SSC CHSL Tier 1 2016 Quantitative Aptitude Questions with Solutions

Explanation

In compound interest, the amount at the end of the second year acts as the principal for the third year. Therefore, the interest earned during the third year is the difference between the amount at the end of the third year and the amount at the end of the second year.

The rate of interest (r) is calculated using the formula: r = ((A₃ - A₂) / A₂) × 100

Given: Amount at the end of 2nd year (A₂) = 30250 Amount at the end of 3rd year (A₃) = 33275

Substituting these values into the formula: r = ((33275 - 30250) / 30250) × 100 r = (3025 / 30250) × 100 r = 10%

Explanation

The relationship between the marked price (M), cost price (C), discount rate (d), and profit rate (p) is given by: M × (1 - d/100) = C × (1 + p/100)

For the first case, a 20% discount yields a 43% profit: M × 0.80 = C × 1.43 M = (1.43 / 0.80) × C M = 1.7875 × C

For the second case, when the discount is 28%, the new selling price (SP) is: SP = M × 0.72 SP = 1.7875 × C × 0.72 SP = 1.287 × C

This represents a profit of: (1.287 - 1) × 100% = 28.7%

Explanation

To convert speed from kilometres per hour (km/h) to metres per second (m/s), the standard conversion factor is 5/18.

Speed in m/s = Speed in km/h × 5/18

Substituting the given speed of 1440 km/h:

Speed = 1440 × 5/18 m/s Speed = 80 × 5 m/s Speed = 400 m/s

This means the missile travels a distance of 400 metres in one second.

Explanation

The relation between Marked Price (MP), Selling Price (SP), and discount percentage (d%) is: SP = MP × (100 - d) / 100

For a 13% discount, the selling price is Rs 18000: 18000 = MP × (100 - 13) / 100 18000 = MP × 87 / 100 MP = 18000 × 100 / 87

For a 27.5% discount, the new selling price is: New SP = MP × (100 - 27.5) / 100 New SP = MP × 72.5 / 100

Substituting the value of MP: New SP = (18000 × 100 / 87) × (72.5 / 100) New SP = 18000 × 72.5 / 87 New SP = 1305000 / 87 New SP = 15000

Explanation

To find the average bonus, first calculate the total bonus given to all employees across each category and then divide it by the total number of employees.

For the manager category, there are 3 employees, each with an annual salary of 54 lakhs (₹5,400,000) and a 50% bonus rate. This gives a bonus of ₹2,700,000 per manager, totaling ₹8,100,000.

For the executive category, there are 5 employees, each earning an annual salary of 20 lakhs (₹2,000,000) with a 20% bonus rate. The bonus per executive is ₹400,000, which sums to ₹2,000,000.

For the trainee category, there are 3 employees, each with an annual salary of 2 lakhs (₹200,000) and a 20% bonus rate. The bonus per trainee is ₹40,000, totaling ₹120,000.

The total bonus paid to all 11 employees (3 + 5 + 3) is ₹8,100,000 + ₹2,000,000 + ₹120,000 = ₹10,220,000.

Dividing the total bonus by the total number of employees gives the average bonus: 10,220,000 ÷ 11 = 929090.91 rupees, which rounds to 929091.

Explanation

To find the correct pair of years, we calculate the sum of exports from all three companies (Company A, Company B, and Company C) for each year.

For the year 2011: Total exports = 4000 + 2000 + 4000 = 10000 lakh rupees.

For the year 2015: Total exports = 2000 + 4000 + 4000 = 10000 lakh rupees.

Since the total exports for both 2011 and 2015 are equal to 10000 lakh rupees, this pair of years has equal total exports.

Explanation

The total profit or loss of the company over the last 5 years is the algebraic sum of the individual values for each year:

Total = 15 + (-10) + 10 + 20 + (-5) Total = 15 - 10 + 10 + 20 - 5 Total = 30

Since the resulting sum is positive, the company made a total profit of ₹30 crore over the 5-year period.

