SSC CHSL Tier 1 2016 Quantitative Aptitude Questions with Solutions

Explanation

Let the three numbers be x, y, and z. Since their average is 77, their sum is: x + y + z = 77 × 3 = 231

We are given that the first number x is 3/4 times the sum of the other two numbers: x = (3/4) × (y + z) y + z = (4/3) × x

Substituting this value of y + z into the sum equation: x + (4/3) × x = 231 (7/3) × x = 231 x = 231 × 3/7 x = 33 × 3 x = 99

Explanation

In compound interest, the amount at the end of any year acts as the principal for the next year. Therefore, the interest earned in the third year is the difference between the amounts at the end of the third and second years.

Interest for the third year = Rs 37791.36 - Rs 34992 = Rs 2799.36

The rate of interest R can be calculated directly using the formula: R = (Interest / Principal) × 100

Substituting the values: R = (2799.36 / 34992) × 100 R = 279936 / 34992 R = 8 percent

Explanation

In a rectangle ABCD, the adjacent sides DA and AB are perpendicular to each other. The product of the slopes of two perpendicular lines is always equal to -1. Let m₁ be the slope of side DA and m₂ be the slope of side AB.

m₁ × m₂ = -1

Substituting the given slope of side DA into the formula:

(-3/4) × m₂ = -1

Multiplying both sides by -4/3 yields:

m₂ = 4/3

Explanation

We know the trigonometric values: cot 30° = √3 cos 45° = 1/√2

Substituting these values into the given equation: x = cot 30° - cos 45° x = √3 - 1/√2

Taking the common denominator √2: x = (√3 × √2 - 1) / √2 x = (√6 - 1)/√2

Explanation

By Pythagoras' theorem, the diagonal d, length l, and breadth b of a rectangle satisfy the relation: d² = l² + b²

Given that the diagonal d = 10 cm and one side l = 8 cm, the other side b is calculated as: 10² = 8² + b² 100 = 64 + b² b² = 36 b = 6 cm

The area of the rectangle is given by the product of its adjacent sides: Area = l × b Area = 8 × 6 = 48 sq cm

Explanation

The fundamental relationship between two numbers, their Highest Common Factor (HCF), and their Lowest Common Multiple (LCM) is given by the formula:

Product of two numbers = HCF × LCM

Substituting the given values into the formula:

55 × 99 = 11 × LCM

LCM = (55 × 99) ÷ 11

LCM = 5 × 99

LCM = 495

Explanation

Assume the quantity of pure milk purchased is 5 litres. At Rs 25 per litre, the total Cost Price of this milk is 5 × 25 = Rs 125.

The milkman adds 1/5 of water to the milk, which means the volume of water added is 1/5 × 5 = 1 litre. The total quantity of the mixture now becomes 5 + 1 = 6 litres.

He sells this mixture at Rs 29 per litre. The total Selling Price for 6 litres of the mixture is 6 × 29 = Rs 174.

The total gain made is Selling Price - Cost Price = 174 - 125 = Rs 49.

The gain percentage is calculated as (Gain / Cost Price) × 100 = (49 / 125) × 100 = 39.2%.

Explanation

We can solve this system of linear equations by adding the two equations to eliminate the variable y.

Adding the two equations: (9x - 6y) + (x + 6y) = 15 + 15 10x = 30 x = 3

Substituting x = 3 into the second equation: 3 + 6y = 15 6y = 12 y = 2

This yields x = 3 and y = 2.

Explanation

To divide 111a²b²c² by 37a², we write the division as a fraction:

(111a²b²c²) / (37a²)

We divide the numerical coefficients and the algebraic variables separately:

111 / 37 = 3

a² / a² = 1

Multiplying the remaining terms together:

3 × 1 × b²c² = 3b²c²

Explanation

The volume of the solid is the sum of the volume of the cone and the volume of the hemisphere.

