SSC CHSL Tier 1 2024 Quantitative Aptitude Questions with Solutions

Explanation

Using the BODMAS rule, the expression 18 ÷ (7 × 2 - 5) × 5 × 24 ÷ 30 is simplified step-by-step:

First, evaluate the term inside the parentheses: 7 × 2 - 5 = 14 - 5 = 9

Substitute this back into the expression: 18 ÷ 9 × 5 × 24 ÷ 30

Since division and multiplication have the same precedence, perform the operations from left to right: 18 ÷ 9 = 2 2 × 5 = 10 10 × 24 = 240 240 ÷ 30 = 8

Explanation

Two linear equations of the form a₁x + b₁y = c₁ and a₂x + b₂y = c₂ represent parallel lines if they satisfy the condition: a₁/a₂ = b₁/b₂ ≠ c₁/c₂

For the given system of equations: x + 2y = 15 4x + 8y = 13

Comparing the coefficients: a₁/a₂ = 1/4 b₁/b₂ = 2/8 = 1/4 c₁/c₂ = 15/13

Since the ratios satisfy the relation 1/4 = 1/4 ≠ 15/13, the two lines are parallel.

Explanation

For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

Area(ΔPQR) / Area(ΔXYZ) = (QR / YZ)²

Substituting the given values into the formula:

12.96 / 635.04 = (2.9 / YZ)²

Taking the square root on both sides:

√(12.96) / √(635.04) = 2.9 / YZ

Since 3.6² = 12.96 and 25.2² = 635.04, this simplifies to:

3.6 / 25.2 = 2.9 / YZ

Simplifying the fraction on the left side:

1 / 7 = 2.9 / YZ

YZ = 2.9 × 7 = 20.3 cm

Explanation

In triangle ABC, since XY is parallel to BC, triangle AXY is similar to triangle ABC by Angle-Angle similarity.

The length of AX is determined by subtracting BX from AB: AX = AB - BX = 5.4 - 3 = 2.4 cm

For similar triangles, the ratio of corresponding sides is equal: XY / BC = AX / AB

Substituting the given values into the relation: XY / 7.2 = 2.4 / 5.4

Simplifying the ratio of the sides: XY = 7.2 × (2.4 / 5.4) XY = 7.2 × (4 / 9) XY = 0.8 × 4 = 3.2 cm

Explanation

To find the number of integers strictly between 2000 and 2020 that are divisible by 8, we first identify the multiples of 8 in this range.

The number 2000 is divisible by 8 since 2000 ÷ 8 = 250.

Since we are looking for numbers strictly between 2000 and 2020, we exclude 2000 itself. The multiples of 8 that lie in this range are: 2000 + 8 = 2008 2008 + 8 = 2016

The next multiple is 2016 + 8 = 2024, which lies outside the given range. Therefore, there are exactly 2 such numbers, which are 2008 and 2016.

Explanation

The angle subtended by the arc PQR at the centre O is 240°. This means the reflex angle ∠POR is 240°.

The remaining central angle subtended by the minor arc PR at the centre O is: 360° - 240° = 120°

According to the inscribed angle theorem, the angle subtended by an arc at any point on the circle is half the angle subtended by the same arc at the centre. Since Q lies on the major arc, the angle ∠PQR is half of the central angle of the minor arc: ∠PQR = 120° / 2 = 60°

Since PQ is extended to A, PQA forms a straight line. The sum of angles on a straight line is 180°: ∠PQR + ∠AQR = 180° 60° + ∠AQR = 180° ∠AQR = 120°

Explanation

The initial number of females in the group is calculated as 60% of 250: 60% of 250 = (60 / 100) × 250 = 150

When 30 more females join the group, both the number of females and the total number of persons increase by 30: New number of females = 150 + 30 = 180 New total number of persons = 250 + 30 = 280

The percentage of females in the new group is: (New number of females / New total number of persons) × 100 = (180 / 280) × 100 = (9 / 14) × 100 ≈ 64.29%

Explanation

When two items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, the transaction always results in a net loss.

