SSC CHSL Tier 1 2021 Quantitative Aptitude Questions with Solutions

Explanation

Using the successive percentage change formula, the final selling price to C is given by:

Price paid by C = Cost Price for A × (1 + Gain% of A / 100) × (1 + Gain% of B / 100)

Substituting the given values:

4,06,000 = Cost Price for A × (1 + 10/100) × (1 + 5/100) 4,06,000 = Cost Price for A × 1.1 × 1.05 4,06,000 = Cost Price for A × 1.155

Solving for the Cost Price for A:

Cost Price for A = 4,06,000 / 1.155 Cost Price for A ≈ 3,51,515.15

Considering only the integral part, the cost price of the car for A is ₹3,51,515.

Explanation

When interest is compounded half-yearly, the annual rate of interest is halved and the number of conversion periods is doubled.

The formula for compound interest is: CI = P × [(1 + r/100)ⁿ - 1]

Given: Principal (P) = ₹35,000 Annual interest rate = 6% per annum Half-yearly interest rate (r) = 6% / 2 = 3% Time (t) = 2 years Number of half-yearly periods (n) = 2 × 2 = 4

Substituting these values into the formula: CI = 35000 × [(1 + 3/100)⁴ - 1] CI = 35000 × (1.03⁴ - 1)

First, compute 1.03⁴: 1.03² = 1.0609 1.03⁴ = (1.0609)² = 1.12550881

Now, calculate the compound interest: CI = 35000 × (1.12550881 - 1) CI = 35000 × 0.12550881 CI = 4392.808

Rounding to the nearest rupee, the compound interest is ₹4,393.

Explanation

For a number to be divisible by 18, it must be divisible by both 2 and 9. A number is divisible by 2 if its last digit is even, and it is divisible by 9 if the sum of its digits is a multiple of 9.

The number 245798 ends in 8, so it is an even number and divisible by 2.

Calculating the sum of its digits to check divisibility by 9: 2 + 4 + 5 + 7 + 9 + 8 = 35

Since the sum of the digits, 35, is not a multiple of 9, the number is not divisible by 9. As it fails the divisibility test for 9, it is not divisible by 18.

Explanation

The effective discount percentage for two successive discounts of a% and b% is calculated using the formula: Effective Discount = a + b - (a × b) / 100

Substituting the given values of 20% and 20%: Effective Discount = 20 + 20 - (20 × 20) / 100 = 36%

The difference between this effective discount of 36% and the single discount of 35% is: 36% - 35% = 1%

Let the total amount of the bill be x. The difference in the discount value is ₹22: 1% of x = 22 x = 2,200

Explanation

Let the speed of Prerna be v. Since Riya runs 3/2 times as fast as Prerna, Riya's speed is 3v/2.

The ratio of the speed of Riya to the speed of Prerna is 3/2 : 1, which simplifies to 3 : 2.

Since speed is directly proportional to distance covered in the same duration of time, the ratio of the distance covered by Riya to the distance covered by Prerna is also 3 : 2.

Let the distance run by Riya be 3x and the distance run by Prerna be 2x.

Riya gives Prerna a head start of 100 m, which means the difference between their distances when they meet is 100 m.

3x - 2x = 100 x = 100 m

The distance Riya has to run before they meet is: 3 × 100 = 300 m.

Explanation

The second addition operator in the inner square bracket represents a division operator (÷), which gives the expression:

50% of [6 - {15 - [6 + 8 ÷ (5 - 3)] + 2}]

Applying the BODMAS rule step-by-step:

First, solve the innermost parentheses: 5 - 3 = 2

Next, perform the division inside the inner square brackets: 8 ÷ 2 = 4

Then, perform the addition inside the inner square brackets: 6 + 4 = 10

This reduces the expression inside the curly braces to: {15 - 10 + 2}

Following the literal BODMAS order where addition is performed before subtraction: 10 + 2 = 12 15 - 12 = 3

Substitute this value into the outer square brackets: 6 - 3 = 3

Finally, calculate 50% of the remaining value: 50% of 3 = 0.5 × 3 = 1.5

Explanation

Let the marked price of the article be MP.