Volume of the cone = (1/3) × π × r² × h Volume of the hemisphere = (2/3) × π × r³

Total Volume = (1/3) × π × r² × (h + 2r)

Given that the diameter of both the cone and hemisphere is 21 cm, the radius r is 21/2 cm. The height of the cone h is 25 cm. Substituting these values into the formula with π = 22/7:

Total Volume = (1/3) × (22/7) × (21/2) × (21/2) × (25 + 2 × (21/2)) Total Volume = 11 × (21/2) × (25 + 21) Total Volume = 11 × (21/2) × 46 Total Volume = 11 × 21 × 23 Total Volume = 5313 cubic cm

Explanation

Average speed is calculated using the formula: Speed = Distance / Time

Substituting the given values: Speed = 297 km / 4.4 hours = 67.5 km/h

To convert the speed from kilometers per hour (km/h) to meters per second (m/s), multiply by the conversion factor 5/18: Speed in m/s = 67.5 × 5/18 = 18.75 m/s

Explanation

Let the radius of the circle be r and the side of the square be s.

The area of a circle is given by the formula π × r². Since the area of the circle is 36π sq cm, we can find the radius by setting up the equation:

π × r² = 36π r² = 36 r = 6 cm

The diameter of the circle is twice the radius:

Diameter = 2 × r = 2 × 6 = 12 cm

The side of the square is equal to the diameter of the circle, so:

s = 12 cm

The area of the square is given by the formula s²:

Area of the square = 12² = 144 sq cm

Explanation

The marked price of one item is Rs 100, so the total marked price of 6 items is 6 × Rs 100 = Rs 600.

To buy 6 items under the given discount scheme, the purchase is split into one group of 4 items and one group of 2 items.

For the purchase of 4 items, the discount is 43%: Discount on 4 items = 43% of (4 × Rs 100) = 0.43 × Rs 400 = Rs 172

For the purchase of 2 items, the discount is 25%: Discount on 2 items = 25% of (2 × Rs 100) = 0.25 × Rs 200 = Rs 50

Total discount received on all 6 items = Rs 172 + Rs 50 = Rs 222

The effective discount percentage is the total discount divided by the total marked price, multiplied by 100: Effective discount = (222 / 600) × 100 = 37%

Explanation

The double-angle trigonometric identity for the tangent of 2A is given by the formula:

tan(2A) = 2tanA / (1 - tan²A)

Given that tan(2A) = x, we have:

x = 2tanA / (1 - tan²A)

In standard typographical representation, the exponent in the denominator tan²A is written as tan2A. Substituting this notation yields:

x = 2tanA / (1 - tan2A)

Explanation

The value of the total stock is calculated by summing the products of the quantity and the average cost for each item type:

Mobile Phones value = 40 × 10000 = 4,00,000 Rs Cameras value = 93 × 20000 = 18,60,000 Rs TVs value = 97 × 52000 = 50,44,000 Rs Refrigerators value = 21 × 22000 = 4,62,000 Rs ACs value = 39 × 23000 = 8,97,000 Rs

Total stock value = 4,00,000 + 18,60,000 + 50,44,000 + 4,62,000 + 8,97,000 = 86,63,000 Rs

To convert the total stock value into lakh rupees, divide the sum by 1,00,000: Value in lakh rupees = 86,63,000 / 1,00,000 = 86.63 lakh Rs

Explanation

Let the imports and exports of a year be represented by I and E respectively.

For the year 2012: Import/Export ratio = 1.2 Given that the imports in 2012 (I₁₂) is Rs. 1000 crores: I₁₂ / E₁₂ = 1.2 1000 / E₁₂ = 1.2 E₁₂ = 1000 / 1.2 = 833.33 crores

For the year 2013: Given that the total exports in 2012 and 2013 together (E₁₂ + E₁₃) is Rs. 3600 crores: E₁₃ = 3600 - E₁₂ E₁₃ = 3600 - 833.33 = 2766.67 crores

The Import/Export ratio for 2013 is 0.8: I₁₃ / E₁₃ = 0.8 I₁₃ = 0.8 × E₁₃ I₁₃ = 0.8 × 2766.67 = 2213.33 crores

Explanation

To find the increase in the height of the child from the 7th Birthday to the 15th Birthday, the formula is:

Height Increase = Height at 15th Birthday - Height at 7th Birthday

From the data table, the height of the child is: Height at 15th Birthday = 185 cms Height at 7th Birthday = 120 cms

Substituting these values into the formula:

Height Increase = 185 - 120 = 65 cms

Explanation

The total time duration between 10:00 PM and 6:00 AM is 8 hours.