The net loss percentage is calculated using the formula: Loss % = x² / 100

Substituting x = 20 into the formula: Loss % = 20² / 100 = 400 / 100 = 4%

Explanation

The formula for simple interest is SI = P × R × T / 100, where P is the principal sum, R is the rate of interest per annum, and T is the time in years.

For the first case, the rate is 10% and the time is 1½ years (1.5 years). The simple interest is: SI₁ = P × 10 × 1.5 / 100 = 15P / 100

For the second case, the rate is 12% and the time is 1 year. The simple interest is: SI₂ = P × 12 × 1 / 100 = 12P / 100

The difference between the two interests is given as ₹ 30: SI₁ - SI₂ = 30 15P / 100 - 12P / 100 = 30 3P / 100 = 30 3P = 3000 P = 1000

The principal sum is ₹ 1,000.

Explanation

Total income is the sum of total expenditure and total savings.

First, calculate the total expenditure for the entire year by multiplying the average expenditure of each period by the number of months in that period: Total Expenditure = (4 × 2,500) + (5 × 2,750) + (3 × 3,550) Total Expenditure = 10,000 + 13,750 + 10,650 = 34,400

Next, add the total annual savings to find the total annual income: Total Income = Total Expenditure + Total Savings Total Income = 34,400 + 5,500 = 39,900

Finally, divide the total annual income by 12 to find the average monthly income: Average Monthly Income = 39,900 ÷ 12 = 3,325

Explanation

Let the number be x.

Increasing the number by 8 makes it equal to 120% of itself, which can be written as 120/100 of x, or 1.2x.

We can set up the linear equation: x + 8 = 1.2x

Subtracting x from both sides gives: 0.2x = 8

Solving for x: x = 8 / 0.2 x = 40

Explanation

The volume of a cube is given by the formula V = s³, where s is the side of the cube. Let the initial volume be V₁ and the final volume be V₂.

According to the question, the final volume is reduced to 72.9% of the initial volume: V₂ = 0.729 V₁

Since the volume is proportional to the cube of its side, the ratio of the final side s₂ to the initial side s₁ is: s₂/s₁ = ³√(V₂/V₁)

Substituting the values: s₂/s₁ = ³√(0.729 V₁ / V₁) s₂/s₁ = ³√0.729 s₂/s₁ = 0.9

This means the final side of the cube is 90% of its initial length. The percentage reduction in the side of the cube is: Percentage reduction = (1 - s₂/s₁) × 100% Percentage reduction = (1 - 0.9) × 100% = 10%

Explanation

To simplify the given expression, apply the VBODMAS rule, which defines the order of operations as Brackets, Of, Division, Multiplication, Addition, and Subtraction.

The given expression is: (3 - 3 × 3 + 3 ÷ 3 + 3 × 5) × 2 of 5 + (2 + 2 ÷ 2 + 2 × 2 - 2)

First, simplify the terms inside the first set of parentheses: 3 - 3 × 3 + 3 ÷ 3 + 3 × 5 Perform division: 3 ÷ 3 = 1 Perform multiplication: 3 × 3 = 9 and 3 × 5 = 15 Substitute these values back: 3 - 9 + 1 + 15 = 10

Next, evaluate the "of" operation, which takes precedence over multiplication: 2 of 5 = 2 × 5 = 10

Now, multiply the result of the first parentheses by this value: 10 × 10 = 100

Next, simplify the terms inside the second set of parentheses: 2 + 2 ÷ 2 + 2 × 2 - 2 Perform division: 2 ÷ 2 = 1 Perform multiplication: 2 × 2 = 4 Substitute these values back: 2 + 1 + 4 - 2 = 5

Finally, add the two simplified parts: 100 + 5 = 105

Explanation

Let CP be the cost price and SP be the selling price of the article.

