SSC CHSL Tier 1 2016 Quantitative Aptitude Questions with Solutions

Explanation

Cost of daily tickets for 29 days = 29 × ₹60 = ₹1740.

Cost of the Monthly Pass = ₹1566.

The amount saved by purchasing the Monthly Pass instead of daily tickets = ₹1740 - ₹1566 = ₹174.

Percentage of savings = (Savings / Cost of daily tickets) × 100 = (174 / 1740) × 100 = 10%.

Explanation

To convert the speed of the missile from kilometers per hour (km/h) to meters per second (m/s), we use the conversion factor 5/18.

Distance traveled in one second = Speed in m/s = 1206 × 5/18

First, divide 1206 by 18: 1206 ÷ 18 = 67

Next, multiply the result by 5: 67 × 5 = 335

This means the missile travels 335 metres in one second.

Explanation

The total value of each type of stock is calculated by multiplying its quantity by its average cost.

Value of Mobile Phones = 61 × 18000 = 1,098,000 rupees Value of Cameras = 42 × 11000 = 462,000 rupees Value of TVs = 26 × 47000 = 1,222,000 rupees Value of Refrigerators = 96 × 49000 = 4,704,000 rupees Value of ACs = 84 × 23000 = 1,932,000 rupees

Summing these individual values gives the total value of all stock: 1,098,000 + 462,000 + 1,222,000 + 4,704,000 + 1,932,000 = 9,418,000 rupees

To express this value in lakh rupees, divide the total rupees by 100,000: 9,418,000 ÷ 100,000 = 94.18 lakh rupees

Explanation

The total duration recorded between 10pm and 6am is 8 hours.

The values given in the table represent percentages, as their sum equals 100% (15 + 25 + 15 + 30 + 15 = 100).

The percentage of time spent Dreaming is 25%, and the percentage of time spent in Extremely light sleep is 30%.

The combined percentage for these two states is: 25% + 30% = 55%

To find the duration in hours, multiply the total time by this combined percentage: 8 hours × 55% = 8 × 0.55 = 4.4 hours

Explanation

To find the value of x, simplify the given linear equation:

(6x - 1) - (8x - 5) = 7

Distribute the negative sign to expand the brackets:

6x - 1 - 8x + 5 = 7

Combine the like terms on the left side of the equation:

-2x + 4 = 7

Subtract 4 from both sides to isolate the term with x:

-2x = 7 - 4

-2x = 3

Divide both sides by -2 to solve for x:

x = -3/2

Explanation

Let the number be x. According to the question, 7/8th of 5/4th of this number is 315. This relation can be written in the form of a mathematical equation as:

(7/8) × (5/4) × x = 315

Simplifying the fraction on the left side gives:

(35/32) × x = 315

Solving for x:

x = 315 × (32/35)

Dividing 315 by 35 gives 9:

x = 9 × 32 x = 288

Now, to find 5/9th of this number:

(5/9) × 288 = 5 × 32 = 160

Explanation

Using the formula for correction of average:

Correct average = Incorrect average + (Correct value - Incorrect value) / Total number of observations

Substituting the given values into the formula:

Correct average = 60 + (29 - 92) / 56 Correct average = 60 - 63 / 56 Correct average = 60 - 9/8 Correct average = 60 - 1.125 Correct average = 58.875 marks

Explanation

Solving the first inequality: 2 + 2x < 3 + 5x 2 - 3 < 5x - 2x -1 < 3x x > -1/3

Solving the second inequality: 3(x - 2) < 5 - x 3x - 6 < 5 - x 3x + x < 5 + 6 4x < 11 x < 11/4

Combining both inequalities yields the solution interval: -1/3 < x < 11/4

In decimal form, this interval is approximately: -0.33 < x < 2.75

The value 1 falls within this range, satisfying both conditions simultaneously.