Using the standard relationship between Selling Price (SP) and Marked Price (MP) with a given discount percentage d%: SP = MP × (1 - d/100)

Given that the selling price SP is ₹1,326 and the discount percentage d is 15%: 1326 = MP × (1 - 15/100) 1326 = MP × 85/100 1326 = MP × 17/20

Solving for MP: MP = (1326 × 20) / 17 MP = 78 × 20 MP = 1560

The marked price of the article is ₹1,560.

Explanation

Since (x + 2) and (x - 3) are the factors of the quadratic expression x² + k₁x + k₂, the expression is equal to the product of these factors:

x² + k₁x + k₂ = (x + 2)(x - 3)

Expanding the right-hand side of the equation:

(x + 2)(x - 3) = x² - 3x + 2x - 6 = x² - x - 6

By comparing the coefficients of the corresponding terms on both sides of x² + k₁x + k₂ = x² - x - 6:

The coefficient of x gives k₁ = -1. The constant term gives k₂ = -6.

Explanation

Since the cross-section is made through the midpoint of the height parallel to the base, the upper portion forms a smaller cone that is similar to the original cone.

The height of this upper cone is half of the original height: h = 48 / 2 = 24 cm

The radius of this upper cone is half of the original base radius: r = 14 / 2 = 7 cm

The volume of a cone is calculated using the formula V = (1/3) × π × r² × h. Substituting the values: V = (1/3) × (22 / 7) × 7² × 24 V = (1/3) × (22 / 7) × 49 × 24 V = 22 × 7 × 8 V = 1232 cm³

Explanation

For a period of 2 years, the relationship between compound interest (CI), simple interest (SI), and the rate of interest per annum (r) is given by the formula:

CI - SI = SI × r / 200

Substituting the given values of CI = ₹300 and SI = ₹250 into the formula:

300 - 250 = 250 × r / 200

50 = 1.25 × r

r = 50 / 1.25

r = 40%

Explanation

For a number to be divisible by 15, it must be divisible by both 3 and 5.

Divisibility by 5: The last digit, a, must be either 0 or 5.

Divisibility by 3: The sum of the digits of 143b203a must be divisible by 3. Sum of digits = 1 + 4 + 3 + b + 2 + 0 + 3 + a = 13 + a + b

To find the greatest possible value of a + b, we evaluate the two possible values of a:

Case 1: If a = 5 Sum of digits = 13 + 5 + b = 18 + b For 18 + b to be divisible by 3, the single digit b can be 0, 3, 6, or 9. The maximum value of b is 9, which gives the greatest value of a + b = 5 + 9 = 14.

Case 2: If a = 0 Sum of digits = 13 + 0 + b = 13 + b For 13 + b to be divisible by 3, the single digit b can be 2, 5, or 8. The maximum value of b is 8, which gives the greatest value of a + b = 0 + 8 = 8.

Comparing both cases, the greatest possible value of a + b is 14.

Explanation

Let the distance of each of the three equal segments AB, BC, and CD be d.

The times taken to travel each segment are: Time from A to B = d/5 Time from B to C = d/10 Time from C to D = d/15

The total distance covered is 3d.

The total time taken is: Total Time = d/5 + d/10 + d/15

Taking the LCM of 5, 10, and 15, which is 30, we get: Total Time = (6d + 3d + 2d) / 30 = 11d/30

The average speed is the total distance divided by the total time: Average Speed = Total Distance / Total Time Average Speed = 3d / (11d/30) = 90/11 = 8 2/11 km/h

This simplifies to approximately 8 km/h.

Explanation

To find the ratio P : Q : R, we make the value of Q equal in both ratios by finding the common multiple of 17 and 15.

Multiplying the ratio P : Q = 16 : 17 by 15 gives P : Q = 240 : 255. Multiplying the ratio Q : R = 15 : 16 by 17 gives Q : R = 255 : 272.

Combining these gives the joint ratio P : Q : R = 240 : 255 : 272.

The sum of the ratio parts is 240 + 255 + 272 = 767.

Given the total runs scored is 956, the runs scored by R are calculated as: Runs scored by R = (272 / 767) × 956 Runs scored by R = 260024 / 767 ≈ 339.01

Rounding to the nearest integer, the number of runs scored by R is 339.

