SSC CHSL Tier 1 2024 Quantitative Aptitude Questions with Solutions

Explanation

The total number of votes is 7,500. Since 20% of the votes were invalid, the percentage of valid votes is 80%.

Total valid votes = 7,500 × 80% = 7,500 × 0.80 = 6,000

One candidate obtained 65% of the total valid votes. Therefore, the other candidate received the remaining percentage of the valid votes, which is 100% - 65% = 35%.

Number of valid votes for the other candidate = 6,000 × 35% = 6,000 × 0.35 = 2,100

Explanation

According to the BODMAS rule, the operations inside the parentheses are solved first: 25/44 × 11/5 = (25 ÷ 5) / (44 ÷ 11) = 5/4

Now, substitute this value back into the original expression: 3/2 × 11/5 ÷ 5/4 ÷ 33/15

Next, convert the division operations into multiplication by taking the reciprocals of the fractions: 3/2 × 11/5 × 4/5 × 15/33

Combine and simplify the terms in the numerator and denominator: (3 × 11 × 4 × 15) ÷ (2 × 5 × 5 × 33)

Since 3 × 11 = 33, these terms cancel with the 33 in the denominator: (4 × 15) ÷ (2 × 5 × 5)

Simplify the remaining terms: (4 × 15) ÷ (2 × 25) = 60 ÷ 50 = 6/5

Explanation

To find the time taken by A, B, and C to complete the work together, we use the combined work rate formula. The individual rates of work for A, B, and C are 1/12, 1/15, and 1/20 of the work per day respectively.

Combined rate of work per day = 1/12 + 1/15 + 1/20

To add these fractions, we find the Least Common Multiple (LCM) of the denominators 12, 15, and 20, which is 60.

Combined rate of work per day = (5 + 4 + 3) / 60 = 12/60 = 1/5

Since they complete 1/5 of the work in one day, the total number of days required to finish the work together is the reciprocal of their combined rate:

Number of days = 1 / (1/5) = 5 days.

Explanation

The total amount A obtained from a principal sum P at a simple interest rate of R% per annum for T years is given by the formula:

A = P × (1 + RT/100)

Substituting the given values, where A = 6,600, T = 4 years, and R = 5% per annum:

6,600 = P × (1 + (5 × 4)/100) 6,600 = P × (1 + 20/100) 6,600 = P × 1.20 P = 6,600 / 1.20 P = 5,500

Explanation

To find the point of intersection of the lines x + y = 2 and 2x - y = 1, solve the system of linear equations by adding them: (x + y) + (2x - y) = 2 + 1 3x = 3 x = 1

Substituting x = 1 into the first equation gives: 1 + y = 2 y = 1

The point of intersection is (1, 1). Since this point lies on the line y = Kx + 5, substitute x = 1 and y = 1 into the equation: 1 = K(1) + 5 K = 1 - 5 K = -4

Explanation

For two successive discounts of d₁% and d₂%, the single equivalent discount rate is given by the formula d₁ + d₂ - (d₁ × d₂)/100.

For the first offer of two successive discounts of 20% and 20%: Equivalent discount = 20 + 20 - (20 × 20)/100 = 40 - 4 = 36%

For the second offer of successive discounts of 30% and 10%: Equivalent discount = 30 + 10 - (30 × 10)/100 = 40 - 3 = 37%

The difference in the two discount rates is 37% - 36% = 1%.

Since the marked price of the watch is ₹1,600, opting for the better plan (the second offer) yields additional savings of: 1% of ₹1,600 = (1/100) × 1600 = ₹16

Explanation

To find the total number of digits required to number a book with 428 pages, the page numbers are broken down by the number of digits they contain.

For single-digit page numbers from 1 to 9, there are 9 pages, which require 9 × 1 = 9 digits.

For double-digit page numbers from 10 to 99, there are 90 pages, which require 90 × 2 = 180 digits.

For triple-digit page numbers from 100 to 428, there are 428 - 100 + 1 = 329 pages, which require 329 × 3 = 987 digits.

Adding these together, the total number of digits required is 9 + 180 + 987 = 1176.