Explanation

The area of a circle is given by the formula A = πr², where r is the radius. Since the area is proportional to the square of the radius, the net percentage increase in the area when the radius increases by x% is calculated using the successive percentage change formula:

Net increase = 2x + x²/100 %

Substituting the given radius increase of x = 17 into the formula:

Net increase = 2(17) + 17²/100 % Net increase = 34 + 289/100 % Net increase = 34 + 2.89 % Net increase = 36.89 %

Alternatively, if the initial radius is 100 units, the initial area is π × 100² = 10000π. When the radius increases by 17%, the new radius becomes 117 units, making the new area π × 117² = 13689π. This represents an increase of 3689π, which is exactly 36.89% of the original area.

Explanation

The compound interest amount formula is A = P(1 + r)ⁿ, where P is the principal, r is the rate of interest per compounding period, and n is the number of compounding periods.

In this case, the interest is compounded half-yearly, so the rate of interest per half year is r = 20% = 0.20.

For the first deposit of ₹2800 made on 1st January, the money remains in the bank for the entire year, which equals 2 compounding periods (n = 2). Amount from the first deposit, A₁ = 2800 × (1 + 0.20)² = 2800 × 1.44 = ₹4032

For the second deposit of ₹2800 made on 1st July, the money remains in the bank for half a year, which equals 1 compounding period (n = 1). Amount from the second deposit, A₂ = 2800 × (1 + 0.20)¹ = 2800 × 1.20 = ₹3360

Total accumulated amount at the end of the year = A₁ + A₂ = 4032 + 3360 = ₹7392

Total principal deposited = 2800 + 2800 = ₹5600

Interest gained = Total accumulated amount - Total principal deposited = 7392 - 5600 = ₹1792

Explanation

The total cost of the tickets without any discount is calculated by adding the individual ticket costs for adults and children. With 17 adults at Rs 1000 per ticket and 5 children at Rs 500 per ticket, the total cost without discount is 17 × 1000 + 5 × 500 = Rs 19500.

The promotional offer allows one child to go free with every two adults. Since there are 17 adults in the group, they are eligible to bring up to 8 children for free (since 17 ÷ 2 = 8.5). Since the group contains only 5 children, all 5 children can enter for free. This makes the total discount amount equal to the cost of 5 children's tickets, which is 5 × 500 = Rs 2500.

The discount percentage is calculated as the discount amount divided by the total cost without discount, multiplied by 100. This gives (2500 / 19500) × 100, which simplifies to 500 / 39, resulting in approximately 12.82%.

Explanation

For three terms a, b, and c to be in arithmetic progression, the common difference between consecutive terms must be equal, which yields the standard relation: 2b = a + c

In this problem, the three terms in arithmetic progression are: a = -3x - 11 b = x + p c = 5x + 7

Substituting these expressions into the relation: 2(x + p) = (-3x - 11) + (5x + 7)

Simplifying both sides of the equation: 2x + 2p = 2x - 4

Subtracting 2x from both sides: 2p = -4

Dividing by 2 gives: p = -2

Explanation

By the section formula, the coordinates of a point P dividing the line segment joining (x₁, y₁) and (x₂, y₂) in the ratio m:n are given by ((m x₂ + n x₁) / (m + n), (m y₂ + n y₁) / (m + n)).

Here, the given points are (x, 0) and (0, y), which are divided by P(-4, 1) in the ratio 3:2.

Applying the formula for the x-coordinate: -4 = (3 × 0 + 2 × x) / (3 + 2) -4 = 2x / 5 -20 = 2x x = -10

Applying the formula for the y-coordinate: 1 = (3 × y + 2 × 0) / (3 + 2) 1 = 3y / 5 5 = 3y y = 5/3

Explanation

Using the slope-intercept form of a linear equation, y = mx + c, where m is the slope and c is the y-intercept:

Substituting m = -2/5 and c = 6: y = (-2/5)x + 6

Multiplying the entire equation by 5 to eliminate the fraction: 5y = -2x + 30

Rearranging the terms to the standard form: 2x + 5y = 30

Explanation

The efficiency of Amal is 5 times that of Bhairav, which means the ratio of their efficiencies is 5:1. Since efficiency is inversely proportional to the time taken to complete a work, the ratio of the time taken by Amal to that of Bhairav is 1:5.