Explanation

Using the direct formula for replacement: Weight of the new man = Weight of the replaced man + (Total number of men × Increase in average weight)

Given: Weight of the replaced man = 65 kg Total number of men = 8 Increase in average weight = 1.5 kg

Substitute the values: Weight of the new man = 65 + (8 × 1.5) Weight of the new man = 65 + 12 Weight of the new man = 77 kg

Explanation

Given the algebraic equation:

k + 1/k = 2

Multiplying the entire equation by k yields:

k² + 1 = 2k

Rearranging the terms into a standard quadratic equation:

k² - 2k + 1 = 0

This quadratic expression can be factored as a perfect square:

(k - 1)² = 0

Taking the square root of both sides gives:

k - 1 = 0 k = 1

Now we substitute this value of k into the expression we need to evaluate:

8k × k × k = 8k³

Using k = 1:

8 × 1³ = 8 × 1 = 8

Explanation

Using the compound growth formula: A = P × (1 + R/100)ⁿ

Where: A is the present population = 18522 P is the population 3 years ago R is the annual growth rate = 5% n is the number of years = 3

Substituting the values into the formula: 18522 = P × (1 + 5/100)³ 18522 = P × (1 + 1/20)³ 18522 = P × (21/20)³ 18522 = P × 9261/8000

Solving for P: P = 18522 × 8000 / 9261 P = 2 × 8000 P = 16000

Explanation

The earnings of workers are directly proportional to both the number of workers and the number of days worked. This relationship is expressed by the formula:

E₁ / (M₁ × D₁) = E₂ / (M₂ × D₂)

where M is the number of boys, D is the number of days, and E is the total earnings.

Substituting the given values: M₁ = 15 boys, D₁ = 5 days, E₁ = 900 M₂ = 20 boys, D₂ = 7 days

900 / (15 × 5) = E₂ / (20 × 7)

900 / 75 = E₂ / 140

12 = E₂ / 140

E₂ = 12 × 140 = 1680

Explanation

Let the center of the circle be O. Since AB and CD are perpendicular diameters, they intersect at O at a right angle, making triangle AOC a right-angled triangle at O.

The segments OA and OC are radii of the circle, so OA = OC = r, where r is the radius of the circle. The length of diameter AB is 2r, which means r = AB/2.

Applying the Pythagorean theorem to right-angled triangle AOC, where the chord AC is the hypotenuse: AC² = OA² + OC² AC² = r² + r² AC² = 2r² AC = r√2

Substituting r = AB/2 into the expression: AC = (AB/2) × √2 = AB/√2

Explanation

Let the initial expenditure of the company be 100.

The successive percentage changes are an increase of 25%, an increase of 30%, and a decrease of 20%.

The final expenditure is calculated using the formula for successive percentage changes: Final Expenditure = 100 × (1 + 25/100) × (1 + 30/100) × (1 - 20/100) Final Expenditure = 100 × 1.25 × 1.3 × 0.8 Final Expenditure = 100 × (5/4) × (13/10) × (4/5)

Simplifying the fractions: Final Expenditure = 100 × 13/10 = 130

The overall percentage change in expenditure is: Overall Change = (130 - 100) / 100 × 100% = 30%

Explanation

To determine the subject with the highest average percentage marks, we compute the sum of the percentage marks for each subject. Since there are six students for each subject, the subject with the highest sum of percentage marks will yield the highest average.

The sum of the percentage marks for Geography is: 85 + 85 + 85 + 90 + 90 + 90 = 525

The average percentage marks for Geography is: 525 / 6 = 87.5%

For the other subjects, the sums and averages are: Physics: 85 + 75 + 80 + 90 + 95 + 90 = 515, which gives an average of 85.83% Chemistry: 90 + 75 + 60 + 85 + 90 + 90 = 490, which gives an average of 81.67% Math: 70 + 75 + 75 + 75 + 85 + 95 = 475, which gives an average of 79.17%

The average of Geography (87.5%) is the highest among all the four subjects.

Explanation

Using the algebraic identity, if x + y + z = 0, then x³ + y³ + z³ = 3xyz.