The values given in the data table represent percentages since their sum is 5 + 10 + 10 + 20 + 55 = 100%.

The combined percentage of time the user spent Dreaming or Awake is: 10% + 55% = 65%

Multiplying the total duration of 8 hours by this combined percentage yields the duration: 8 hours × 0.65 = 5.2 hours

Explanation

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

When a discount of 30% is offered on the list price, the selling price is: SP = 0.70 × MP

Since this results in a 16% loss, the selling price is also: SP = 0.84 × CP

Equating these two expressions: 0.70 × MP = 0.84 × CP MP = (0.84 / 0.70) × CP MP = 1.2 × CP

When a discount of 20% is offered on the list price, the new selling price is: New SP = 0.80 × MP New SP = 0.80 × 1.2 × CP New SP = 0.96 × CP

Since the new selling price is 96% of the cost price, the merchant makes a loss of 4%.

Explanation

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

First inequality: 5x - 4 ≤ 2 - x 6x ≤ 6 x ≤ 1

Second inequality: 4x + 5 > 2x - 5 2x > -10 x > -5

Combining both inequalities, we get the range for x: -5 < x ≤ 1

Among the given choices, only -1 lies within this interval since -5 < -1 ≤ 1.

Explanation

The deposit made on 1st January remains in the bank for two half-years. Using the compound interest formula, the accumulated amount for this deposit at the end of the year is: Amount = Principal × (1 + Rate/100)² Amount₁ = 8800 × (1 + 15/100)² = 8800 × 1.15² = 8800 × 1.3225 = ₹11638

The deposit made on 1st July remains in the bank for only one half-year. The accumulated amount for this deposit at the end of the year is: Amount₂ = 8800 × (1 + 15/100)¹ = 8800 × 1.15 = ₹10120

The total accumulated amount at the end of the year is: ₹11638 + ₹10120 = ₹21758

The total principal deposited by the customer is: ₹8800 + ₹8800 = ₹17600

The total interest gained is the difference between the total accumulated amount and the total principal deposited: Interest = ₹21758 - ₹17600 = ₹4158

Explanation

To find the value of x - y, solve the system of linear equations:

4x - 5y = -37 7x + y = -16

From the second equation, express y in terms of x: y = -16 - 7x

Substitute this expression for y into the first equation: 4x - 5(-16 - 7x) = -37 4x + 80 + 35x = -37 39x = -117 x = -3

Substitute the value of x back into the expression for y: y = -16 - 7(-3) y = 5

Calculate x - y: x - y = -3 - 5 = -8

Explanation

The centroid of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by the formula: (x_g, y_g) = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)

Let the coordinates of vertex C be (x, y). Given the coordinates of A(-2, 5), B(6, -2), and the centroid G(3, -2), we can set up the equations:

3 = (-2 + 6 + x) / 3 9 = 4 + x x = 5

-2 = (5 - 2 + y) / 3 -6 = 3 + y y = -9

Explanation

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

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the given points (-5, 1) and (x, -4), and the slope m = -5/8 into the formula:

-5/8 = (-4 - 1) / (x - (-5))

-5/8 = -5 / (x + 5)

Since the numerators on both sides are equal to -5, the denominators must also be equal:

x + 5 = 8

x = 3

Explanation

Euler's formula for a convex polyhedron relates the number of faces (F), vertices (V), and edges (E) by the equation: F + V = E + 2

A triangular prism consists of 2 triangular bases and 3 rectangular side faces, which gives a total of F = 5 faces. Given that the prism has E = 9 edges, substituting these values into the formula yields: 5 + V = 9 + 2 5 + V = 11 V = 6

Alternatively, a triangular prism is formed by two parallel triangular bases connected by lateral edges. Since each triangle has 3 vertices, the total number of vertices is 2 × 3 = 6.

Explanation

Let s be the side of the square and d be its diagonal. The area of the square is s² = 12. The diagonal of a square is related to its side by the formula d = s√2. Squaring both sides gives d² = 2s². Substituting the value of s², we get d² = 2 × 12 = 24.

Since the diagonal of the square equals the side a of the equilateral triangle, we have a = d, and thus a² = d² = 24.