Explanation

The surface area of a sphere with radius r is given by the formula: A = 4πr²

Given the diameter of the sphere is 10 m, the radius r is 5 m.

Substituting this value to find the surface area: A = 4 × π × 5² = 100π m²

The total cost of painting is the product of the surface area and the rate of painting per square meter: Cost = Area × Rate Cost = 100π × (80/π) = 8000

Explanation

To find the total percentage of students who qualified in the year 2016, calculate the sum of students who appeared and the sum of students who qualified across all districts in that year.

Total Appeared in 2016 = 55 + 35 + 48 + 50 + 55 + 60 = 303 thousand

Total Qualified in 2016 = 42 + 22 + 26 + 30 + 27 + 19 = 166 thousand

Percentage of qualified students = (Total Qualified / Total Appeared) × 100

Percentage of qualified students = (166 / 303) × 100 ≈ 54.78%

Explanation

In triangle EFG, since XY is parallel to FG, triangle EXY is similar to triangle EFG.

The ratio of the sides is EX / EF = EX / (EX + XF).

Given EX:XF = 2:3, the ratio of the sides is EX / EF = 2 / (2 + 3) = 2/5.

The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding sides: Area(ΔEXY) / Area(ΔEFG) = (EX / EF)² = (2/5)² = 4/25

Let Area(ΔEXY) = 4A and Area(ΔEFG) = 25A.

The area of the quadrilateral XFGY is the difference between the areas of the two triangles: Area(XFGY) = Area(ΔEFG) - Area(ΔEXY) = 25A - 4A = 21A

Given Area(XFGY) = 44 m²: 21A = 44 A = 44/21

The area of triangle EXY is: Area(ΔEXY) = 4A = 4 × (44/21) = 176/21 ≈ 8.38 m²

Explanation

Given the trigonometric relation √13 sin θ = 2, we have sin θ = 2/√13.

Using a right-angled triangle where the perpendicular is 2 and the hypotenuse is √13, the base is calculated using the Pythagorean theorem: Base = √((√13)² - 2²) = √(13 - 4) = √9 = 3.

From this, the other trigonometric ratios are: cos θ = 3/√13 tan θ = 2/3

Substituting these values into the given expression: Numerator = 3 tan θ + √13 sin θ = 3 × (2/3) + √13 × (2/√13) = 2 + 2 = 4 Denominator = √13 cos θ - 3 tan θ = √13 × (3/13) - 3 × (2/3) = 3 - 2 = 1

The value of the expression is 4/1 = 4.

Explanation

At the start of day 1, Rajesh has 500 eggs.

By the end of day 1, he sells 20% of the eggs: Remaining eggs at the end of day 1 = 500 × (1 - 0.20) = 400

At the beginning of day 2, he adds b% of the eggs: Eggs at the start of day 2 = 400 × (1 + b/100)

By the end of day 2, he sells 20% of the eggs: Remaining eggs at the end of day 2 = 400 × (1 + b/100) × (1 - 0.20) = 320 × (1 + b/100)

At the beginning of day 3, he adds b% of the eggs: Eggs at the start of day 3 = 320 × (1 + b/100) × (1 + b/100) = 320 × (1 + b/100)²

By the end of day 3, he sells 20% of the eggs: Remaining eggs at the end of day 3 = 320 × (1 + b/100)² × (1 - 0.20) = 256 × (1 + b/100)²

Since the number of eggs left at the end of the third day is 1024: 256 × (1 + b/100)² = 1024 (1 + b/100)² = 1024 / 256 (1 + b/100)² = 4

Taking the square root on both sides: 1 + b/100 = 2 b/100 = 1 b = 100

Explanation

To find the ratio of the shares of Ravi, Reeta, and Rahul, we set the given relation equal to a constant k:

5 × Ravi = 3 × Reeta = 11 × Rahul = k

This gives the individual shares as: Ravi = k/5 Reeta = k/3 Rahul = k/11

The ratio of their shares is: Ravi : Reeta : Rahul = 1/5 : 1/3 : 1/11

To convert this fractional ratio into an integer ratio, we multiply each term by the least common multiple of the denominators, which is 5 × 3 × 11 = 165: Ravi : Reeta : Rahul = (165/5) : (165/3) : (165/11) Ravi : Reeta : Rahul = 33 : 55 : 15

Explanation

Profit is defined as the difference between the selling price and the cost price. The profit percentage is calculated on the cost price.

