SSC CHSL Tier 1 2024 Quantitative Aptitude Questions with Solutions

Explanation

Since the transformation from percentage to raw score is linear and monotonically increasing, the median raw score corresponds directly to the raw score of the median percentage.

The percentages obtained by the seven students in Chemistry are: 35%, 50%, 60%, 65%, 65%, 75%, 80%

Arrangling these percentages in ascending order: 35%, 50%, 60%, 65%, 65%, 75%, 80%

With N = 7 observations, the median is the (7 + 1)/2 = 4th term. The 4th term in the ordered list is 65%.

Using the maximum marks for Chemistry (130), the median raw score is: 65% of 130 = 0.65 × 130 = 84.5

Explanation

In a right-angled triangle, the area can be calculated in two ways: using the two perpendicular sides as base and height, or using the hypotenuse and the altitude drawn to it.

Area = ½ × side₁ × side₂ = ½ × hypotenuse × altitude

This gives the relation:

altitude = (side₁ × side₂) / hypotenuse

Substituting the given values:

K = (12 × 16) / 20

K = 192 / 20

K = 9.6 cm

Explanation

Correct Answer: D

The curved surface area of a cone is given by the formula π × r × l, where r is the radius and l is the slant height of the cone.

Given: Curved surface area = 2200 cm² Radius (r) = 28 cm π = 22/7

Substituting these values into the formula: 2200 = (22/7) × 28 × l

Simplifying the equation: 2200 = 22 × 4 × l 2200 = 88 × l l = 2200 / 88 l = 25

The slant height of the cone is 25 cm.

Explanation

For a cuboid with length l, width w, and height h, the areas of the three adjacent faces are given by: A₁ = l × w = 120 A₂ = w × h = 72 A₃ = l × h = 60

Multiplying these three equations: A₁ × A₂ × A₃ = (l × w) × (w × h) × (l × h) = l² × w² × h² = (l × w × h)²

Since the volume V of a cuboid is V = l × w × h, we have: V² = A₁ × A₂ × A₃

Taking the square root on both sides gives the standard formula for the volume: V = √(A₁ × A₂ × A₃)

Substituting the given values: V = √(120 × 72 × 60) V = √(7200 × 72) V = √(72 × 100 × 72) V = √(72² × 10²) V = 72 × 10 V = 720 cm³

Explanation

Using the Pythagorean relation for a cone, the height h, slant height l, and base radius r are related by the formula: l² = r² + h²

Given the base radius r = 6 cm and slant height l = 10 cm, we substitute these values to find the height: 10² = 6² + h² 100 = 36 + h² h² = 64 h = 8 cm

The volume V of a cone is calculated using the formula: V = ⅓πr²h

Substituting the values of r and h into the volume formula: V = ⅓ × π × 6² × 8 V = ⅓ × π × 36 × 8 V = 12 × 8 × π V = 96π cm³

Explanation

The radius r of the circle is half of its diameter: r = 24/2 = 12 cm

The radius at the point of contact is perpendicular to the tangent. This forms a right-angled triangle where the hypotenuse is the distance from the center to the external point (d = 37 cm), one leg is the radius (r = 12 cm), and the other leg is the length of the tangent (t).

Applying the Pythagorean theorem: t² + r² = d² t² + 12² = 37² t² + 144 = 1369 t² = 1225 t = √1225 = 35 cm

Explanation

Let the original price of the car be P. Since the selling price is 20% less than the original price, the selling price is equal to 80% of P.

Selling Price = P × (1 - 0.20) = 0.80 × P

Given that the selling price is 5,00,000, we set up the equation:

5,00,000 = 0.80 × P

Solving for P:

P = 5,00,000 ÷ 0.80 P = 5,00,000 × 5/4 P = 1,25,000 × 5 P = 6,25,000

Explanation

Correct Answer: D

Using the rule of alligation to find the ratio of boys to girls:

Subtract the class average from the girls' average and the boys' average from the class average to find the inverse ratio of boys to girls.

Difference for girls: 90 - 75 = 15 Difference for boys: 75 - 70 = 5

Ratio of boys to girls = (Girls' average - Class average) ÷ (Class average - Boys' average) = 15 ÷ 5 = 3 / 1

The ratio of boys to girls in the class is 3:1.

Percentage of boys = (Ratio of boys ÷ Total ratio) × 100 = (3 ÷ (3 + 1)) × 100 = (3 / 4) × 100 = 75%

Explanation

To find the value of the given expression, apply the BODMAS rule, which specifies the order of operations: Brackets, Orders, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).

The given expression is: (45 + 9) ÷ 2 - 7 × 33 ÷ 7 + [(7 + 18) × 6] + 9 × 8 - 89

First, simplify the operations inside the inner parentheses: 45 + 9 = 54 7 + 18 = 25

Substitute these values back into the expression: 54 ÷ 2 - 7 × 33 ÷ 7 + [25 × 6] + 9 × 8 - 89

Next, simplify the square bracket: 25 × 6 = 150

Now, substitute this value into the expression: 54 ÷ 2 - 7 × 33 ÷ 7 + 150 + 9 × 8 - 89

Now perform the division and multiplication operations from left to right: 54 ÷ 2 = 27 7 × 33 ÷ 7 = 231 ÷ 7 = 33 9 × 8 = 72

Substitute these values back: 27 - 33 + 150 + 72 - 89

Finally, perform the addition and subtraction operations from left to right: 27 - 33 = -6 -6 + 150 = 144 144 + 72 = 216 216 - 89 = 127

Explanation

Let the total number of votes polled in the election be V.