According to the given condition: 70% of CP = 40% of SP

This can be written as: 0.70 × CP = 0.40 × SP

Rearranging the terms gives the ratio of selling price to cost price: SP/CP = 70/40 = 7/4

The formula for profit percentage is: Profit % = ((SP - CP) / CP) × 100%

Dividing SP and CP by CP inside the formula gives: Profit % = (SP/CP - 1) × 100%

Substituting the ratio SP/CP = 7/4 into the formula: Profit % = (7/4 - 1) × 100% Profit % = 3/4 × 100% Profit % = 75%

Explanation

Under the "buy five and get one free" scheme, a customer receives a total of 6 items (5 paid items plus 1 free item) but pays only for 5 items. The value of the discount is equivalent to the price of the 1 free item.

Using the discount formula: Discount % = (Number of free items / Total number of items) × 100

Substituting the values into the formula: Discount % = (1 / (5 + 1)) × 100 Discount % = (1 / 6) × 100 Discount % = 16.67%

Explanation

The length of a transverse common tangent to two circles is given by the formula: Length = √(d² - (r₁ + r₂)²)

where d is the distance between the centres of the two circles, and r₁ and r₂ are their respective radii.

Given: d = 10 cm r₁ = 4 cm r₂ = 2 cm

Substituting these values into the formula: Length = √(10² - (4 + 2)²) Length = √(100 - 6²) Length = √(100 - 36) Length = √64 Length = 8 cm

Explanation

By definition, the mean proportional of two numbers a and b is given by the formula √(ab).

Let the two numbers be 25 and x. Since 35 is their mean proportional: √(25 × x) = 35

Squaring both sides of the equation: 25 × x = 35² 25 × x = 1225

Solving for x: x = 1225 / 25 x = 49

Explanation

Let the two concentric circles have center O. The radius of the outer circle is R = 17 cm and the radius of the inner circle is r = 15 cm. Let AB be the chord of the outer circle that is tangent to the inner circle at point P.

The radius OP drawn to the point of contact P is perpendicular to the tangent AB, making triangle OPA a right-angled triangle at P. Since the perpendicular from the center of a circle to a chord bisects the chord, P is the midpoint of AB, meaning AB = 2 × AP.

Using the Pythagorean theorem in right-angled triangle OPA: OA² = OP² + AP² 17² = 15² + AP² 289 = 225 + AP² AP² = 289 - 225 AP² = 64 AP = 8 cm

The length of the chord AB is: AB = 2 × AP = 2 × 8 = 16 cm

Explanation

Let the side of the square be s cm.

Since opposite sides of the square form the diameters of the two circles, the diameter of each circle is s and the radius is r = s/2.

Because the diameters lie on the boundaries of the square, only a semicircle of each circle lies inside the square. Thus, the two semicircles inside the square have a combined area equal to one full circle of radius r.

Area of the square = s² Area of the two semicircles = π r² = π (s/2)² = π s² / 4

The remaining area of the square is given by: Remaining Area = s² - π s² / 4 = s² (1 - π/4)

Using π = 22/7: Remaining Area = s² (1 - 22/28) = s² (6/28) = 3/14 s²

Given that the remaining area is 42 cm²: 3/14 s² = 42 s² = 42 × 14 / 3 s² = 196 s = 14 cm

Since the side of the square forms the diameter of each circle, the diameter of each circle is 14 cm.

Explanation

For a constant distance, speed is inversely proportional to time. If the speed is scaled by a factor of 6/7, the time taken must scale by the reciprocal factor of 7/6.

Let T be the usual time taken to cover the journey. New Time = (7/6) × T

The difference between the new time and the usual time is 20 minutes: (7/6)T - T = 20 (1/6)T = 20 T = 120 minutes

Converting 120 minutes into hours gives: 120 ÷ 60 = 2 hours

Explanation

Since triangle ABC is similar to triangle PQR, the ratio of their perimeters is equal to the ratio of their corresponding sides, AB/PQ. The perimeter of triangle PQR is 12 + 18 + 24 = 54 cm, and the ratio of AB to PQ is 8/12 = 2/3, which gives the perimeter of triangle ABC as 54 * (2/3) = 36 cm.