Profit = Profit Percentage × Cost Price

Given that the profit is ₹1,800 and the profit percentage is 20%:

1,800 = (20/100) × Cost Price

1,800 = 0.2 × Cost Price

Cost Price = 1,800 / 0.2 = 9,000

Explanation

To find the time taken for the two trains to completely cross each other, the formula for relative speed and total distance is used.

The total distance to be covered by the trains to cross each other is the sum of the lengths of both trains and the distance between them: Total Distance = 310 + 330 + 160 = 800 m

Since the trains are moving towards each other, their relative speed is the sum of their individual speeds: Relative Speed = 130 + 158 = 288 km/h

Converting this speed into meters per second (m/s): Relative Speed = 288 × 5/18 = 16 × 5 = 80 m/s

The time taken to cross each other is: Time = Total Distance / Relative Speed = 800 / 80 = 10 seconds

Explanation

Let the monthly income of the man be x.

The portion of income remaining after spending 35% on food is: 100% - 35% = 65% of x = 13x/20

He spends 4/13 of this remaining amount on transport. The remaining balance after transport is: (1 - 4/13) × 13x/20 = 9/13 × 13x/20 = 9x/20

His monthly savings of Rs. 6,300 are equal to 20% of this balance: 20% of 9x/20 = 6,300 1/5 × 9x/20 = 6,300 9x/100 = 6,300 x = 6,300 × 100/9 x = 70,000

Explanation

Correct Answer: B

According to the Midpoint Theorem of triangles, the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half of its length.

Here, L and M are the midpoints of AB and AC respectively, and LM is parallel to BC.

Therefore, LM = ½ × BC

Substituting the given value of BC = 18 cm:

LM = ½ × 18 = 9 cm

Explanation

By the Basic Proportionality Theorem (Thales's Theorem), since PQ is parallel to BC in triangle ABC, the line PQ divides the sides AB and AC in the same ratio: AP/PB = AQ/QC

Let the length of AP and QC be x. Since the total length of AB is 12 cm, the length of PB is: PB = AB - AP = 12 - x

Given that AQ = 2 cm and QC = x, substituting these values into the proportionality relation yields: x/(12 - x) = 2/x

Cross-multiplying the terms gives: x² = 2(12 - x) x² = 24 - 2x x² + 2x - 24 = 0

Solving this quadratic equation by factoring: (x + 6)(x - 4) = 0

This gives two solutions: x = -6 or x = 4. Since length must be positive, we take x = 4. Therefore, the length of CQ is 4 cm.

Explanation

A triangle with side lengths 3 cm, 4 cm, and 5 cm is a right-angled triangle because these lengths satisfy the Pythagorean theorem: 3² + 4² = 5². The side of length 5 cm is the hypotenuse, and the sides of length 3 cm and 4 cm are the perpendicular sides.

The area of this right-angled triangle is: Area = ½ × base × height = ½ × 3 × 4 = 6 cm²

The area can also be expressed using the hypotenuse as the base and the perpendicular from the opposite vertex, h, as the height: Area = ½ × hypotenuse × h = ½ × 5 × h = 2.5 × h

Equating the two expressions for the area: 2.5 × h = 6 h = 6 / 2.5 = 2.4 cm

Explanation

The average daily balance in a bank account is calculated using the weighted average formula:

Average Balance = Total Balance-Days / Total Number of Days

First, calculate the total balance-days by multiplying each balance by the number of days it was maintained: 5000 × 25 = 125000 20000 × 2 = 40000 1500 × 3 = 4500

Summing these values gives the total balance-days for the month of June: 125000 + 40000 + 4500 = 169500

The total number of days in June for these periods is: 25 + 2 + 3 = 30 days

Now, divide the total balance-days by the total number of days to find the average daily balance: 169500 ÷ 30 = 5650

Explanation

Let the radius (r) and the height (h) of the cylinder be 6x and 7x respectively.