Explanation

To find the percentage of total exports represented by Steel, first calculate the sum of all exports: Total exports = 525 + 875 + 650 + 975 + 625 = 3650 million USThe export value of Steel is 975 million US.

The formula for the percentage of Steel exports is: Percentage of Steel = (Steel exports / Total exports) × 100

Substituting the values into the formula: Percentage of Steel = (975 / 3650) × 100 ≈ 26.71%

Explanation

Total cost of daily tickets for 30 days is calculated by multiplying the daily ticket cost by the number of days: 140 × 30 = 4200

Cost of the Monthly Pass is 3276.

The amount saved by purchasing the Monthly Pass instead of daily tickets is: 4200 - 3276 = 924

The saving percentage is calculated using the formula: Saving percentage = (Amount saved / Total daily ticket cost) × 100 Saving percentage = (924 / 4200) × 100 = 22%

Explanation

Since segment AB is parallel to segment CD and AD intersects BC at E, the alternate interior angles BAE and CDE are equal, and the vertically opposite angles AEB and DEC are also equal. This makes triangle ABE similar to triangle DCE (ΔABE ~ ΔDCE).

For similar triangles, the ratio of corresponding sides is equal: AE / DE = BE / CE

Given that the total length of segment BC is 15 cm, if we let the length of EC be x, then the length of BE is 15 - x.

Substituting the given values into the ratio: 10 / 15 = (15 - x) / x

Simplifying the fraction on the left side: 2 / 3 = (15 - x) / x

Cross-multiplying to solve for x: 2x = 3(15 - x) 2x = 45 - 3x 5x = 45 x = 9

The length of EC is 9 cm.

Explanation

For the first deposit made on 1st January, the interest is compounded for two half-year periods (n = 2) at a rate of 5% per half year. Using the compound interest formula, the accumulated amount A₁ is:

A₁ = P(1 + R/100)ⁿ A₁ = 8000 × (1 + 5/100)² A₁ = 8000 × (21/20)² A₁ = 8000 × 441/400 A₁ = 20 × 441 = Rs 8820

For the second deposit made on 1st July, the interest is compounded for one half-year period (n = 1) at the rate of 5% per half year. The accumulated amount A₂ is:

A₂ = 8000 × (1 + 5/100)¹ A₂ = 8000 × 21/20 A₂ = 400 × 21 = Rs 8400

The total accumulated amount at the end of the year is: Total Amount = A₁ + A₂ = 8820 + 8400 = Rs 17220

The total principal deposited by the customer during the year is: Total Principal = 8000 + 8000 = Rs 16000

The interest gained by the customer is the difference between the total accumulated amount and the total principal deposited: Interest Gained = Total Amount - Total Principal Interest Gained = 17220 - 16000 = Rs 1220

Explanation

Using the standard algebraic identity (a + b)² - (a - b)² = 4ab, we can simplify the right-hand side of the given equation by substituting a = 2x and b = y:

(2x + y)² - (2x - y)² = 4 × 2x × y = 8xy

Now, equating this result to the left-hand side of the equation:

16qxy = 8xy

Dividing both sides by xy:

16q = 8

q = 8/16 = 0.5

Explanation

To find the greatest four-digit number divisible by both 15 and 35, we first determine the least common multiple (LCM) of 15 and 35.

The prime factorization of 15 is 3 × 5, and for 35, it is 5 × 7. LCM(15, 35) = 3 × 5 × 7 = 105.

The greatest four-digit number is 9999. Dividing 9999 by 105 gives: 9999 ÷ 105 = 95 with a remainder of 24.

Subtracting this remainder from 9999 gives the largest multiple of 105: 9999 - 24 = 9975.

This number is the greatest four-digit number divisible by both 15 and 35.

Explanation

A point lies on a given line if its coordinates satisfy the equation of the line.