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

Substituting the value of a²: Area = (√3/4) × 24 = 6√3 sq cm.

Explanation

The total profit of ₹936000 is divided among the three partners in the ratio 2:3:5.

To find Charudatta's share, we first determine the sum of the ratio parts:

Total ratio parts = 2 + 3 + 5 = 10

Charudatta's share corresponds to 5 parts out of this total of 10 parts.

Charudatta's share = (5 / 10) × 936000 = ½ × 936000 = 468000

Explanation

If the price of an article is decreased by r%, the percentage increase required to restore it to its original value is given by the formula:

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

Substituting r = 36 into the formula:

Percentage Increase = (36 / (100 - 36)) × 100 = (36 / 64) × 100 = (9 / 16) × 100 = 56.25%

Explanation

The combined mean of multiple groups is calculated using the weighted mean formula: Combined Mean = (n₁x̄₁ + n₂x̄₂ + n₃x̄₃) / (n₁ + n₂ + n₃), where n represents the number of students and x̄ represents the mean of each division.

For division A, n₁ = 50 and x̄₁ = 61. For division B, n₂ = 25 and x̄₂ = 57. For division C, n₃ = 50 and x̄₃ = 55.

Substituting these values into the formula:

Combined Mean = (50 × 61 + 25 × 57 + 50 × 55) / (50 + 25 + 50)

Combined Mean = (3050 + 1425 + 2750) / 125

Combined Mean = 7225 / 125 = 57.8

Explanation

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

SP = MP × (100 - Discount%) / 100

Substituting SP = 1680 and Discount% = 16 into the formula:

1680 = MP × (100 - 16) / 100 1680 = MP × 84 / 100 MP = (1680 × 100) / 84 MP = 20 × 100 MP = 2000

Explanation

To find the sum, we first expand each of the three algebraic expressions:

First expression: 6xy(2x - 4z) = 12x²y - 24xyz

Second expression: 3yz(2x - 3z) = 6xyz - 9yz²

Third expression: 4xz(3y - 2y²) = 12xyz - 8xy²z

Now, we add the three expanded expressions together: Sum = 12x²y - 24xyz + 6xyz - 9yz² + 12xyz - 8xy²z

Combining the like terms involving xyz: -24xyz + 6xyz + 12xyz = -6xyz

Grouping and arranging the remaining terms results in: 12x²y - 6xyz - 9yz² - 8xy²z

Explanation

Let the Cost Price be CP and the Marked Price be MP.

When a discount of 25% is given, the Selling Price (SP₁) is: SP₁ = 0.75 × MP

Since this results in a profit of 41%, we also have: SP₁ = 1.41 × CP

Equating the two expressions for SP₁: 0.75 × MP = 1.41 × CP MP = (1.41 / 0.75) × CP

When the discount is 26%, the new Selling Price (SP₂) is: SP₂ = 0.74 × MP

Substituting the value of MP in terms of CP: SP₂ = 0.74 × (1.41 / 0.75) × CP SP₂ = (1.0434 / 0.75) × CP SP₂ = 1.3912 × CP

This represents a profit of 1.3912 - 1 = 0.3912, which is 39.12%.

Explanation

Let the present ages of Ranjini and Shahid be represented as 5x and 4x, where x is a common multiplier.

After 13 years, their ages will be 5x + 13 and 4x + 13. The ratio of their ages at that time is given as 6:5, which gives the equation:

(5x + 13) / (4x + 13) = 6/5

Cross-multiplying to solve for x:

5(5x + 13) = 6(4x + 13) 25x + 65 = 24x + 78 x = 13

Ranjini's present age is 5x, which is 5 × 13 = 65.

Alternatively, the ratio changes from 5:4 to 6:5 over a period of 13 years. Since the difference in parts for both Ranjini (6 - 5 = 1) and Shahid (5 - 4 = 1) is equal, 1 ratio unit directly corresponds to 13 years. Therefore, Ranjini's present age of 5 units is 5 × 13 = 65 years.