The volume of a cylinder is given by the formula V = πr²h.

Substituting the given values: 792 = (22/7) × (6x)² × 7x 792 = (22/7) × 36x² × 7x 792 = 22 × 36x³ 792 = 792x³ x³ = 1 x = 1

Thus, the radius is 6 cm and the height is 7 cm.

The curved surface area of the cylinder is given by the formula 2πrh.

Substituting these values: Curved Surface Area = 2 × (22/7) × 6 × 7 = 2 × 22 × 6 = 264 cm²

Explanation

Car 1 starts from station T1 at 8 am and travels for 2 hours before Car 2 starts at 10 am.

Distance covered by Car 1 in these 2 hours is: 45 km/hr × 2 hr = 90 km

The remaining distance between the two cars at 10 am is: 300 km - 90 km = 210 km

From 10 am, both cars move towards each other, so their relative speed is: 45 km/hr + 60 km/hr = 105 km/hr

The time taken for them to meet after 10 am is: 210 km ÷ 105 km/hr = 2 hours

Adding 2 hours to the starting time of 10 am gives: 10:00 am + 2 hours = 12:00 p.m.

Explanation

Since ST is parallel to QR, triangle PST is similar to triangle PQR. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. This gives the relation:

Area(ΔPST) / Area(ΔPQR) = (PS / PQ)²

Since ST divides triangle PQR into two parts of equal areas, the area of triangle PST is equal to the area of the quadrilateral STRQ. This means the total area of triangle PQR is twice the area of triangle PST:

Area(ΔPQR) = 2 × Area(ΔPST)

Substituting this into the area ratio equation:

Area(ΔPST) / (2 × Area(ΔPST)) = (PS / PQ)² 1/2 = (PS / PQ)² PS / PQ = 1 / √2

Since PQ is the sum of PS and QS (PQ = PS + QS), we can substitute this into the ratio:

PS / (PS + QS) = 1 / √2 √2 PS = PS + QS (√2 - 1) PS = QS PS / QS = 1 / (√2 - 1)

This gives the ratio of PS to QS as 1 : √2 - 1.

Explanation

The volume of one cardboard box is calculated using the formula for the volume of a cuboid:

Volume = length × breadth × height

Substituting the given dimensions:

Volume of one box = 6 cm × 10 cm × 12 cm = 720 cm³

To find the number of boxes needed to pack a total volume of 2160 cm³, divide the total volume by the volume of a single box:

Number of boxes = Total volume / Volume of one box = 2160 / 720 = 3

Explanation

By the Tangent-Secant Theorem, when a tangent segment and a secant segment are drawn to a circle from an exterior point, the square of the length of the tangent segment is equal to the product of the lengths of the external secant segment and the entire secant segment.

DC² = BC × AC

Substitute the given values DC = 12 cm and BC = 6 cm into the formula:

12² = 6 × AC 144 = 6 × AC AC = 144 / 6 AC = 24 cm

Since the entire secant segment AC is the sum of AB and BC:

AC = AB + BC 24 = AB + 6 AB = 24 - 6 AB = 18 cm

Explanation

The total distance of the trip is 240 km, to be completed in 4 hours.

In the first 3 hours, the bus travels at an average speed of 70 km/h. Using the formula: Distance = Speed × Time

The distance covered in the first 3 hours is: 70 km/h × 3 hours = 210 km

The remaining distance to be covered in the final 1 hour is: Total distance - Covered distance = 240 km - 210 km = 30 km

To cover this remaining distance of 30 km in the last 1 hour, the driver must travel at a speed of: 30 km / 1 hour = 30 km/h

Explanation

The curved surface area of a cylinder is given by the formula CSA = 2πrh, where r is the radius and h is the height of the cylinder.

Given that CSA = 88 cm² and h = 14 cm, we find the radius by substituting these values into the formula: 2 × 22/7 × r × 14 = 88 88 × r = 88 r = 1 cm

The total surface area of a cylinder is the sum of its curved surface area and the area of its two circular bases, given by the formula TSA = CSA + 2πr².