Let x = r - s, y = s - t, and z = t - r. Adding these variables gives: x + y + z = (r - s) + (s - t) + (t - r) = 0

Since the sum is zero, the numerator simplifies to: (r - s)³ + (s - t)³ + (t - r)³ = 3(r - s)(s - t)(t - r)

Substituting this back into the original expression: 3(r - s)(s - t)(t - r) / (6(r - s)(s - t)(t - r))

Canceling the common term (r - s)(s - t)(t - r) from the numerator and denominator yields: 3 / 6 = ½

Explanation

When the shopkeeper buys rice, he cheats to the extent of 6%, meaning he receives 106 units of rice while paying for only 100 units. If the cost of 1 unit of rice is ₹1, his total Cost Price (CP) for 106 units is ₹100.

When he sells rice, he cheats to the extent of 6%, meaning he delivers only 94 units while charging the customer for 100 units. Thus, his Selling Price (SP) for 94 units is ₹100.

To find the overall gain percentage, we compare the cost price and selling price for the same quantity of rice.

Since the SP of 94 units is ₹100, the SP of 106 units is: (100 / 94) × 106 = ₹112.7659...

Since the CP for 106 units is ₹100, the gain percentage is: ((112.7659 - 100) / 100) × 100 = 12.77%

Explanation

The area of the playground leveled by the roller is equal to the total distance covered by its curved surface area in 235 complete revolutions.

Curved surface area of the cylindrical roller = 2 × π × r × h

Substituting the given radius r = 14 cm, length h = 20 cm, and π = 22/7: Curved surface area = 2 × (22/7) × 14 × 20 Curved surface area = 2 × 22 × 2 × 20 Curved surface area = 1760 cm²

The total area of the playground is obtained by multiplying the curved surface area by the number of revolutions: Total area = 1760 × 235 Total area = 413600 cm²

Expressing this value in exponential form: Total area = 4136 × 10² cm²

Explanation

The expression 1/cos α is equal to sec α. For an acute angle α, sec α is equal to cosec α only when α equals 45°. For any other acute angle, the two values are different. For instance, if α equals 30°, then 1/cos 30° equals 2/√3, which is not equal to cosec 30° (which equals 2).

Explanation

The total surface area of a cylinder is calculated using the formula: A = 2πr(r + h)

Here, r is the radius of the base and h is the height of the cylinder.

Given that the diameter of the base is 28 cm, the radius r is: r = 28 / 2 = 14 cm

The height h is given as 70 cm.

Substituting these values into the formula: A = 2 × (22/7) × 14 × (14 + 70) A = 2 × 22 × 2 × 84 A = 88 × 84 A = 7392 cm²

Explanation

First, determine the speed of the tractor: Speed of the tractor = 1150 km ÷ 23 hours = 50 km/h

Next, the speed of the bus is twice the speed of the tractor: Speed of the bus = 2 × 50 km/h = 100 km/h

The speed of the car is 1 3/5 (or 8/5) times the speed of the bus: Speed of the car = 8/5 × 100 km/h = 160 km/h

Finally, find the distance covered by the car in 4 hours: Distance = Speed × Time = 160 km/h × 4 hours = 640 km

Explanation

Given the quadratic equation x² - 9x + 1 = 0.

Since x cannot be 0, dividing both sides by x gives: x - 9 + 1/x = 0 x + 1/x = 9

Squaring both sides of this equation yields: (x + 1/x)² = 9² x² + 2 + 1/x² = 81 x² + 1/x² = 79

Squaring both sides again yields: (x² + 1/x²)² = 79² x⁴ + 2 + 1/x⁴ = 6241 x⁴ + 1/x⁴ = 6239

We can rewrite the given expression x⁸ - 6239x⁴ + 1 by factoring out x⁴: x⁸ - 6239x⁴ + 1 = x⁴(x⁴ - 6239 + 1/x⁴)

Substituting x⁴ + 1/x⁴ = 6239 into this expression: x⁴(6239 - 6239) = x⁴ × 0 = 0

Explanation

We simplify the expression by substituting the trigonometric definitions of cosec θ and cot θ in terms of sin θ and cos θ:

cosec θ = 1/sin θ cot θ = cos θ/sin θ

Substituting these into the expression:

