupees

Summing these values gives the total amount of ₹11: 4x + x + 0.5x = 11 5.5x = 11 x = 2

The number of 50-paise coins is represented by 2x. Substituting x = 2 gives 2 × 2 = 4.

Explanation

The effective discount on purchasing 5 items is calculated by finding the total discount on the combination of 1 item and 4 items, and then dividing it by the total marked price of all 5 items.

Marked price of 1 item = Rs 800 Marked price of 5 items = 5 × 800 = Rs 4000

Discount on 1 item = 15% of 800 = 15/100 × 800 = Rs 120 Discount on 4 items = 38% of (4 × 800) = 38/100 × 3200 = Rs 1216

Total discount obtained = 120 + 1216 = Rs 1336

Effective discount percentage = (Total discount / Total marked price) × 100 Effective discount percentage = (1336 / 4000) × 100 = 33.4%

Explanation

To find the possible values of x, we solve the system of inequalities.

First inequality: 2 + 2x < 5 - x/2

Multiplying the entire inequality by 2 to clear the fraction: 4 + 4x < 10 - x

Adding x to both sides: 4 + 5x < 10

Subtracting 4 from both sides: 5x < 6 x < 1.2

Second inequality: 5x + 3 > 5 - 5x

Adding 5x to both sides: 10x + 3 > 5

Subtracting 3 from both sides: 10x > 2 x > 0.2

Combining both inequality results gives the range: 0.2 < x < 1.2

The value 1 lies within this range.

Explanation

Let the non-zero number be x. According to the given condition, the sum of the number and thrice its reciprocal is 13/2:

x + 3/x = 13/2

Multiplying the entire equation by 2x to clear the denominators yields:

2x² + 6 = 13x

Rearranging the terms into a standard quadratic equation:

2x² - 13x + 6 = 0

Factoring the quadratic equation by splitting the middle term:

2x² - 12x - x + 6 = 0 2x(x - 6) - 1(x - 6) = 0 (2x - 1)(x - 6) = 0

This gives the solutions:

x = 6 or x = ½

Substituting x = 6 back into the original relation confirms the statement:

6 + 3/6 = 6 + ½ = 13/2

Explanation

According to the properties of similar triangles, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Area(ΔDEF) / Area(ΔGHI) = (DE / GH)²

Substituting the given side lengths of DE = 16 cm and GH = 25 cm into the formula:

Area(ΔDEF) / Area(ΔGHI) = (16 / 25)² = 256 / 625

Explanation

The slope of a line passing through the points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Since parallel lines have equal slopes, the slope of the line passing through (2, -1) and (y, -2) must be equal to the slope of the line passing through (-3, 4) and (0, 3).

Calculating the slope of the second line: m₂ = (3 - 4) / (0 - (-3)) = -1 / 3

Calculating the slope of the first line: m₁ = (-2 - (-1)) / (y - 2) = -1 / (y - 2)

Equating the two slopes: -1 / (y - 2) = -1 / 3

Solving for y: y - 2 = 3 y = 5

Explanation

The sum of the interior angles of a polygon with n sides is given by the formula (n - 2) × 180°. For a polygon with 10 sides, substitute n = 10 into the formula:

Sum = (10 - 2) × 180° Sum = 8 × 180° Sum = 1440°

Explanation

Let the two diagonals of the rhombus be d₁ and d₂. Since one diagonal is half the other, we can express them as d₁ = x and d₂ = 2x.

The diagonals of a rhombus bisect each other at right angles. The relationship between the side s of the rhombus and its diagonals is given by: s² = (d₁/2)² + (d₂/2)²

Substituting the given values, where s = 10 cm: 10² = (x/2)² + (x)² 100 = x²/4 + x² 100 = 5x²/4 x² = 400 / 5 x² = 80

The area of a rhombus is given by the formula: Area = ½ × d₁ × d₂

Substituting the expressions for the diagonals into the area formula: Area = ½ × x × 2x = x²

Since x² = 80, the area of the rhombus is 80 sq cm.

Explanation

The curved surface area (CSA) of a hemisphere is given by the formula: CSA = 2πr²

Substituting the given value of CSA = 110.88 sq cm and π ≈ 22/7: 110.88 = 2 × (22/7) × r² 110.88 = (44/7) × r² r² = (110.88 × 7) / 44 r² = 2.52 × 7 r² = 17.64 r = √17.64 = 4.2 cm

This value of the radius is verified by the volume of the hemisphere: Volume = (2/3)πr³ Volume = (2/3) × (22/7) × 4.2³ Volume = (44/21) × 74.088 = 155.232 cubic cm

Explanation

Correct Answer: D

Using the trigonometric identity tan(-θ) = -tan(θ), the given expression tan(-7π/4) can be simplified as:

tan(-7π/4) = -tan(7π/4)

The angle 7π/4 lies in the fourth quadrant and can be written as 2π - π/4. Applying the periodic property of the tangent function where tan(2π - θ) = -tan(θ), we get:

-tan(7π/4) = -tan(2π - π/4) = -(-tan(π/4)) = tan(π/4)

Since the value of tan(π/4) is 1, the value of x is 1.