Substituting the known values: TSA = 88 + 2 × 22/7 × 1² TSA = 88 + 44/7 TSA ≈ 88 + 6.28 TSA ≈ 94.28 cm²

Explanation

Let the cost price of the bike for A be CP.

Using the successive percentage change formula: Final price paid by C = CP × (1 + Profit Rate A) × (1 + Profit Rate B)

Substitute the given values: 43355 = CP × 1.45 × 1.30 43355 = CP × 1.885 CP = 43355 / 1.885 CP = 23000

Explanation

When two circles touch each other externally at a point M, the angle subtended by the direct common tangent PQ at the point of contact M is always a right angle.

Therefore, ∠PMQ = 90°.

In triangle PMQ, the sum of the angles is 180°: ∠MPQ + ∠MQP + ∠PMQ = 180°

Substituting the given values: 38° + ∠MQP + 90° = 180° ∠MQP = 180° - 128° ∠MQP = 52°

Explanation

Let the marked price of the article be MP.

The first selling price is SP₁ = 66% of MP = 0.66 MP. Since the merchant makes a 10% profit at this price, the cost price CP is: CP = SP₁ / (1 + 0.10) = 0.66 MP / 1.1 = 0.6 MP

The second selling price is SP₂ = 80% of MP = 0.80 MP.

The new profit percentage is: Profit % = ((SP₂ - CP) / CP) × 100 Profit % = ((0.8 MP - 0.6 MP) / 0.6 MP) × 100 Profit % = (0.2 / 0.6) × 100 = ⅓ × 100 = 33 ⅓%

Explanation

By using the co-function trigonometric identity, we have cos(x) = sin(90 - x).

Applying this identity to the term cos(60 - θ): cos(60 - θ) = sin(90 - (60 - θ)) = sin(30 + θ)

Substituting this back into the original expression: sin(30 + θ) - cos(60 - θ) = sin(30 + θ) - sin(30 + θ) = 0

Explanation

The area of a rectangular field is given by the formula: Area = length × width

Given that the area is 3600 m² and the length is 45 m, the width of the field is: width = Area / length width = 3600 / 45 = 80 m

The perimeter of a rectangular field is given by the formula: Perimeter = 2 × (length + width)

Substituting the length and width into the formula: Perimeter = 2 × (45 + 80) = 2 × 125 = 250 m

Explanation

In a right-angled triangle ABC with ∠BAC = 90° and AD perpendicular to BC, the triangle ACD is similar to the triangle ABC (ΔACD ~ ΔABC) because they share the angle C and both contain a 90° angle (∠ADC = ∠BAC = 90°).

For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. In these two triangles, the side opposite to the 90° angle (the hypotenuse) of ΔACD is AC, and the hypotenuse of ΔABC is BC.

Area(ΔACD) / Area(ΔABC) = (AC / BC)²

Substituting the given values into this relation:

7 / 63 = (5 / BC)²

1 / 9 = 25 / BC²

BC² = 25 × 9

BC² = 225

BC = √225 = 15 cm

Explanation

Following the BODMAS rule, the operations are performed in the order of Brackets, Division and Multiplication, and then Addition and Subtraction.

First, evaluate the terms inside the parentheses: 17 + 15 = 32 -16 + 13 = -3

Substitute these values back into the expression: 32 ÷ 2 - 11 + 16 × 4 - 28 + 13 × (-3)

Next, perform the division and multiplication operations: 32 ÷ 2 = 16 16 × 4 = 64 13 × (-3) = -39

Substitute these values back into the expression: 16 - 11 + 64 - 28 - 39

Now, perform the remaining addition and subtraction operations from left to right: 16 - 11 = 5 5 + 64 = 69 69 - 28 = 41 41 - 39 = 2

Explanation

The given distances between the three points are AB = 11 cm, BC = 13 cm, and AC = 24 cm. Summing the two shorter distances gives AB + BC = 11 + 13 = 24 cm, which is exactly equal to the longest distance AC. This relationship satisfies the condition for collinearity, meaning the points A, B, and C lie on the same straight line, with point B located between A and C. Since three collinear points cannot lie on the circumference of a single circle, no circle can pass through all three of these points. Therefore, the number of circles passing through A, B, and C is 0.