Explanation

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

Substituting the given values into the formula: r = 6.2 cm π = 3.14

Total surface area = 3 × 3.14 × (6.2)² Total surface area = 9.42 × 38.44 Total surface area = 362.1048 sq. cm

Rounding to two decimal places yields 362.10 sq. cm.

Explanation

Let the number be N. According to the division algorithm, N can be expressed as: N = 304k + 43 where k is a non-negative integer.

To find the remainder when N is divided by 16, we write N modulo 16: N mod 16 = (304k + 43) mod 16

Since 304 is a multiple of 16 (304 = 16 × 19), the term 304k is completely divisible by 16, leaving a remainder of 0. Thus, the remainder of N divided by 16 is determined solely by the remainder of 43 divided by 16: 43 = 16 × 2 + 11

The remainder is 11.

Explanation

Let the five consecutive even numbers be represented as x - 4, x - 2, x, x + 2, and x + 4, where x is the middle (third) number.

The sum of these five numbers is: (x - 4) + (x - 2) + x + (x + 2) + (x + 4) = 5x

We are given that the sum is 2720: 5x = 2720 x = 544

Thus, the third number is 544.

The fifth number is: x + 4 = 544 + 4 = 548

The sum of the third and fifth numbers is: 544 + 548 = 1092

Explanation

The length of the trench dug is directly proportional to the number of masons employed when the time duration remains constant.

M₁ / W₁ = M₂ / W₂

Here, M₁ is 47 masons, W₁ is 35 m, and W₂ is 105 m. Substituting these values into the formula:

M₂ = 47 × (105 / 35)

M₂ = 47 × 3

M₂ = 141

Explanation

The percentage increase in the area of a square when its side is increased can be directly computed using the successive percentage change formula:

Percentage increase = x + y + (x × y)/100

Since the side of the square is increased by 5% in both dimensions, we substitute x = 5 and y = 5 into the formula:

Percentage increase = 5 + 5 + (5 × 5)/100 Percentage increase = 10 + 25/100 Percentage increase = 10 + 0.25 = 10.25%

This gives the exact percentage increase in the area of the square.

Explanation

The number of bricks required is calculated by dividing the total volume of the wall by the volume of a single brick.

First, convert all dimensions of the wall into centimeters to maintain uniform units: Length of the wall = 10 m = 1000 cm Breadth of the wall = 22.5 cm Height of the wall = 6 m = 600 cm

Volume of the wall = Length × Breadth × Height = 1000 × 22.5 × 600 cm³

The dimensions of one brick are given as 25 cm × 12 cm × 9 cm. Volume of one brick = 25 × 12 × 9 cm³

Number of bricks = Volume of the wall ÷ Volume of one brick Number of bricks = (1000 × 22.5 × 600) ÷ (25 × 12 × 9)

Simplifying the division: 1000 ÷ 25 = 40 600 ÷ 12 = 50 22.5 ÷ 9 = 2.5

Now, multiply these simplified values: 40 × 50 × 2.5 = 2000 × 2.5 = 5000

Explanation

Since sin θ = 15/17 and θ lies in the first quadrant (0° < θ < 90°), we can use the Pythagorean identity to find the remaining trigonometric ratios.

Using the Pythagorean triple (8, 15, 17): Adjacent side = √(17² - 15²) = 8

Thus, we have: cos θ = 8/17 tan θ = 15/8 cot θ = 8/15 sec θ = 17/8

Substituting these values into the given expression: Numerator = 15 cot θ + 17 sin θ = 15(8/15) + 17(15/17) = 8 + 15 = 23

Denominator = 8 tan θ + 16 sec θ = 8(15/8) + 16(17/8) = 15 + 34 = 49

Evaluating the fraction: (15 cot θ + 17 sin θ) / (8 tan θ + 16 sec θ) = 23/49

Explanation

The length of a direct common tangent to two circles is given by the formula:

L = √(d² - (r₁ - r₂)²)

where d is the distance between the centers of the circles, and r₁ and r₂ are their radii.

Given the diameters of the circles are 16 cm and 20 cm, their radii are r₁ = 8 cm and r₂ = 10 cm. The distance between their centers d is 13 cm.