Substituting the coordinates of the point (-2, 3) into the equation 5x + 4y = 2:

5(-2) + 4(3) = -10 + 12 = 2

Since the left-hand side equals the right-hand side, the point satisfies the equation.

Explanation

The total surface area of a hemisphere is given by the formula 3πr², where r is the radius of the hemisphere.

Given that the total surface area is 1848 sq cm, we can set up the equation:

3 × (22/7) × r² = 1848

(66/7) × r² = 1848

r² = (1848 × 7) / 66

r² = 28 × 7

r² = 196

r = √196

r = 14 cm

Explanation

Correct Answer: D

Since PQ is parallel to BC, triangle APQ is similar to triangle ABC. For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

Area(APQ) / Area(ABC) = (AP / AB)²

Substituting the given ratio of areas:

(AP / AB)² = 9/16

Taking the square root of both sides gives:

AP / AB = 3/4

Since the side AB is composed of the segments AP and PB, we have AB = AP + PB. Substituting this into the ratio gives:

AP / (AP + PB) = 3/4

Cross-multiplying to solve for the relation between AP and PB:

4 × AP = 3 × (AP + PB)

4 × AP = 3 × AP + 3 × PB

AP = 3 × PB

AP / PB = 3/1

Explanation

For a standard quadratic equation of the form ax² + bx + c = 0, the sum of the roots is given by the relation: Sum of roots = -b/a

For the equation x² - 7x + 10 = 0, the coefficients are a = 1, b = -7, and c = 10. Substituting these values into the formula gives: Sum of roots = -(-7)/1 = 7

Alternatively, the roots of the equation can be found by factoring the quadratic expression: x² - 7x + 10 = 0 x² - 5x - 2x + 10 = 0 x(x - 5) - 2(x - 5) = 0 (x - 5)(x - 2) = 0

This yields the roots x = 5 and x = 2. Adding these roots together: 5 + 2 = 7

Explanation

We can solve this quickly by substituting a standard angle, for example, A = 45°.

Substituting A = 45° into the expression: (cosec 45° - sin 45°)(sec 45° - cos 45°)(tan 45° + cot 45°)

Using standard trigonometric values: cosec 45° = √2 sin 45° = 1/√2 sec 45° = √2 cos 45° = 1/√2 tan 45° = 1 cot 45° = 1

The expression becomes: (√2 - 1/√2)(√2 - 1/√2)(1 + 1) = (1/√2) × (1/√2) × 2 = ½ × 2 = 1

Alternatively, using fundamental identities, we can simplify each term: cosec A - sin A = 1/sin A - sin A = (1 - sin² A)/sin A = cos² A/sin A sec A - cos A = 1/cos A - cos A = (1 - cos² A)/cos A = sin² A/cos A tan A + cot A = sin A/cos A + cos A/sin A = (sin² A + cos² A)/(sin A cos A) = 1/(sin A cos A)

Multiplying the three simplified terms: (cos² A/sin A) × (sin² A/cos A) × (1/(sin A cos A)) = (sin² A cos² A) / (sin² A cos² A) = 1

Explanation

The mean proportion of two numbers x and y is given by √(x × y) = 6. Squaring both sides yields the relation: x × y = 36

The third proportion of x and y is 48, which implies that x : y = y : 48. This can be written as: y² = 48x x = y² / 48

Substituting this expression for x into the mean proportion equation: (y² / 48) × y = 36 y³ = 36 × 48 y³ = 1728 y = 12

Using y = 12 in the equation x × y = 36 gives x = 3.

Explanation

The mean of marks of students of all three divisions can be calculated using the weighted mean formula:

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

Here, the number of students in divisions A, B, and C are n₁ = 55, n₂ = 45, and n₃ = 40 respectively. Their corresponding mean marks are x₁ = 55, x₂ = 51, and x₃ = 49.