Explanation

To find the time taken by the policeman to catch the thief, we use the formula of relative speed. Since both are running in the same direction:

Relative speed = Speed of policeman - Speed of thief Relative speed = 36 km/h - 18 km/h = 18 km/h

Converting the relative speed from km/h to m/s: Relative speed = 18 × 5/18 = 5 m/s

The initial distance between them is 500 m.

Time taken to catch the thief = Distance / Relative speed Time = 500 / 5 = 100 seconds

Explanation

The total surface area of a cuboid is calculated using the formula A = 2(lb + bh + hl), where l is the length, b is the breadth, and h is the height.

Given: Surface area A = 108 m² Length l = 6 m Breadth b = 3 m

Substituting these values into the formula: 108 = 2(6 × 3 + 3 × h + h × 6) 108 = 2(18 + 3h + 6h) 108 = 2(18 + 9h)

Dividing both sides by 2: 54 = 18 + 9h

Subtracting 18 from both sides: 36 = 9h

Solving for h: h = 36/9 = 4 m

Explanation

The relationship between the number of men (M), days (D), and work (W) is given by the formula:

(M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

Substituting the given values into the formula:

M₁ = 18 D₁ = 10 W₁ = 1/5

M₂ = ? D₂ = 5 W₂ = 2/5

(18 × 10) / (1/5) = (M₂ × 5) / (2/5)

By simplifying the denominators, we get:

180 × 5 = (M₂ × 5 × 5) / 2

900 = 12.5 × M₂

M₂ = 900 / 12.5 = 72

Thus, 72 people are required to complete the specified work.

Explanation

The radius of the circle r is half of the diameter, which is 26 / 2 = 13 cm.

A perpendicular drawn from the center of a circle to a chord bisects the chord. For a chord of length 10 cm, the length of the half-chord is 10 / 2 = 5 cm.

Using the Pythagorean theorem, the perpendicular distance (d) from the center of the circle to each chord is: d = √(r² - 5²) d = √(13² - 5²) d = √(169 - 25) d = √144 = 12 cm

Since the two equal parallel chords lie on opposite sides of the center, the total distance between them is the sum of their perpendicular distances from the center: Distance = 12 + 12 = 24 cm.

Explanation

The formula for the average monthly salary is: Average Salary = Total Salary of 12 Months / 12

For the 12 months of the year, the salaries are: Four months of ₹12,000 Three months of ₹15,000 Three months of ₹21,000 Two months of ₹30,000

Total Salary = (4 × 12,000) + (3 × 15,000) + (3 × 21,000) + (2 × 30,000) Total Salary = 48,000 + 45,000 + 63,000 + 60,000 = 216,000

Average Salary = 216,000 / 12 = 18,000

Explanation

Using the relation: Income = Expenditure + Savings.

Let the initial income be 100. Since Ramana spends 75% of his income, the initial expenditure is 75, and the initial savings are 25.

The income increases by 25%, making the new income 125. The expenditure increases by 10%, making the new expenditure 75 + (10% of 75) = 75 + 7.5 = 82.5.

The new savings are calculated as: New Savings = 125 - 82.5 = 42.5

The absolute increase in savings is: 42.5 - 25 = 17.5

The percentage increase in savings is: (17.5 / 25) × 100 = 70%

Explanation

To find the combined ratio a : b : c from the individual ratios a : b = 3 : 7 and b : c = 4 : 9, make the term representing b equal in both ratios.

The value of b in the first ratio is 7 and in the second ratio is 4. The least common multiple of 7 and 4 is 28.

Multiply the terms of the ratio a : b by 4: a : b = (3 × 4) : (7 × 4) = 12 : 28

Multiply the terms of the ratio b : c by 7: b : c = (4 × 7) : (9 × 7) = 28 : 63

Combining these yields the ratio: a : b : c = 12 : 28 : 63

Explanation

According to the properties of modular arithmetic, the remainder of the product of numbers is equal to the product of their individual remainders when divided by the divisor. That is, (a × b × c) mod n = ((a mod n) × (b mod n) × (c mod n)) mod n.