If Amal takes x days, Bhairav takes 5x days. The difference in their time is given as: 5x - x = 48 4x = 48 x = 12 days

Thus, Amal takes 12 days and Bhairav takes 60 days to complete the work individually.

Working together, the time taken to finish the job is given by the formula: Time = (Amal's time × Bhairav's time) / (Amal's time + Bhairav's time) Time = (12 × 60) / (12 + 60) Time = 720 / 72 Time = 10 days

Explanation

In triangle ABC, since DE is parallel to BC, the smaller triangle ADE is similar to the larger triangle ABC.

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

The length of side AB is the sum of AD and DB: AB = AD + DB = 9 + 6 = 15 cm

Substituting the given values into the ratio: 9/15 = 5.4/BC

Solving for BC: BC = (5.4 × 15) / 9 BC = 0.6 × 15 BC = 9 cm

Explanation

Let the number of selected and unselected candidates be 6x and 1x respectively.

The total number of candidates who applied is: Total = Selected + Unselected = 6x + x = 7x

According to the given condition, if 90 fewer candidates had applied and 30 fewer were selected: New Total Applied = 7x - 90 New Selected = 6x - 30

The new number of unselected candidates is: New Unselected = New Total Applied - New Selected New Unselected = (7x - 90) - (6x - 30) = x - 60

The new ratio of selected to unselected candidates is 8:1: (6x - 30) / (x - 60) = 8 / 1

Solving the equation: 6x - 30 = 8(x - 60) 6x - 30 = 8x - 480 2x = 450 x = 225

The total number of candidates who originally applied is: 7x = 7 × 225 = 1575

Explanation

According to the law of sines for any triangle, the ratio of a side length to the sine of its opposite angle is constant:

a / sin A = b / sin B

Here, the side opposite to the angle measuring A = 30° is a = 12 cm. We need to find the side b opposite to the angle measuring B = 60°.

Substituting these values into the formula:

12 / sin 30° = b / sin 60°

Using the standard trigonometric values sin 30° = ½ and sin 60° = √3/2:

12 / (½) = b / (√3/2)

b = 12 × √3

b = 12√3 cm

Explanation

The circumference of the base of the cylinder is given by C = 2πr = 132 cm.

Using π = 22/7, we find the radius r: 2 × 22/7 × r = 132 r = (132 × 7) / 44 = 21 cm

The curved surface area (CSA) of a cylinder is CSA = 2πrh, and its volume is V = πr²h. These two quantities are related by the formula: CSA = 2V / r

Substituting the given volume V = 13860 cubic cm and the calculated radius r = 21 cm: CSA = (2 × 13860) / 21 = 27720 / 21 = 1320 sq cm

Explanation

The angle 4π/3 radians lies in the third quadrant of the coordinate plane, where the tangent function is positive.

We can express the angle 4π/3 as: 4π/3 = π + π/3

Using the trigonometric reduction identity for the tangent function: tan(π + θ) = tan θ

Substituting θ = π/3 into the identity: tan(4π/3) = tan(π + π/3) = tan(π/3)

The standard value of tan(π/3) is √3. Thus, the value of tan 4π/3 is √3.