Explanation

The standard trigonometric identity for the cotangent of the difference of two angles is: cot(A - B) = cos(A - B) / sin(A - B)

Expanding the cosine and sine of the difference of two angles: cot(A - B) = (cos A cos B + sin A sin B) / (sin A cos B - cos A sin B)

Dividing both the numerator and the denominator by sin A sin B: cot(A - B) = ((cos A cos B) / (sin A sin B) + 1) / ((sin A cos B) / (sin A sin B) - (cos A sin B) / (sin A sin B))

Simplifying each term: cot(A - B) = (cot A cot B + 1) / (cot B - cot A)

Since this matches the given equation, x equals cot(A - B).

Explanation

Simple interest is distributed equally over the years, meaning the simple interest for the first year is 2400 / 2 = Rs 1200.

For any investment, the compound interest and simple interest are identical in the first year. The difference between the compound interest and simple interest over two years is due to the interest earned on the first year's interest.

The difference between the compound interest and simple interest for two years is: 2544 - 2400 = Rs 144

This Rs 144 is the interest earned on the first year's interest of Rs 1200 over the course of the second year.

The rate of interest (R) is calculated as: R = (Interest earned on first year's interest / Simple interest for first year) × 100 R = (144 / 1200) × 100 = 12%

Explanation

We simplify the expression:

1/(1 + sinA) + 1/(1 - sinA)

By finding a common denominator, the expression becomes:

((1 - sinA) + (1 + sinA)) / ((1 + sinA)(1 - sinA))

= 2 / (1 - sin²A)

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

= 2 / cos²A

Since secA = 1/cosA, this expression simplifies directly to 2sec²A, which is equal to x.

Explanation

The total number of boys across all divisions is: 30 + 25 + 10 + 40 + 40 + 30 = 175

The total number of girls across all divisions is: 90

The ratio of the total number of boys to the total number of girls is: 175 : 90 = 35 : 18

Explanation

To find the number of students who scored 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.

From the cumulative frequency table: Number of students scoring 20 and above = 70 Number of students scoring 40 and above = 21

Subtracting these two values gives the number of students in the range of 20 to less than 40: 70 - 21 = 49

Explanation

The end of the year 2012 is equivalent to the beginning of the year 2013. The beginning of the year 2014 is equivalent to the end of the year 2013. Therefore, to find the GDP at the beginning of 2014, we apply the growth rate of 2013 to the GDP at the end of 2012.

Using the percentage change formula: GDP at the beginning of 2014 = GDP at the end of 2012 × (1 + Growth rate of 2013 / 100)

Substituting the given values: GDP at the beginning of 2014 = 4 × (1 - 3/100) GDP at the beginning of 2014 = 4 × 0.97 = 3.88 trillion

Explanation

The average marks scored by the student is calculated by dividing the sum of marks obtained in all subjects by the total number of subjects.

Sum of marks = 70 + 75 + 30 + 75 + 60 = 310 Number of subjects = 5

Initial average marks = 310 / 5 = 62

Since 5 points are deducted from the average due to poor attendance, the net average marks scored by the student are: 62 - 5 = 57

Explanation

The standard trigonometric values are sin 60° = √3/2 and cos 45° = 1/√2.

Substituting these values into the given expression: x = √3/2 + 1/√2

To add the terms, express them with a common denominator of 2 by multiplying the numerator and denominator of the second term by √2: 1/2 = (1 × √2) / (√2 × √2) = √2/2

Thus: x = √3/2 + √2/2 x = (√3 + √2)/2

Explanation

We are given that x = cot(A/2).

By applying the standard half-angle trigonometric identities: 1 + cosA = 2 cos²(A/2) sinA = 2 sin(A/2) cos(A/2)

Dividing the first expression by the second: (1 + cosA) / sinA = [2 cos²(A/2)] / [2 sin(A/2) cos(A/2)]

Simplifying the fraction by cancelling the common terms 2 and cos(A/2) from both the numerator and the denominator yields: (1 + cosA) / sinA = cos(A/2) / sin(A/2) = cot(A/2)

Since x = cot(A/2), we have: x = (1 + cosA) / sinA

Explanation

The cost price (CP) of the pistachios is calculated using the formula: CP = SP / (1 - Loss%)

Substituting the given selling price (SP) of ₹1140 and a 5% loss: CP = 1140 / (1 - 0.05) CP = 1140 / 0.95 CP = 1200

The cost price of the pistachios is ₹1200 per kg.