(cosec θ - cot θ)² = (1/sin θ - cos θ/sin θ)²

Combine the terms inside the parentheses under a single denominator:

(cosec θ - cot θ)² = ((1 - cos θ)/sin θ)²

Square the numerator and denominator separately:

(cosec θ - cot θ)² = (1 - cos θ)² / sin² θ

By the Pythagorean identity, sin² θ = 1 - cos² θ. Substituting this into the denominator gives:

(cosec θ - cot θ)² = (1 - cos θ)² / (1 - cos² θ)

Factor the denominator using the difference of squares, a² - b² = (a - b)(a + b):

(cosec θ - cot θ)² = (1 - cos θ)² / ((1 - cos θ)(1 + cos θ))

Divide both the numerator and the denominator by the common factor (1 - cos θ):

(cosec θ - cot θ)² = (1 - cos θ) / (1 + cos θ)

Explanation

The total earnings of the shopkeeper in February 2021 are obtained by summing the weekly earnings: 21,980 + 20,580 + 22,380 + 22,616 = 87,556. Since February 2021 is a non-leap year containing 28 days, the average daily income is calculated by dividing the total earnings by 28, which gives 87,556 / 28 = 3,127.

Explanation

Let m and w be the daily work rate of a man and a woman respectively.

The total work done is the product of the number of workers and the days taken. Therefore, the total work can be represented in two ways: Total Work = 10 × (3m + 7w) = 30m + 70w Total Work = 8 × (4m + 6w) = 32m + 48w

Equating the two expressions for the total work: 30m + 70w = 32m + 48w 22w = 2m m = 11w

This shows that the daily work of 1 man is equivalent to that of 11 women.

Substituting m = 11w into the first total work equation: Total Work = 30 × 11w + 70w = 330w + 70w = 400w

The time taken by 10 women to complete the same task is given by dividing the total work by the daily work rate of 10 women: Time = 400w ÷ 10w = 40 days

Explanation

The volume of a cylinder is calculated using the formula V = π × r² × h, where r is the radius of the base and h is the height of the cylinder.

Given: Radius, r = 15 cm Height, h = 119 cm π = 22/7

Substituting these values into the formula: V = (22/7) × 15² × 119

Since 119 divided by 7 equals 17, the expression simplifies to: V = 22 × 225 × 17 V = 4950 × 17 V = 84150 cm³

Explanation

Let the original cost price of the table fan be 100.

The first dealer makes a profit of 25%. Therefore, the selling price for the first dealer, which serves as the cost price for the second dealer (CP₂), is: CP₂ = 100 × (1 + 0.25) = 125

The fan is finally sold at a profit of 30% of the original cost price. Therefore, the final selling price (SP) is: SP = 100 × (1 + 0.30) = 130

The profit earned by the second dealer is: Profit = SP - CP₂ = 130 - 125 = 5

The profit percentage made by the second dealer is: Profit % = (Profit / CP₂) × 100 Profit % = (5 / 125) × 100 = 4%

Explanation

When a rectangular piece of paper of length 52 cm and breadth 22 cm is rolled along its breadth, the breadth of the paper forms the circumference of the circular base of the cylinder, and the length of the paper becomes the height of the cylinder.

For the cylinder: Height, h = 52 cm Circumference of the base, 2πr = 22 cm

Substituting π = 22/7: 2 × (22/7) × r = 22 r = 7/2 cm

The volume of the cylinder (V) is calculated as: V = πr²h V = (22/7) × (7/2)² × 52 V = (22/7) × (49/4) × 52 V = 11 × 7 × 26 V = 2002 cm³

Explanation

Using the method of alligation, the ratio of the number of boys to the number of girls is determined by comparing their individual average scores with the combined average score.

Average score of boys = 52 Average score of girls = 72 Combined average score = 60

Ratio of boys to girls = (Average score of girls - Combined average) : (Combined average - Average score of boys) = (72 - 60) : (60 - 52) = 12 : 8 = 3 : 2

Explanation

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For the number 123456, the last two digits form the number 56. Since 56 is divisible by 4 (56 ÷ 4 = 14), the entire number 123456 is divisible by 4.