Substituting these values into the formula:

L = √(13² - (10 - 8)²)

L = √(169 - 2²)

L = √(169 - 4)

L = √165 cm

Explanation

The weight of the empty closed iron box is calculated by finding the volume of the iron sheet used and multiplying it by the weight density of iron.

External volume (Vₑxt) of the box with dimensions 60 cm, 40 cm, and 20 cm: Vₑxt = 60 × 40 × 20 = 48000 cm³

Since the sheet is 1 cm thick, the internal dimensions are reduced by 2 cm (1 cm on each side): Internal Length = 60 - 2 = 58 cm Internal Width = 40 - 2 = 38 cm Internal Height = 20 - 2 = 18 cm

Internal volume (Vᵢnt): Vᵢnt = 58 × 38 × 18 = 39672 cm³

Volume of the iron sheet used: Volume = Vₑxt - Vᵢnt = 48000 - 39672 = 8328 cm³

Given that 1 cm³ of iron weighs 50 gm, the total weight of the empty box is: Weight = 8328 × 50 = 416400 gm

Converting the weight into kilograms (1 kg = 1000 gm): Weight = 416400 ÷ 1000 = 416.40 kg

Explanation

The equivalent single percentage increase for two successive percentage increases of a% and b% is given by the formula:

Equivalent Increase = a + b + (ab / 100)

Substituting the given values, a = 15 and b = 10:

Equivalent Increase = 15 + 10 + (15 × 10 / 100) Equivalent Increase = 25 + 1.5 = 26.5%

Explanation

The total debt discharged by n equal annual instalments of value x at a simple interest rate r% per annum is given by the formula:

Debt = n × x + [x × r × n × (n - 1)] / 200

Here, the annual instalment x = 200, the number of instalments n = 5, and the rate of interest r = 5% per annum.

Substituting these values into the formula:

Debt = 5 × 200 + [200 × 5 × 5 × 4] / 200

Debt = 1000 + 20000 / 200

Debt = 1000 + 100

Debt = 1100

Explanation

To find the car type with the minimum manufacturing from 2007 to 2012, we sum the production numbers for each car type over these years.

The total production of Ertiga (corresponding to Option A) is: 128 + 150 + 142 + 170 + 180 + 230 = 1000

Comparing this with the total production of the other car types: Swift: 250 + 200 + 230 + 245 + 260 + 275 = 1460 Sx4: 200 + 230 + 225 + 210 + 135 + 155 = 1155 Zen: 140 + 155 + 160 + 175 + 185 + 220 = 1035

The sum of 1000 is the lowest among all the categories, making it the minimum manufactured car type during the period from 2007 to 2012.

Explanation

The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

Given that the diameter of the hemisphere is 42 cm, the radius r is half of the diameter: r = 42 / 2 = 21 cm

Substituting the values of r and π into the volume formula: V = (2/3) × (22/7) × 21³ V = (2/3) × (22/7) × 21 × 21 × 21

The denominator 3 × 7 equals 21, which cancels out one of the 21s in the numerator: V = 2 × 22 × 21 × 21 V = 44 × 441 V = 19404 cm³

Explanation

We evaluate the expression in two parts.

First part: {(3³ + 2³) × 22/7}

Since 3³ = 27 and 2³ = 8, the sum inside the parentheses is: 27 + 8 = 35

Multiplying this by 22/7 gives: 35 × 22/7 = 5 × 22 = 110

Second part: {(6² + 3² - 4²) ÷ 14½}

Evaluating the squares: 6² = 36 3² = 9 4² = 16

So the term inside the first parentheses is: 36 + 9 - 16 = 29

The mixed fraction 14½ is equal to 29/2. Dividing by this fraction gives: 29 ÷ (29/2) = 29 × 2/29 = 2

Finally, we multiply the results of the two parts: 110 × 2 = 220

Explanation

The net percentage change after two successive percentage changes of a% and b% is calculated using the formula:

Net change = a + b + ab/100

Substituting a = +40 for the increase and b = -45 for the decrease:

Net change = 40 - 45 + (40 × (-45))/100 Net change = -5 - 1800/100 Net change = -5 - 18 Net change = -23%

The negative sign indicates a net decrease of 23%.