Explanation

The triple-angle identity for the cotangent function is given by the formula:

cot 3A = (cot³A - 3cot A) / (3cot²A - 1)

To express cot³A in terms of cot A and cot 3A, we multiply both sides by the denominator (3cot²A - 1):

cot 3A (3cot²A - 1) = cot³A - 3cot A

Since (3cot²A - 1) can be rewritten as -(1 - 3cot²A), we substitute this into the equation:

-cot 3A (1 - 3cot²A) = cot³A - 3cot A

Rearranging the terms to isolate cot³A on one side:

cot³A = 3cot A - cot 3A (1 - 3cot²A)

Explanation

Using standard trigonometric identities, sec²A and cosec²A can be expressed in terms of cos²A and sin²A:

sec²A cosec²A = (1 / cos²A) × (1 / sin²A) = 1 / (sin²A cos²A)

Since sin²A + cos²A = 1, substituting this into the numerator yields:

(sin²A + cos²A) / (sin²A cos²A)

Splitting the fraction into two terms:

sin²A / (sin²A cos²A) + cos²A / (sin²A cos²A) = 1 / cos²A + 1 / sin²A = sec²A + cosec²A

Explanation

To find the value of the total stock, we calculate the sum of the product of quantity and average cost for each item:

Value of Mobile Phones = 97 × 5000 = 4,85,000 Value of Cameras = 28 × 20000 = 5,60,000 Value of TVs = 80 × 33000 = 26,40,000 Value of Refrigerators = 79 × 29000 = 22,91,000 Value of ACs = 94 × 27000 = 25,38,000

Total value of stock = 4,85,000 + 5,60,000 + 26,40,000 + 22,91,000 + 25,38,000 = 85,14,000

Converting the total value into lakh rupees: Value in lakh rupees = 85,14,000 ÷ 1,00,000 = 85.14

Explanation

For the year 2012, the ratio of Import to Export is 0.9, and the import is ₹500 crores. Using the relation Ratio = Import / Export:

Export in 2012 = 500 / 0.9 = 555.56 crores

The combined export for the years 2012 and 2013 is ₹3200 crores. Therefore, the export in 2013 is calculated as:

Export in 2013 = 3200 - 555.56 = 2644.44 crores

For the year 2013, the ratio of Import to Export is 1. Using the ratio relation:

Import in 2013 = Export in 2013 × 1 = 2644.44 crores

Rounding to the nearest integer gives 2644 crores.

Explanation

To find the increase in the height of the child from the 10th birthday to the 15th birthday, the height recorded on the 10th birthday is subtracted from the height recorded on the 15th birthday.

From the given data table: Height on the 10th birthday = 145 cm Height on the 15th birthday = 185 cm

The increase in height is calculated as: 185 cm - 145 cm = 40 cm

Explanation

The total duration tracked from 10 pm to 6 am is 8 hours.

The percentages of each sleep category sum up to 100%, indicating that the values in the table represent the percentage of the total time: 20% + 25% + 5% + 10% + 40% = 100%

The combined percentage of time spent in Deep sleep or Awake is: 20% + 40% = 60%

To find the duration in hours, multiply this combined percentage by the total tracked time of 8 hours: Duration = 60% of 8 hours = 0.60 × 8 = 4.8 hours

Explanation

Given equation: (6 - 18x) - (x - 7) = 8

Simplify the equation by opening the parentheses: 6 - 18x - x + 7 = 8

Combine the like terms on the left side: 13 - 19x = 8

Isolate the term with x by subtracting 13 from both sides: -19x = 8 - 13 -19x = -5

Divide both sides by -19 to solve for x: x = 5/19

Explanation

The discount offered on an item is calculated using the formula:

Discount = Marked Price - Selling Price

Substituting the given values:

Discount = ₹600 - ₹450 = ₹150

The discount percentage is calculated with respect to the Marked Price using the formula:

Discount Percentage = (Discount / Marked Price) × 100

Discount Percentage = (150 / 600) × 100 = 25%

Explanation

We can solve the quadratic equation 27x² + 57x - 14 = 0 by splitting the middle term. We look for two numbers whose product is 27 × (-14) = -378 and whose sum is 57. These numbers are 63 and -6.