Explanation

We are given: x = (cotA - cosecA)²

By expressing the trigonometric functions in terms of sine and cosine, we have: cotA = cosA / sinA cosecA = 1 / sinA

Substituting these into the equation: cotA - cosecA = (cosA / sinA) - (1 / sinA) = (cosA - 1) / sinA

Now, square this expression to find x: x = ((cosA - 1) / sinA)² x = (cosA - 1)² / sin²A

Since (cosA - 1)² is equal to (1 - cosA)², and using the fundamental identity sin²A = 1 - cos²A, we can rewrite the expression as: x = (1 - cosA)² / (1 - cos²A)

Factoring the denominator as a difference of squares: 1 - cos²A = (1 - cosA)(1 + cosA)

Substituting this back into the equation: x = (1 - cosA)² / [(1 - cosA)(1 + cosA)]

Canceling the common term (1 - cosA) from the numerator and the denominator gives: x = (1 - cosA) / (1 + cosA)

Explanation

Since A completes 30% of the work in 30 days, A's daily rate of work is 30% ÷ 30 = 1% per day.

The remaining work is 100% - 30% = 70%. A and B together finish this remaining 70% of the work in 20 days, which means their combined daily rate of work is 70% ÷ 20 = 3.5% per day.

By subtracting A's daily rate from their combined daily rate, we find B's daily rate: 3.5% - 1% = 2.5% per day.

To find how long B alone would take to complete the entire 100% of the work: Time = 100% ÷ 2.5% = 40 days.

Explanation

We simplify the given algebraic equation by first expanding the bracket: 14.35 - 1.956 + x - 83.92 = 3.858

Combining the constant terms on the left side: 14.35 - 1.956 = 12.394 12.394 - 83.92 = -71.526

Now substitute these combined values back into the equation: -71.526 + x = 3.858

To solve for x, add 71.526 to both sides of the equation: x = 3.858 + 71.526 x = 75.384

Explanation

In a rhombus ABCD, the diagonals bisect the interior angles of the vertices they connect. This means the diagonal AC bisects angle DAB, giving:

angle DAB = 2 × angle CAB = 2 × 25° = 50°

In any rhombus, adjacent angles are supplementary, meaning they sum to 180°. Therefore:

angle DAB + angle ABC = 180°

Substituting the known value:

50° + angle ABC = 180° angle ABC = 180° - 50° = 130°

Explanation

The volume V of a cuboid is given by the formula V = l × b × h, where l is the length, b is the breadth, and h is the height.

Substituting the given values: 320 = 10 × 8 × h 320 = 80 × h h = 4 cm

The total surface area (TSA) of a cuboid is calculated using the formula: TSA = 2(l × b + b × h + h × l)

Substituting the values of length, breadth, and height into this formula: TSA = 2(10 × 8 + 8 × 4 + 4 × 10) TSA = 2(80 + 32 + 40) TSA = 2(152) TSA = 304 sq cm

Explanation

The circumference of a circle is given by the formula 2πr. Given the radius r = 7 cm and using the standard value of π ≈ 22/7:

Circumference = 2 × (22/7) × 7 = 44 cm

The perimeter of an equilateral triangle with side length s is given by the formula 3s. Equating the perimeter of the triangle to the circumference of the circle:

3s = 44 s = 44/3 cm

Explanation

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

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the coordinates of the points (2, -1) and (x, 5), and the given slope m = -1 into the formula:

-1 = (5 - (-1)) / (x - 2)

-1 = 6 / (x - 2)

Multiplying both sides by (x - 2) to solve for x:

-(x - 2) = 6

-x + 2 = 6

-x = 4

x = -4

Explanation

Let the present ages of the father and the son be f and s respectively.

According to the first condition, the sum of their present ages is 33: f + s = 33 s = 33 - f

According to the second condition, two years ago, the product of their ages was 28: (f - 2) × (s - 2) = 28

Substituting the value of s in this equation: (f - 2) × (33 - f - 2) = 28 (f - 2) × (31 - f) = 28 31f - f² - 62 + 2f = 28 f² - 33f + 90 = 0 (f - 30) × (f - 3) = 0

Solving this quadratic equation gives f = 30 or f = 3. Since a father must be older than his son, the present age of the father is 30 years and the present age of the son is 3 years.

Explanation

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

Substituting the given values: Distance covered in the first 6 hours = 45 km/hr × 6 hours = 270 km

Remaining distance to be covered = Total distance - Distance covered in the first part Remaining distance = 405 km - 270 km = 135 km

The time taken to cover this remaining distance is 3 hours.