Substituting these values into the formula:

Weighted Mean = (55 × 55 + 45 × 51 + 40 × 49) / (55 + 45 + 40)

Weighted Mean = (3025 + 2295 + 1960) / 140

Weighted Mean = 7280 / 140

Weighted Mean = 52

Explanation

The double-angle formula for cosine is: cos(2θ) = 2 cos²(θ) - 1

By rearranging the terms to express cos²(θ), we get: 2 cos²(θ) = 1 + cos(2θ) cos²(θ) = (1 + cos(2θ))/2

Substituting θ = A/2 into the equation gives: cos²(A/2) = (1 + cos(A))/2

Explanation

Let the two diagonals of the rhombus be d₁ and d₂. We are given that one diagonal is half of the other, so d₁ = ½ d₂.

The diagonals of a rhombus bisect each other at right angles, which relates the side of the rhombus (a) to its diagonals by the formula: a² = (d₁/2)² + (d₂/2)²

Substituting a = 10 and d₂ = 2d₁ into the formula: 10² = (d₁/2)² + (2d₁/2)² 100 = d₁²/4 + d₁² 100 = 5d₁²/4 d₁² = 80 d₁ = √80 = 4√5 cm

Using d₁ to find d₂: d₂ = 2d₁ = 8√5 cm

The area of a rhombus is given by the formula: Area = ½ × d₁ × d₂ Area = ½ × 4√5 × 8√5 Area = ½ × 32 × 5 = 80 sq cm

Explanation

The time taken by two people working together to complete a job can be calculated using the formula: Combined Time = (a × b) / (a + b)

Substituting the given values: Combined Time = (24 × 12) / (24 + 12) = 288 / 36 = 8 days

Since they only need to complete 50% of the work, the time required is half of the total time: Time for 50% work = 8 / 2 = 4 days

Explanation

Total Cost Price (CP) of 16 quintals of rice = ₹1,280 Desired profit = 23% Required Total Selling Price (SP) = CP × (1 + Profit%) = 1280 × 1.23 = ₹1,574.4

Since 18% of the rice is lost in transportation, the quantity of rice left for sale = 16 × (1 - 0.18) = 16 × 0.82 = 13.12 quintals

Selling rate per quintal = Total SP / Remaining Quantity = 1574.4 / 13.12 = ₹120 per quintal

Explanation

Let the speed of the Rajdhani train be R km/hr and the speed of the Express train be E km/hr.

Using the relation Time = Distance / Speed, for a distance of 780 km: The time taken by Rajdhani is 780/R hours. The initial time taken by the Express train is 780/E hours.

According to the first condition: 780/E = 780/R + 8 --- (Equation 1)

According to the second condition, when the speed of the Express train is doubled: 780/2E = 780/R - 6 --- (Equation 2)

Substituting the value of 780/E from Equation 1 into Equation 2: ½ × (780/R + 8) = 780/R - 6 390/R + 4 = 780/R - 6 4 + 6 = 780/R - 390/R 10 = 390/R R = 390/10 = 39

Explanation

Using the trigonometric identity cot(-θ) = -cot(θ), we have: cot(-11π/6) = -cot(11π/6)

We can express the angle 11π/6 as 2π - π/6. Using the periodic property cot(2π - θ) = -cot(θ), we get: cot(11π/6) = cot(2π - π/6) = -cot(π/6)

Substituting this back into our equation: cot(-11π/6) = -(-cot(π/6)) = cot(π/6)

Since the standard trigonometric value of cot(π/6) is √3, we find: cot(-11π/6) = √3

Explanation

First inequality: 5x + 2 > 3x + 1 Subtracting 3x and 2 from both sides: 2x > -1 x > -½

Second inequality: 4(x - 4) - 2 ≤ 3x - 1 Expanding the terms: 4x - 16 - 2 ≤ 3x - 1 4x - 18 ≤ 3x - 1 Subtracting 3x and adding 18 to both sides: x ≤ 17

Combining both inequalities: -½ < x ≤ 17

The value 16 satisfies this interval because -½ < 16 ≤ 17.