When the pistachios are sold at a new selling price of ₹1260 per kg, the profit is: Profit = New SP - CP Profit = 1260 - 1200 = 60

The profit percentage is calculated as: Profit% = (Profit / CP) × 100 Profit% = (60 / 1200) × 100 = 5%

Explanation

Let the work rate of Samarth be R. Since Samarth can complete the job alone in 28 days, Samarth's rate of work is 1/28 of the job per day.

Because Mandar works 3 times as fast as Samarth, Mandar's rate of work is 3 × (1/28) = 3/28 of the job per day.

When working together, their combined rate of work is the sum of their individual rates: Combined rate = 1/28 + 3/28 = 4/28 = 1/7 of the job per day.

The time taken to complete the job together is the reciprocal of their combined rate: Time taken = 1 / (1/7) = 7 days.

Explanation

The discount percentage is calculated using the formula:

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

Given: Marked Price = Rs 3250 Selling Price = Rs 2275

Discount = 3250 - 2275 = Rs 975

Discount Percentage = (975 / 3250) × 100 = 30%

Explanation

Since the time of travel is the same for both the policeman and the thief, the distance covered by each is directly proportional to their speeds.

Ratio of distance covered by policeman to distance covered by thief = 18 : 10 = 9 : 5

Let the distance covered by the policeman be 9x and that by the thief be 5x. The difference in their distances is the initial gap of 500 metres: 9x - 5x = 500 4x = 500 x = 125

The distance run by the thief before being overtaken is: 5x = 5 × 125 = 625 metres

Explanation

To find the smallest number that should be added to 2957 to make it completely divisible by 17, we first divide 2957 by 17 to find the remainder.

2957 ÷ 17 = 173 with a remainder of 16

The smallest number to be added is the difference between the divisor and the remainder.

Required number = 17 - 16 = 1

Adding 1 to 2957 results in 2958, which is exactly divisible by 17 (2958 ÷ 17 = 174).

Explanation

The given expression is x = (sin²A - sin²B) / (cos²A cos²B).

Consider the expression tan²A - tan²B. By converting tangent to sine and cosine, we get:

tan²A - tan²B = (sin²A / cos²A) - (sin²B / cos²B)

Taking the common denominator cos²A cos²B, the expression becomes:

(sin²A cos²B - sin²B cos²A) / (cos²A cos²B)

Using the trigonometric identity cos²θ = 1 - sin²θ to rewrite the numerator:

sin²A cos²B - sin²B cos²A = sin²A (1 - sin²B) - sin²B (1 - sin²A) = sin²A - sin²A sin²B - sin²B + sin²A sin²B = sin²A - sin²B

Substituting this back into the fraction gives:

(sin²A - sin²B) / (cos²A cos²B)

This matches the given expression for x, meaning x is equal to tan²A - tan²B.

Explanation

The volume of a sphere is given by the formula V = 4/3 π r³, where r is the radius of the sphere.

When a larger ball is melted to form smaller balls, the total volume remains conserved.

The number of smaller balls (N) that can be made is given by: N = Volume of the bigger ball / Volume of each smaller ball N = (4/3 π R³) / (4/3 π r³) N = (R / r)³

Given that the diameter of the bigger ball is 48 cm, its radius (R) is: R = 48 / 2 = 24 cm

The radius of each smaller ball (r) is 3 cm.

Substituting the values into the formula: N = (24 / 3)³ N = 8³ N = 512

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 9x and the new price be 13x. Let the initial number of visitors be 7y and the new number of visitors be 4y.

Initial total collection = 9x × 7y = 63xy New total collection = 13x × 4y = 52xy

Comparing the initial collection to the new collection, the ratio is 63xy : 52xy, which simplifies to 63 : 52. Since the value has reduced from 63 to 52, the total collection has decreased in the ratio 63:52.

Explanation

Let the number be the least common multiple of the denominators 5 and 7, which is 35.

The correct calculation is: 35 × 7/5 = 49

The incorrect calculation is: 35 × 5/7 = 25

The magnitude of the error is: 49 - 25 = 24

The percentage error is given by the formula: Percentage Error = (Error / Correct Value) × 100 Percentage Error = (24 / 49) × 100 Percentage Error = 2400 / 49 ≈ 48.98%

Explanation

For two similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides.

Perimeter(ΔGHI) / Perimeter(ΔKLM) = GH / KL

Substituting the given values into the formula:

9/4 = 27 / KL

KL = (27 × 4) / 9

KL = 12 cm

Explanation

The diagonals of a square are perpendicular to each other and bisect each other. Therefore, the midpoint of diagonal AC is also the midpoint of diagonal BD.