Evaluating the remainder for each term when divided by 17: 179 = (17 × 10) + 9, so 179 ≡ 9 (mod 17) 172 = (17 × 10) + 2, so 172 ≡ 2 (mod 17) 173 = (17 × 10) + 3, so 173 ≡ 3 (mod 17)

Now, multiply the individual remainders: 9 × 2 × 3 = 54

Finally, find the remainder when 54 is divided by 17: 54 = (17 × 3) + 3, which leaves a remainder of 3.

Explanation

The original cost of one chair is calculated by dividing the total cost of the chairs by the number of chairs, which is 4500 / 10 = ₹450.

With a 20% discount on each chair, the new cost per chair becomes 450 × (1 - 0.20) = ₹360.

The person decides to purchase 10% more chairs than the original quantity of 10, which means the new quantity of chairs purchased is 10 × (1 + 0.10) = 11 chairs.

The total cost for these 11 chairs at the discounted price is 11 × 360 = ₹3,960.

Explanation

The simple interest on a principal sum with varying rates of interest over different time periods is calculated using the effective rate of interest.

Effective Rate of Interest = (R₁ × T₁) + (R₂ × T₂) Effective Rate of Interest = (10% × 2) + (12% × 3) = 20% + 36% = 56%

Simple Interest = Principal × Effective Rate of Interest / 100 Simple Interest = 5000 × 56 / 100 = 50 × 56 = 2800

The total interest earned by the man at the end of 5 years is ₹2,800.

Explanation

The original fraction is 3/5.

Decreasing this fraction by 2/5 gives: 3/5 - 2/5 = 1/5

Increasing this resulting fraction by 20% gives: 1/5 × (1 + 20%) = 1/5 × 1.2 = 1/5 × 6/5 = 6/25

To find the percentage change relative to the original fraction: Percentage change = (Final Value - Original Value) / Original Value × 100% Percentage change = (6/25 - 3/5) / (3/5) × 100% Percentage change = (6/25 - 15/25) / (15/25) × 100% Percentage change = (-9/25) / (15/25) × 100% Percentage change = -9/15 × 100% Percentage change = -3/5 × 100% = -60%

The negative sign indicates a decrease of 60%.

Explanation

To find the area of the triangular region bounded by the lines 2x + y = 6 and 2x - y = -2 and the x-axis, we first determine the coordinates of the vertices of the triangle.

The x-intercepts of the lines are found by setting y = 0: For 2x + y = 6, setting y = 0 gives x = 3. For 2x - y = -2, setting y = 0 gives x = -1. The length of the base of the triangle along the x-axis is the distance between these two intercepts: base = 3 - (-1) = 4 units.

The third vertex is the point of intersection of the two lines. Solving the system of equations by adding them: 4x = 4 x = 1

Substituting x = 1 into 2x + y = 6: 2(1) + y = 6 y = 4

The height of the triangle is the perpendicular distance from the intersection point to the x-axis, which is the y-coordinate: height = 4 units.

Using the area of a triangle formula: Area = ½ × base × height Area = ½ × 4 × 4 = 8 sq. units.

Explanation

The growth rate for any course from 2015 to 2020 is calculated using the formula: Growth Rate = (Value in 2020 - Value in 2015) ÷ Value in 2015 × 100%.

Applying this formula to the given courses:

For Arts: Growth Rate = (750 - 450) ÷ 450 × 100% = 300 ÷ 450 × 100% ≈ 66.67%

For Management: Growth Rate = (320 - 240) ÷ 240 × 100% = 80 ÷ 240 × 100% ≈ 33.33%

For Engineering: Growth Rate = (1400 - 1200) ÷ 1200 × 100% = 200 ÷ 1200 × 100% ≈ 16.67%

For Science: Growth Rate = (950 - 850) ÷ 850 × 100% = 100 ÷ 850 × 100% ≈ 11.76%

Comparing these percentages, Arts registered the highest growth rate of approximately 66.67% during this period.