Explanation

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

5x + 3 = 7x - 3

Subtracting 5x from both sides:

3 = 2x - 3

Adding 3 to both sides:

6 = 2x

Dividing both sides by 2:

x = 3

Explanation

Let the number be the least common multiple of the denominators 5 and 8, which is 40.

The correct value is 40 × 8/5 = 64.

The incorrect value is 40 × 5/8 = 25.

The error is the difference between the correct value and the incorrect value, which is 64 - 25 = 39.

The percentage error is calculated using the formula: Percentage Error = (Error / Correct Value) × 100

Substituting the values: Percentage Error = (39 / 64) × 100 = 60.9375%

Rounding this value to two decimal places gives 60.94%.

Explanation

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

Mobile Phones: 59 × 15000 = 885000 rupees Cameras: 72 × 16000 = 1152000 rupees TVs: 77 × 36000 = 2772000 rupees Refrigerators: 100 × 28000 = 2800000 rupees ACs: 98 × 23000 = 2254000 rupees

Total value = 885000 + 1152000 + 2772000 + 2800000 + 2254000 = 9863000 rupees

To convert this value into lakh rupees, divide by 100000:

9863000 ÷ 100000 = 98.63 lakh rupees

Explanation

Let I₂₀₁₂ and E₂₀₁₂ be the imports and exports in 2012, and I₂₀₁₃ and E₂₀₁₃ be the imports and exports in 2013.

From the table, the ratio of imports to exports in 2012 is 1.1. I₂₀₁₂ / E₂₀₁₂ = 1.1 Since imports in 2012 (I₂₀₁₂) is 900 crores: E₂₀₁₂ = 900 / 1.1 = 818.18 crores

The total exports in 2012 and 2013 together is 2800 crores: E₂₀₁₂ + E₂₀₁₃ = 2800 E₂₀₁₃ = 2800 - 818.18 = 1981.82 crores

From the table, the ratio of imports to exports in 2013 is 0.7. I₂₀₁₃ / E₂₀₁₃ = 0.7 I₂₀₁₃ = 0.7 × E₂₀₁₃ I₂₀₁₃ = 0.7 × 1981.82 = 1387.27 crores

Rounding to the nearest integer, the imports in 2013 was Rs. 1387 crores.

Explanation

According to the given table, the height of the child measured on their 9th birthday is 130 cms, and the height measured on their 15th birthday is 170 cms.

The increase in height is calculated by subtracting the height at the 9th birthday from the height at the 15th birthday:

Increase in height = Height at 15th birthday - Height at 9th birthday Increase in height = 170 cms - 130 cms = 40 cms

Explanation

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

The values given in the table represent the percentage distribution of the sleep cycle, as they sum up to 100 (20 + 20 + 5 + 15 + 40 = 100%).

The combined percentage of time spent in Deep Sleep (20%) or Extremely light sleep (15%) is: 20% + 15% = 35%

To find the actual duration spent in these states, calculate 35% of the total 8 hours: Duration = 35% of 8 hours = 0.35 × 8 = 2.8 hours

Explanation

Dadiji's rate of baking cakes is 30 ÷ 6 = 5 cakes per hour.

Dadiji and Kakiji's combined rate of baking cakes is 150 ÷ 15 = 10 cakes per hour.

Subtracting Dadiji's rate from the combined rate gives Kakiji's rate of baking cakes: 10 - 5 = 5 cakes per hour.

Therefore, in 25 hours, Kakiji can bake 5 × 25 = 125 cakes.