Explanation

When two people run around a circular track in opposite directions with speeds u and v, the number of distinct meeting points is given by (u + v) / gcd(u, v). Substituting the given speeds of 8 m/s and 6 m/s, we get (8 + 6) / gcd(8, 6) = 14 / 2 = 7 distinct meeting points.

Explanation

First, evaluate the expression inside the innermost parentheses: 21 - 13 × 8 + 4 × 3 Using multiplication first: 13 × 8 = 104 4 × 3 = 12 This simplifies to: 21 - 104 + 12 = -71

Next, evaluate the expression inside the curly braces: 1491 ÷ 3(-71) Evaluating the multiplication associated with the bracket first: 3 × (-71) = -213 Then performing the division: 1491 ÷ (-213) = -7

Now, evaluate the term in the square brackets: 119 ÷ (-7) = -17

Finally, substitute this back into the main expression: 272 ÷ 16 + [-17] Since 272 ÷ 16 = 17, we have: 17 - 17 = 0

Explanation

The final price Khushi has to pay is calculated using the selling price formula:

Selling Price = Marked Price × (1 - Discount Percentage)

Substituting the given values:

Selling Price = 6000 × (1 - 20/100) Selling Price = 6000 × 0.80 Selling Price = 4800

Explanation

Let C₁ and C₂ be the centres of the two circles with radii r₁ = 4 cm and r₂ = 6 cm, respectively. Let the transverse common tangent touch the two circles at points T₁ and T₂, and let it intersect the line joining the centres C₁C₂ at point P.

The radii C₁T₁ and C₂T₂ are perpendicular to the tangent line T₁T₂ at the points of contact. Therefore, the triangles C₁T₁P and C₂T₂P are right-angled triangles with ∠C₁T₁P = ∠C₂T₂P = 90°.

The vertically opposite angles ∠C₁PT₁ and ∠C₂PT₂ are equal. By the Angle-Angle similarity criterion, triangle C₁T₁P is similar to triangle C₂T₂P.

By the property of similar triangles, the ratio of corresponding sides is equal to the ratio of their radii:

C₁P / C₂P = C₁T₁ / C₂T₂ = r₁ / r₂ = 4 / 6 = 2 / 3

Thus, the transverse common tangent divides the line segment joining the centres internally in the ratio 2:3.

Explanation

To find the required percentage, first calculate the total number of units manufactured in March for all four products: 300 + 268 + 236 + 292 = 1096

Next, calculate the total number of spoons manufactured across all four given months: 284 + 236 + 220 + 260 = 1000

Now, calculate the percentage of total March units relative to the total spoons manufactured: Percentage = (1096 ÷ 1000) × 100 = 109.6%

Explanation

Let the income, expenditure, and savings of the person be represented as parts of a total.

Given the ratio of income to expenditure is 8:5, we have: Income = 8 units Expenditure = 5 units Savings = Income - Expenditure = 8 - 5 = 3 units

Let the percentage increase in savings be x%.

By the weighted average relation, the total increase in income is equal to the sum of the increases in expenditure and savings: Percentage increase in Income × Income = (Percentage increase in Expenditure × Expenditure) + (Percentage increase in Savings × Savings)

Substituting the given values: 25 × 8 = (28 × 5) + (x × 3) 200 = 140 + 3x 3x = 60 x = 20

Explanation

The arithmetic mean (x̄) of a grouped frequency distribution is calculated using the formula:

x̄ = ∑(f × x) / ∑f

where x represents the marks obtained, and f represents the frequency of students obtaining those marks.

First, calculate the total frequency (∑f): ∑f = 3 + 2 + 2 + 4 + 6 + 7 + 7 + 5 + 3 + 4 + 2 = 45

Next, calculate the sum of the products of marks and their corresponding frequencies (∑(f × x)): ∑(f × x) = (0 × 3) + (1 × 2) + (2 × 2) + (3 × 4) + (4 × 6) + (5 × 7) + (6 × 7) + (7 × 5) + (8 × 3) + (9 × 4) + (10 × 2) ∑(f × x) = 0 + 2 + 4 + 12 + 24 + 35 + 42 + 35 + 24 + 36 + 20 = 234

Now, substitute these values into the formula to find the arithmetic mean: x̄ = 234 ÷ 45 = 5.2