The coordinates of the midpoint M of AC are: x = (7 + 1)/2 = 4 y = (-8 + 4)/2 = -2 Thus, M is (4, -2).

The slope of diagonal AC is: m = (4 - (-8)) / (1 - 7) = 12 / -6 = -2

Since diagonal BD is perpendicular to AC, its slope is: m_BD = -1 / m = -1 / (-2) = ½

Using the point-slope form with the midpoint (4, -2) and slope ½, the equation of diagonal BD is: y - (-2) = ½(x - 4) y + 2 = ½(x - 4) 2(y + 2) = x - 4 2y + 4 = x - 4 x - 2y = 8

Explanation

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

Exterior Angle = 360° / n

A regular dodecagon has 12 sides, which means n = 12. Substituting this value into the formula:

Exterior Angle = 360° / 12 = 30°

Explanation

The perimeter of a square is given by the formula P = 4s, where s represents the length of a side. Substituting the given perimeter:

4s = 40 s = 10 cm

The area of a square is given by the formula A = s². Substituting the side length:

A = 10² = 100 sq cm

Explanation

To find the coefficient of x² in the expression (x + 3)(2 - 4x)(5x - 6), we first expand the product of the first two terms:

(x + 3)(2 - 4x) = 2x - 4x² + 6 - 12x = -4x² - 10x + 6

Next, we multiply this intermediate quadratic expression by the third term:

(-4x² - 10x + 6)(5x - 6)

The terms that contain x² in this product are obtained from: The quadratic term of the first expression multiplied by the constant term of the second expression: (-4x²) × (-6) = 24x² The linear term of the first expression multiplied by the linear term of the second expression: (-10x) × (5x) = -50x²

Summing these terms yields:

24x² - 50x² = -26x²

This gives the coefficient of x² as -26.

Explanation

Using the algebraic identity: (a + b)² = a² + b² + 2ab

Substituting the given values into the formula: (10)² = 58 + 2ab 100 = 58 + 2ab 2ab = 100 - 58 2ab = 42 ab = 21

Explanation

Let the ten's digit of the two-digit number be t and the units digit be u. The value of the original number is 10t + u.

According to the given conditions: t - u = 2

The number obtained by interchanging the digits is 10u + t. Subtracting 18 from the original number yields: 10t + u - 18 = 10u + t 9t - 9u = 18 t - u = 2

For the number 86, where t = 8 and u = 6: t - u = 8 - 6 = 2

Subtracting 18 from the number: 86 - 18 = 68

The resulting number 68 is formed by interchanging the digits of 86.

Explanation

Total value of stock is calculated using the formula:

Total Value = ∑ (Quantity × Average Cost)

Applying this to each product category:

Mobile Phones: 44 × 11000 = 484000 Rs Cameras: 95 × 6000 = 570000 Rs TVs: 37 × 41000 = 1517000 Rs Refrigerators: 33 × 49000 = 1617000 Rs ACs: 45 × 22000 = 990000 Rs

Summing these individual values to get the total stock value:

Total Value = 484000 + 570000 + 1517000 + 1617000 + 990000 = 5178000 Rs

Converting this value into lakh rupees (since 1 lakh = 100000):

Value in lakh rupees = 5178000 ÷ 100000 = 51.78

Explanation

For the year 2012, the ratio of import to export is 1.3. Given the imports in 2012 is Rs. 1400 crores, the exports in 2012 is calculated as: Exports (2012) = Imports (2012) / 1.3 = 1400 / 1.3 ≈ 1076.92 crores

The total exports for the years 2012 and 2013 combined is Rs. 2400 crores. Therefore, the exports in 2013 is: Exports (2013) = 2400 - Exports (2012) = 2400 - 1076.92 = 1323.08 crores

For the year 2013, the ratio of import to export is 0.7. The imports in 2013 is calculated as: Imports (2013) = Exports (2013) × 0.7 = 1323.08 × 0.7 ≈ 926.16 crores

Rounding this off to the nearest integer gives 926 crores.

Explanation

To find the increase in the height of the child from the 5th Birthday to the 13th Birthday, we calculate the difference between the height of the child on these two birthdays using the formula:

Increase in height = Height on 13th Birthday - Height on 5th Birthday

From the given data table: Height of the child on the 5th Birthday = 110 cm Height of the child on the 13th Birthday = 160 cm

Substituting these values into the formula: Increase in height = 160 cm - 110 cm = 50 cm

Explanation

The total time duration between 10 PM and 6 AM is 8 hours.

From the given data, the percentage of time spent in Light sleep is 10% and the percentage of time spent Awake is 40%.

The combined percentage for Light sleep or Awake is 10% + 40% = 50%.

To find the duration, calculate 50% of the total 8 hours:

Duration = 50% × 8 = 4 hours