Explanation

Using the work-rate formula: 1/A + 1/B = 1/T

where A is the time taken by A alone, B is the time taken by B alone, and T is the total time taken by both working together.

Substituting the given values, T = 15 days and A = 18 days, into the equation: 1/18 + 1/B = 1/15

Subtracting 1/18 from both sides to solve for the rate of B: 1/B = 1/15 - 1/18

Finding the least common multiple of 15 and 18, which is 90, and rewriting the fractions: 1/B = 6/90 - 5/90 1/B = 1/90

Taking the reciprocal gives B = 90 days.

Explanation

The equation of the line is 6x + 8y - 48 = 0.

To find the x-intercept, we substitute y = 0 into the equation: 6x - 48 = 0 x = 8 This gives the point on the x-axis as (8, 0).

To find the y-intercept, we substitute x = 0 into the equation: 8y - 48 = 0 y = 6 This gives the point on the y-axis as (0, 6).

The segment of the line intercepted between the coordinate axes connects the points (8, 0) and (0, 6). The length of this intercept is calculated using the distance formula: Length = √((8 - 0)² + (0 - 6)²) Length = √(64 + 36) Length = √100 = 10 units.

Explanation

Using the BODMAS rule, brackets and "of" operations are simplified first, followed by division, multiplication, addition, and subtraction.

First, simplify the first bracketed term: [40 - 48 ÷ 4 of 3] Since "of" takes precedence over division: 4 of 3 = 4 × 3 = 12 The term becomes: 40 - 48 ÷ 12 = 40 - 4 = 36

Next, simplify the second bracketed term: [(6 + 4) - 4 of 4 + 4 + (6 - 4) + (4 × 4) ÷ 4] Evaluate the individual operations inside: 6 + 6 = 10 (from 6 + 4) 4 of 4 = 16 6 - 4 = 2 (4 × 4) ÷ 4 = 16 ÷ 4 = 4 Substituting these values back: [10 - 16 + 4 + 2 + 4] = 4

Now, substitute these results back into the main expression: 36 ÷ 4 × 3 Solving from left to right: 36 ÷ 4 = 9 9 × 3 = 27

Explanation

Correct Answer: D

Let the required number be x.

According to the given condition, the equation is: x + 20% of 460 = 70% of 920

First, calculate 20% of 460: 20% of 460 = (20/100) × 460 = 92

Next, calculate 70% of 920: 70% of 920 = (70/100) × 920 = 644

Substitute these values back into the equation: x + 92 = 644 x = 644 - 92 x = 552

Explanation

Let the first quantity be q₁ and the second quantity be q₂.

The ratio of the two quantities is given as q₁ : q₂ = 3 : 5.

This relation can be expressed as: q₂ = q₁ × (5/3)

Substituting the given value of the first quantity, q₁ = 155 kg, into the formula: q₂ = 155 × (5/3) q₂ = 775/3 q₂ ≈ 258.33 kg

This matches the approximate value of 258.3 kg.

Explanation

For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Given that ΔABC is similar to ΔQRP, the side BC corresponds to the side RP.

Area(ΔABC) / Area(ΔQRP) = (BC / PR)²

Substituting the given values into the formula:

9/4 = (15 / PR)²

Taking the square root on both sides:

3/2 = 15 / PR

PR = (15 × 2) / 3

PR = 10 cm

Explanation

In quadrilateral OQPR, the radii OQ and OR are perpendicular to the tangents PQ and PR at the points of tangency Q and R. This gives ∠OQP = 90° and ∠ORP = 90°.