Rewriting the equation: 27x² + 63x - 6x - 14 = 0

Grouping the terms to factorize: 9x(3x + 7) - 2(3x + 7) = 0 (9x - 2)(3x + 7) = 0

Setting each factor to zero: 9x - 2 = 0 → x = 2/9 3x + 7 = 0 → x = -7/3

Explanation

Since the compound interest is calculated on a half-year basis, the rate of interest is 20% per half-year period.

The customer makes two deposits of Rs 9200 each.

The first deposit of Rs 9200 is made on 1st January, which remains in the bank for the entire year, corresponding to 2 half-year periods. Amount for the first deposit at the end of the year = 9200 × (1 + 20/100)² = 9200 × 1.2² = 9200 × 1.44 = Rs 13248 Interest earned on the first deposit = 13248 - 9200 = Rs 4048

The second deposit of Rs 9200 is made on 1st July, which remains in the bank for the remaining half of the year, corresponding to 1 half-year period. Amount for the second deposit at the end of the year = 9200 × (1 + 20/100)¹ = 9200 × 1.2 = Rs 11040 Interest earned on the second deposit = 11040 - 9200 = Rs 1840

Total interest gained by the customer at the end of the year = 4048 + 1840 = Rs 5888

Explanation

Since √391 is approximately 19.77, we test the divisibility of 391 by prime numbers up to 19, which are 2, 3, 5, 7, 11, 13, 17, and 19. Dividing 391 by 17 gives a quotient of 23 with no remainder. This means 391 can be factored as 17 × 23, which makes it a composite number rather than a prime number.

Explanation

The total time required to build the cupboard is 64 hours.

After working for 16 hours, the remaining time required to complete the cupboard is: 64 - 16 = 48 hours

The fraction of the cupboard that is yet to be built is the ratio of the remaining hours of work to the total hours required: 48/64 = 3/4 = 0.75

Explanation

The ratio of the original fare to the increased fare is 29 : 31. This indicates that if the original fare is 29 units, the new fare is 31 units, making the increase in fare 31 - 29 = 2 units.

Given that the original fare is Rs 725, we can equate the original fare units to this value: 29 units = 725

To find the value of 1 unit: 1 unit = 725 ÷ 29 = 25

The increase in fare is represented by 2 units: Increase in fare = 2 × 25 = 50

Thus, the increase in fare is Rs 50.

Explanation

Let the third number be 100.

The first number is 35% lesser than the third number, so the first number is 100 - 35 = 65.

The second number is 40% lesser than the third number, so the second number is 100 - 40 = 60.

To make the second number equal to the first number, it needs to be increased by 65 - 60 = 5.

The percentage enhancement required relative to the second number is: Percentage increase = (5 ÷ 60) × 100% = (1 ÷ 12) × 100% = 8.33%

Explanation

Solving the first inequality: 3x + 2 < 2x + 1 Subtracting 2x from both sides: x + 2 < 1 Subtracting 2 from both sides: x < -1

Solving the second inequality: x - 4 ≤ 2x - 1 Subtracting x from both sides: -4 ≤ x - 1 Adding 1 to both sides: -3 ≤ x

Combining these two results gives the range: -3 ≤ x < -1

The value x = -2 satisfies this combined inequality since -3 ≤ -2 < -1.

Explanation

The first multiple of 7 greater than 50 is 56 (7 × 8 = 56). The last multiple of 7 less than 150 is 147 (7 × 21 = 147).

These multiples form an arithmetic progression with the first term a = 56, last term l = 147, and common difference d = 7.