Explanation

By applying the successive percentage formula for two consecutive reductions of a% and b%, the effective discount is given by:

Effective Discount = a + b - (a × b) / 100

Here, the first discount is a = 10% and the cashback discount is b = 4%. Substituting these values into the formula:

Effective Discount = 10 + 4 - (10 × 4) / 100 Effective Discount = 14 - 40 / 100 Effective Discount = 14 - 0.4 Effective Discount = 13.6%

Alternatively, let the initial price of the item be 100. A 10% discount reduces the price to 90. Applying a 4% cashback on this transacted amount of 90 gives a benefit of 4% of 90, which is 3.6. The effective price paid by the customer is 90 - 3.6 = 86.4. Therefore, the total discount received is 100 - 86.4 = 13.6, which corresponds to an effective discount of 13.6%.

Explanation

To find the common factor of the algebraic expressions 27a³b², 36a²b³, and 54a²b², we find the greatest common divisor of both the numerical coefficients and the variables.

First, we find the highest common factor of the numerical coefficients 27, 36, and 54. The prime factorizations are: 27 = 3³ 36 = 2² × 3² 54 = 2 × 3³

The highest common factor among the numerical coefficients is 3² = 9.

Next, for the variable part, we select the lowest exponent of each common variable: For the variable a, the terms contain a³, a², and a², making the lowest power a². For the variable b, the terms contain b², b³, and b², making the lowest power b².

Multiplying the numerical common factor by the variable common factors gives 9a²b².

Explanation

The number of boys in the class is 56 - 33 = 23.

The ratio of the number of girls to the number of boys is 33 : 23.

Let the average weight of the boys be B.

Using the method of alligation: (B - 52.75) / (52.75 - 47) = 33 / 23 (B - 52.75) / 5.75 = 33 / 23

Since 5.75 is exactly equal to 23/4: (B - 52.75) / (23/4) = 33 / 23 4 × (B - 52.75) = 33 B - 52.75 = 8.25 B = 61

Explanation

Let the speed of the goods train be v km/hr.

The goods train passes the station 6 hours before the second train, meaning it has a 6-hour head start. The second train then takes 10 hours to overtake the goods train.

During this entire period, the goods train travels for a total of 16 hours (6 hours of head start plus the 10 hours during the chase). The second train travels for 10 hours at a speed of 56 km/hr.

Because both trains cover the same distance from the station to the point where the overtake occurs, we can equate their distances: v × 16 = 56 × 10 16v = 560 v = 560 / 16 v = 35 km/hr

Explanation

Using the algebraic identity (a + b)(a - b) = a² - b², the given expression simplifies directly:

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

Using the fundamental trigonometric identities cosec²A = 1 + cot²A and sin²A = 1 - cos²A, we substitute these relations into the expression:

cosec²A - sin²A = (1 + cot²A) - (1 - cos²A)

Expanding the terms:

1 + cot²A - 1 + cos²A = cot²A + cos²A

Explanation

Using the compound interest formula: A = P(1 + r/100)ⁿ

Substituting the given values of Amount (A = 11881), Principal (P = 10000), and Time (n = 2): 11881 = 10000(1 + r/100)²

Dividing both sides by 10000: 11881/10000 = (1 + r/100)²

Taking the square root on both sides: 109/100 = 1 + r/100 1.09 = 1 + r/100 r/100 = 0.09 r = 9

Explanation

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

In Δ ABC, since AE is the angle bisector of ∠A, we have:

AB / AC = BE / EC

Substituting the given values into the formula:

12 / AC = 9 / 6

12 / AC = 3 / 2

AC = (12 × 2) / 3

AC = 8 cm

Explanation

The angle 225° lies in the third quadrant, where the cosine function is negative. Using the trigonometric identity cos(180° + θ) = -cos θ, we can express cos 225° as cos(180° + 45°) = -cos 45°. Since the value of cos 45° is 1/√2, the value of cos 225° is -1/√2.