The sum of the interior angles of any quadrilateral is 360°. Therefore, in quadrilateral OQPR: ∠ROQ + ∠OQP + ∠RPQ + ∠ORP = 360°

Substituting the given values into the equation: 110° + 90° + ∠RPQ + 90° = 360° 290° + ∠RPQ = 360° ∠RPQ = 360° - 290° ∠RPQ = 70°

Alternatively, because the angles at the points of tangency are both 90°, the opposite angles ∠ROQ and ∠RPQ must be supplementary, meaning they sum to 180°: ∠RPQ = 180° - ∠ROQ ∠RPQ = 180° - 110° ∠RPQ = 70°

Explanation

Given the trigonometric equation tan θ + cot θ = 2, we can rewrite cot θ as 1 / tan θ. This gives the equation tan θ + 1 / tan θ = 2.

Letting x = tan θ, we have x + 1/x = 2, which simplifies to the quadratic equation x² - 2x + 1 = 0. Solving this gives (x - 1)² = 0, so x = 1.

Thus, tan θ = 1 and cot θ = 1.

Substituting these values into the given expression tan³ θ + cot³ θ + 6 tan³ θ cot² θ yields:

1³ + 1³ + 6 × 1³ × 1² = 1 + 1 + 6 = 8

Explanation

Average speed is calculated as the ratio of the total distance covered to the total time taken for the entire journey, including the rest time.

Total distance = 50 km + 30 km = 80 km

Total time = 90 minutes + 15 minutes + 35 minutes = 140 minutes

Converting the total time from minutes to hours: Total time = 140 / 60 hours = 7/3 hours

Average speed = Total distance / Total time Average speed = 80 / (7/3) = 240/7 km/h

Converting 240/7 to a mixed fraction: 240 / 7 = 34 2/7 km/h

Explanation

Average speed for a journey is given by the formula:

Average Speed = Total Distance / Total Time

The total distance covered by Mithila is the sum of the distance covered by bus and taxi: Total Distance = 50 + 30 = 80 km

The total time for the entire journey includes the travel times and the rest period: Total Time = 90 + 15 + 35 = 140 minutes

To convert the total time into hours: Total Time = 140 / 60 = 7/3 hours

Substituting these values into the average speed formula: Average Speed = 80 / (7/3) = (80 × 3) / 7 = 240 / 7 ≈ 34.28 km/h

Explanation

Marked Price of the article is ₹150. The discount is 25% of the Marked Price, which is 0.25 × 150 = ₹37.5. This gives a selling price of 150 - 37.5 = ₹112.5.

Since the shopkeeper also gives a gift worth ₹2.5, the effective selling price received by him is: Effective Selling Price = 112.5 - 2.5 = ₹110

The shopkeeper makes a 10% profit on the Cost Price (CP). Using the profit percentage formula: Cost Price = Effective Selling Price / (1 + Profit%) Cost Price = 110 / (1 + 0.10) = 110 / 1.1 = ₹100

Explanation

Total Cost Price (CP) of 288 oranges = ₹115.20

Selling Price of the first 50 oranges = 50 × 70 paise = 50 × ₹0.70 = ₹35.00

Selling Price of the remaining oranges = ₹46.20

Total Selling Price (SP) = ₹35.00 + ₹46.20 = ₹81.20

Since CP is greater than SP, there is a loss.

Loss = CP - SP Loss = ₹115.20 - ₹81.20 = ₹34.00

Explanation

The total surface area of a right circular cylinder is the sum of its curved surface area and the area of its two circular bases.

Total Surface Area = 2πrh + 2πr² Curved Surface Area = 2πrh

The difference between the total surface area and the curved surface area is the area of the two bases: Difference = 2πr²

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

Using the value of π ≈ 22/7, substitute the radius into the formula: Difference = 2 × (22/7) × 14 × 14 Difference = 2 × 22 × 2 × 14 Difference = 44 × 28 Difference = 1232 cm²

Explanation

For a given perimeter, the triangle with the maximum area is an equilateral triangle.

Let the side of the equilateral triangle be a. The perimeter of the triangle is given as 3a = 36, which gives a = 12.

The maximum area of this triangle is calculated using the area formula for an equilateral triangle:

Area = (√3/4) × a²

Substituting the value of a:

Area = (√3/4) × 12² = (√3/4) × 144 = 36√3

Thus, the area of the triangle cannot be more than 36√3 square units.