Using the arithmetic progression formula to find the number of terms n: n = (l - a)/d + 1 Substituting the values: n = (147 - 56)/7 + 1 n = 91/7 + 1 n = 13 + 1 n = 14

Alternatively, this can be calculated by finding the total number of multiples from 1 to 150 and subtracting the multiples from 1 to 50: Number of multiples up to 150 = floor(150/7) = 21 Number of multiples up to 50 = floor(50/7) = 7 Total multiples between 50 and 150 = 21 - 7 = 14

Explanation

The distance d between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the given points (11, -5) and (k, 0) along with the distance d = 13 into the formula: 13 = √((k - 11)² + (0 - (-5))²)

Squaring both sides of the equation: 169 = (k - 11)² + 5² 169 = (k - 11)² + 25

Subtracting 25 from both sides: 144 = (k - 11)²

Taking the square root of both sides: k - 11 = ±12

Solving the two resulting linear equations: k - 11 = 12 leads to k = 23 k - 11 = -12 leads to k = -1

Explanation

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

y - y₁ = ((y₂ - y₁) / (x₂ - x₁)) × (x - x₁)

Substituting the coordinates of the given points (3, -2) and (5, 3) into the formula:

y - (-2) = ((3 - (-2)) / (5 - 3)) × (x - 3)

y + 2 = (5/2) × (x - 3)

Multiplying both sides by 2 to eliminate the fraction:

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

2y + 4 = 5x - 15

Rearranging the terms to the standard form Ax + By = C:

5x - 2y = 19

Explanation

According to the Angle Bisector Theorem, the angle bisector of an angle of a triangle divides the opposite side into two segments that are in the same ratio as the adjacent sides.

Therefore, for the angle bisector AE of ∠A: AB / AC = BE / EC

Substituting the given values: 9.6 / AC = 4 / 3

Solving for AC: AC = (9.6 × 3) / 4 AC = 2.4 × 3 AC = 7.2 cm

Explanation

According to the Law of Sines for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant:

a/sin(A) = b/sin(B)

Let the side opposite to the 45° angle be a = 16 cm (where A = 45°), and the side opposite to the 90° angle be b (where B = 90°). Substituting these values into the formula:

16/sin(45°) = b/sin(90°)

Since sin(45°) = 1/√2 and sin(90°) = 1, we get:

16 / (1/√2) = b / 1

b = 16√2 cm

Explanation

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.

Substituting the given values into the formula: 385 = (22/7) × r² × 10

This simplifies to: 385 = (220/7) × r²

Rearranging the terms to solve for r²: r² = (385 × 7) / 220

Dividing both the numerator and the denominator by their common factors: r² = (77 × 7) / 44 r² = (7 × 7) / 4 r² = 49/4

Taking the square root on both sides: r = 7/2 r = 3.5 cm

Explanation

The product-to-sum trigonometric identity states that:

cos X - cos Y = -2 sin((X+Y)/2) sin((X-Y)/2)

Using the negative angle identity of the sine function, sin(-θ) = -sin(θ), we can rewrite the second sine term as:

sin((X-Y)/2) = -sin((Y-X)/2)

Substituting this back into the original identity yields:

cos X - cos Y = -2 sin((X+Y)/2) [-sin((Y-X)/2)]

cos X - cos Y = 2 sin((X+Y)/2) sin((Y-X)/2)

By substituting X = C and Y = D, we get:

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

Explanation

Let the cost price of the cooker be C and that of the stove be S.

The cooker was sold at a profit of 30%, so its selling price is 1.30 × C. The stove was sold at a loss of 20%, so its selling price is 0.80 × S.

Since the selling price of both items is the same: 1.30 × C = 0.80 × S 13 × C = 8 × S C / S = 8 / 13

The ratio of the cost price of the cooker to that of the stove is 8 : 13.

The cheaper item is the cooker, which corresponds to the lower ratio value of 8 parts out of a total of 21 parts (8 + 13 = 21).