Explanation

Solving the first inequality: 5 - x < 1 + 5x 5 - 1 < 5x + x 4 < 6x x > 4/6 x > 2/3

Solving the second inequality: 2x + 3(5 - 2x) ≥ 2 - 3x 2x + 15 - 6x ≥ 2 - 3x -4x + 15 ≥ 2 - 3x 15 - 2 ≥ 4x - 3x 13 ≥ x x ≤ 13

Combining both results gives the range: 2/3 < x ≤ 13

The value 1 satisfies both inequalities because 2/3 < 1 ≤ 13.

Explanation

The trigonometric identity for the cotangent of the difference of two angles, cot(A - B), is derived using the basic definitions of sine and cosine:

cot(A - B) = cos(A - B) / sin(A - B)

Using the difference identities for cosine and sine:

cos(A - B) = cos A cos B + sin A sin B sin(A - B) = sin A cos B - cos A sin B

Substituting these expansions into the fraction:

cot(A - B) = (cos A cos B + sin A sin B) / (sin A cos B - cos A sin B)

To express this relation in terms of cotangents, both the numerator and the denominator are divided by (sin A sin B):

Numerator: (cos A cos B) / (sin A sin B) + (sin A sin B) / (sin A sin B) = cot A cot B + 1

Denominator: (sin A cos B) / (sin A sin B) - (cos A sin B) / (sin A sin B) = cot B - cot A

Combining these parts gives:

cot(A - B) = (cot A cot B + 1) / (cot B - cot A)

Explanation

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

According to the given conditions, the difference in their marks is 23: x - y = 23

The higher score, x, is 60% of the sum of their marks: x = 0.60(x + y)

Substituting y = x - 23 into the second equation: x = 0.60(x + x - 23) x = 0.60(2x - 23) x = 1.2x - 13.8

Rearranging the terms to solve for x: 1.2x - x = 13.8 0.2x = 13.8 x = 13.8 / 0.2 x = 69

Using the value of x to find y: y = 69 - 23 y = 46

The marks obtained by the students are 69 and 46.

Explanation

Let x = 7/6 and y = 1/9. The reciprocal of the sum of the reciprocals of x and y is given by the formula 1 / (1/x + 1/y).

First, find the reciprocals of the given numbers: 1/x = 6/7 1/y = 9

Next, find the sum of these reciprocals: 1/x + 1/y = 6/7 + 9 = 6/7 + 63/7 = 69/7

Finally, take the reciprocal of this sum: 1 / (69/7) = 7/69

Explanation

The total profit of ₹277200 is distributed among Abdullah, Bhanudas, and Chakor in the ratio 3:6:2.

Sum of the ratio terms = 3 + 6 + 2 = 11

Chakor's share corresponds to 2 parts out of the total 11 parts.

Chakor's share = (2 / 11) × 277200 = 2 × 25200 = 50400

Explanation

Using the algebraic identity for the square of a binomial:

(x + y)² = x² + y² + 2xy

Substituting the given values x² + y² = 45 and xy = 18 into the equation:

(x + y)² = 45 + 2(18) (x + y)² = 45 + 36 (x + y)² = 81

Taking the square root on both sides gives:

x + y = 9

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 given points (-1, 2) and (4, -3):

y - 2 = ((-3 - 2) / (4 - (-1))) × (x - (-1))

y - 2 = (-5 / 5) × (x + 1)

y - 2 = -1 × (x + 1)

y - 2 = -x - 1

Rearranging the terms gives:

x + y = 1

Explanation

The curved surface area of a right circular cone is given by the formula: Curved Surface Area = π × r × l

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

Given: Curved Surface Area = 2310 sq cm Slant height (l) = 35 cm π = 22/7

Substituting these values to find the radius (r): 2310 = (22/7) × r × 35 2310 = 110 × r r = 21 cm

The total surface area of a cone is the sum of its curved surface area and the area of its circular base: Total Surface Area = Curved Surface Area + π × r²

Substituting the values: Total Surface Area = 2310 + (22/7) × 21 × 21 Total Surface Area = 2310 + 22 × 3 × 21 Total Surface Area = 2310 + 1386 Total Surface Area = 3696 sq cm