The speed for the remaining journey is: Speed = Remaining distance / Remaining time Speed = 135 km / 3 hours = 45 km/hr

Explanation

First, find the rate of simple interest. Since the amount increases by 40% in 8 years, the simple interest earned is 40% of the principal. Using the simple interest formula: SI = P × R × T / 100 0.40 × P = P × R × 8 / 100 R = 40 / 8 = 5% per annum

Next, calculate the compound interest on ₹10000 for 3 years at a rate of 5% per annum using the compound interest formula: CI = P × ((1 + R/100)ᵀ - 1) CI = 10000 × ((1 + 5/100)³ - 1) CI = 10000 × ((21/20)³ - 1) CI = 10000 × (9261/8000 - 1) CI = 10000 × (1261/8000) CI = 12610 / 8 = 1576.25

Explanation

The curved surface area (CSA) of a right circular cone is given by the formula: CSA = π × r × l

where r is the radius of the base and l is the slant height.

Substituting the given values: 10010 = (22/7) × r × 91 10010 = 22 × 13 × r 10010 = 286 × r r = 35 cm

The total surface area (TSA) of the cone is the sum of its curved surface area and its base area: TSA = CSA + π × r²

Substituting the values: TSA = 10010 + (22/7) × 35 × 35 TSA = 10010 + 22 × 5 × 35 TSA = 10010 + 3850 TSA = 13860 sq cm

Explanation

The trigonometric angles in the equation are given in radians.

Converting radians to degrees: π/3 radians is equal to 60° π/6 radians is equal to 30°

Evaluating the individual terms: tan(π/3) = tan(60°) = √3 cosec(π/6) = cosec(30°) = 1/sin(30°) = 2

Substituting these values into the expression: x = tan(π/3) + cosec(π/6) x = √3 + 2

Explanation

To find the value of x - y, we first solve the system of simultaneous linear equations:

4x - 7y = 3 (Equation 1) 2x - y = 9 (Equation 2)

Multiplying Equation 2 by 2: 4x - 2y = 18 (Equation 3)

Subtracting Equation 1 from Equation 3: (4x - 2y) - (4x - 7y) = 18 - 3 5y = 15 y = 3

Substituting y = 3 into Equation 2: 2x - 3 = 9 2x = 12 x = 6

Subtracting y from x: x - y = 6 - 3 = 3

Explanation

The area of an equilateral triangle with side length a is calculated using the formula Area = (√3/4) × a².

Substituting the given side length a = 6 cm: Area = (√3/4) × 6² Area = (√3/4) × 36 Area = 9√3 sq cm

Explanation

The total value of the stock is the sum of the product of quantity and average cost for all items.

Value of Mobile Phones = 99 × 15000 = 1,485,000 rupees

Value of Cameras = 53 × 13000 = 689,000 rupees

Value of TVs = 29 × 59000 = 1,711,000 rupees

Value of Refrigerators = 21 × 56000 = 1,176,000 rupees

Value of ACs = 97 × 25000 = 2,425,000 rupees

Summing these individual values gives the total stock value: Total value = 1,485,000 + 689,000 + 1,711,000 + 1,176,000 + 2,425,000 = 7,486,000 rupees

To express this value in lakh rupees, divide by 100,000: Total value in lakh rupees = 7,486,000 ÷ 100,000 = 74.86 lakh rupees

Explanation

Based on the given data, the ratio of imports to exports in 2012 was 1.3.

Exports in 2012 = Imports in 2012 / 1.3 = 600 / 1.3 ≈ 461.54 crores

The total exports in the years 2012 and 2013 together was 4400 crores.

Exports in 2013 = 4400 - 461.54 = 3938.46 crores

The ratio of imports to exports in 2013 was 1.

Imports in 2013 = Ratio in 2013 × Exports in 2013 = 1 × 3938.46 = 3938.46 crores, which is approximately 3938 crores.

Explanation

According to the data table, the height of the child on their 10th birthday was 145 cms, and their height on their 13th birthday was 170 cms.

To find the increase in height between these two birthdays, subtract the height on the 10th birthday from the height on the 13th birthday:

170 cms - 145 cms = 25 cms