Explanation

The given expression is of the algebraic form: a³ + b³ + c³ + 3(a + b)(a + c)(b + c)

By using the algebraic identity: (a + b + c)³ = a³ + b³ + c³ + 3(a + b)(b + c)(c + a)

Here, let: a = ½ b = 3/2 c = 6

Now, calculate the sum of the variables: a + b + c = ½ + 3/2 + 6 = 4/2 + 6 = 2 + 6 = 8

Substituting this sum back into the identity gives: (a + b + c)³ = 8³ = 512

Explanation

Cost price of 1 orange = 15 / 5 = ₹3

Selling price of 1 orange = ₹5/3

Loss per orange = Cost price - Selling price = 3 - 5/3 = 4/3

Loss percent = (Loss / Cost price) × 100 Loss percent = ((4/3) / 3) × 100 = (4/9) × 100 = 400/9 % = 44 4/9 %

Explanation

To find the distance travelled at the lower speed, we first convert the initial speed from meters per minute to kilometers per hour: Initial speed = 450 m/min = 450 × 60 / 1000 km/h = 27 km/h

The speed for the rest of the journey is 1.4 times the initial speed: Higher speed = 1.4 × 27 km/h = 37.8 km/h

Let the time spent travelling at the lower speed be t hours. Since the total time for the journey is 1 hour, the time spent travelling at the higher speed is 1 - t hours.

Using the relation for total distance: Distance = Speed × Time 27t + 37.8(1 - t) = 33.3 27t + 37.8 - 37.8t = 33.3 10.8t = 4.5 t = 4.5 / 10.8 = 5/12 hours

The distance travelled at the lower speed is: Distance = 27 × 5/12 = 11.25 km

Explanation

The remaining work can be completed by the initial 40 men in 18 - 9 = 9 days.

Using the work formula: M₁ × D₁ = M₂ × D₂

Here, M₁ = 40 men, D₁ = 9 days, and the new number of men M₂ = 40 + 5 = 45 men.

Substituting these values to find the required number of days (D₂): 40 × 9 = 45 × D₂ D₂ = 360 / 45 D₂ = 8 days

Explanation

In compound interest, the interest earned in the nth year is given by the formula: Iₙ = P × r × (1 + r)ⁿ⁻¹

where P is the principal sum and r is the annual interest rate.

For the first year (n = 1): I₁ = P × r = 400

For the second year (n = 2): I₂ = P × r × (1 + r) = 420

Dividing the interest of the second year by the interest of the first year: I₂ / I₁ = (P × r × (1 + r)) / (P × r) 420 / 400 = 1 + r 1.05 = 1 + r r = 0.05

Using this interest rate in the equation for the first year to find the principal sum P: P × 0.05 = 400 P = 400 / 0.05 = 8000

Explanation

Let the man's monthly salary be S.

The man spends 20% of his salary on food, leaving a remaining balance of: 100% - 20% = 80% of S = 0.8S

He spends one-fourth of this remaining salary on charity: Charity expenditure = 1/4 × 0.8S = 0.2S

The remaining balance after both food and charity expenses is: 0.8S - 0.2S = 0.6S

His monthly savings of 9,600 are equal to half of this balance: Savings = 1/2 × 0.6S = 0.3S 0.3S = 9,600 S = 9,600 / 0.3 = 32,000

Explanation

The length of the arc of a circle (L) is given by the formula:

L = (θ / 360°) × 2πr

where r is the radius of the circle and θ is the angle subtended by the arc at the centre.

Substituting the given values, r = 35 cm, θ = 36°, and π = 22 / 7:

L = (36 / 360) × 2 × (22 / 7) × 35

L = (1 / 10) × 2 × 22 × 5

L = (1 / 10) × 220 = 22 cm

Explanation

When three numbers a, b, and c are given, their third proportional x is defined by placing the unknown variable in the third position of the proportion:

a : b :: x : c

This relation can be written in fractional form as:

a / b = x / c

Substituting the given values, a = 4, b = 15, and c = 24:

4 / 15 = x / 24

Solving for x:

x = (4 × 24) / 15 x = 96 / 15

Dividing both the numerator and the denominator by 3 simplifies the fraction to:

x = 32 / 5