The cost price of the cheaper item is calculated as: (8 / 21) × 13125 = 8 × 625 = 5000

Explanation

Using the difference of squares algebraic identity, (x + y)(x - y) = x² - y², the expression in option B can be written as:

(cosecA + sinA)(cosecA - sinA) = cosec²A - sin²A

Applying the standard trigonometric identities: cosec²A = 1 + cot²A sin²A = 1 - cos²A

Substituting these expressions: cosec²A - sin²A = (1 + cot²A) - (1 - cos²A) = 1 + cot²A - 1 + cos²A = cot²A + cos²A

Explanation

The sum of 7 consecutive years of revenue is calculated as the average revenue multiplied by 7. This gives: Total revenue for 7 years = 7 × 71 = 497 lakhs

Similarly, the sum of revenues for the first 4 years is: Total revenue for first 4 years = 4 × 66 = 264 lakhs

And the sum of revenues for the last 4 years is: Total revenue for last 4 years = 4 × 78 = 312 lakhs

The sum of the first 4 years and the last 4 years includes the revenue of the fourth year twice. Therefore, the revenue of the fourth year is obtained by subtracting the total revenue of 7 years from the combined sum of the first 4 years and the last 4 years: Revenue of the fourth year = (264 + 312) - 497 = 576 - 497 = 79 lakhs

Explanation

First, calculate the total bonus paid to each category of employees:

For Managers: Number of employees = 3 Annual salary per manager = ₹54,00,000 Bonus per manager = 60% of ₹54,00,000 = ₹32,40,000 Total bonus for Managers = 3 × ₹32,40,000 = ₹97,20,000

For Executives: Number of employees = 5 Annual salary per executive = ₹8,00,000 Bonus per executive = 30% of ₹8,00,000 = ₹2,40,000 Total bonus for Executives = 5 × ₹2,40,000 = ₹12,00,000

For Trainees: Number of employees = 5 Annual salary per trainee = ₹4,00,000 Bonus per trainee = 10% of ₹4,00,000 = ₹40,000 Total bonus for Trainees = 5 × ₹40,000 = ₹2,00,000

Next, sum the bonuses to get the overall total bonus: Total Bonus = ₹97,20,000 + ₹12,00,000 + ₹2,00,000 = ₹1,11,20,000

Find the total number of employees: Total Employees = 3 + 5 + 5 = 13

Finally, calculate the average bonus per employee: Average Bonus = Total Bonus ÷ Total Employees = ₹1,11,20,000 ÷ 13 ≈ ₹8,55,385

Explanation

The total profit or loss of the company over the 5-year period is calculated by taking the sum of the profit and loss values for each year:

Total = 25 - 5 + 5 - 5 + 25 = 45

Since the final sum is a positive value, the company earned a net profit of Rs 45 crores over the last 5 years.

Explanation

Without any offer, the total cost for the group is the sum of the individual ticket prices for 25 adults and 5 children: Total normal cost = (25 × 1200) + (5 × 800) = 30000 + 4000 = ₹34000

Under the promotional offer, one child goes free for every two adults. With 25 adults, up to 12 children can get free entry. Since the group contains only 5 children, all 5 children can enter for free. This means the discount amount is equivalent to the price of the 5 child tickets: Discount amount = 5 × 800 = ₹4000

The discount percentage is calculated by dividing the discount amount by the total normal cost and multiplying by 100: Discount percentage = (4000 / 34000) × 100 = (4 / 34) × 100 = (2 / 17) × 100 = 200 / 17 % ≈ 11.76%

Explanation

Let x = 0.363636...

Multiplying both sides by 100 as the repeating block has two digits: 100x = 36.363636...

Subtracting the first equation from the second: 100x - x = 36.363636... - 0.363636... 99x = 36 x = 36/99

Dividing both the numerator and the denominator by 9 gives: x = 4/11

Explanation

Let CP be the cost price of the machine in lakhs.

When the machine is sold for Rs 52 lakhs, the loss incurred is CP - 52.

When the machine is sold for Rs 62 lakhs, the gain obtained is 62 - CP.

As given, the gain is 9 times the loss: 62 - CP = 9 × (CP - 52) 62 - CP = 9CP - 468 10CP = 530 CP = 53