Since there are only two candidates, the winning candidate received the remaining share of the votes: 100% - 35% = 65%

The difference in the percentage of votes between the winning candidate and the defeated candidate is: 65% - 35% = 30%

This 30% difference corresponds to the defeat margin of 381 votes. Therefore, we can set up the relation: 30% of V = 381 0.30 × V = 381 V = 381 / 0.30 V = 1270

Explanation

In triangles STR and MNJ, SU and MV are the medians to the sides TR and NJ respectively. Since TR = NJ and U and V are the midpoints, it follows that TU = NV and UR = VJ.

Comparing triangles STU and MNV: ST = MN (given) TU = NV (since TR = NJ) SU = MV (given)

By SSS congruence, ΔSTU ≅ ΔMNV. This gives ∠NMV = ∠TSU = 46°.

Since V lies on the line NJ, the angle ∠NMJ is split into ∠NMV and ∠VMJ: ∠NMJ = ∠NMV + ∠VMJ 79° = 46° + ∠VMJ ∠VMJ = 33°

Since N, V, and J lie on a straight line, the angles ∠MVN and ∠MVJ form a linear pair: ∠MVJ = 180° - ∠MVN = 180° - 88° = 92°

In triangle MVJ, the sum of angles is 180°: ∠VMJ + ∠MVJ + ∠MJV = 180° 33° + 92° + ∠MJV = 180° 125° + ∠MJV = 180° ∠MJV = 55°

Comparing triangles SUR and MVJ: SU = MV (given) UR = VJ (since TR = NJ) ∠SUR = 180° - ∠TUS and ∠MVJ = 180° - ∠NVM. Since ΔSTU ≅ ΔMNV, we have ∠TUS = ∠NVM, which means ∠SUR = ∠MVJ.

By SAS congruence, ΔSUR ≅ ΔMVJ. Therefore, ∠SRT = ∠SRU = ∠MJV = 55°.

The required value is: (7/11) × ∠SRT = (7/11) × 55° = 35°

Explanation

The percentage increase is calculated using the formula:

Percentage Increase = ((New Value - Original Value) / Original Value) × 100

Substituting the given values into the formula:

Percentage Increase = ((234 - 200) / 200) × 100

Percentage Increase = (34 / 200) × 100

Percentage Increase = 34 / 2 = 17%

Explanation

Using the rule of alligation, the ratio in which the two varieties of pulses must be mixed is given by the formula:

Ratio of cheaper quantity to dearer quantity = (Dearer price - Mean price) / (Mean price - Cheaper price)

Substituting the given values: Cheaper price = ₹60 per kg Dearer price = ₹75 per kg Mean price = ₹65 per kg

Required ratio = (75 - 65) / (65 - 60) Required ratio = 10 / 5 Required ratio = 2 / 1

Thus, the grocer must mix the two varieties in the ratio of 2 : 1.

Explanation

Correct Answer: C

Using the trigonometric identity cos² θ + sin² θ = 1, we find cos θ for an angle θ in the first quadrant where all trigonometric ratios are positive:

cos θ = √(1 - sin² θ)

Substituting sin θ = 7/25:

cos θ = √(1 - (7/25)²) cos θ = √(1 - 49/625) cos θ = √(576/625) cos θ = 24/25

Using the definition of tangent:

tan θ = sin θ / cos θ tan θ = (7/25) / (24/25) tan θ = 7/24

Explanation

Using the standard distance formula for two speeds with a given difference in arrival times:

Distance = (s₁ × s₂) / (s₂ - s₁) × Δt

where s₁ = 6 km/h is the first speed, s₂ = 8 km/h is the second speed, and Δt is the total time difference.

Tanya is 2 minutes late in the first case and 3 minutes early in the second case, making the total time difference: Δt = 2 + 3 = 5 minutes = 5/60 hours = 1/12 hours

Substituting these values into the formula: Distance = (6 × 8) / (8 - 6) × 1/12 Distance = 48 / 2 × 1/12 Distance = 24 × 1/12 = 2 km

This matches the distance Tanya covers to reach the station.

Explanation

Using the work-rate formula, Work = Efficiency × Time.

Let E and S be the daily efficiencies of an engineer and a skilled worker respectively. Since the total work is the same: 6E × 5 = 5S × 7 30E = 35S E/S = 7/6

We can assign the efficiency of an engineer E as 7 units per day, and a skilled worker S as 6 units per day.

The total work is: Work = 30E = 30 × 7 = 210 units

The combined efficiency of 7 engineers and 4 skilled workers is: Combined Efficiency = 7E + 4S = 7(7) + 4(6) = 49 + 24 = 73 units per day

The time taken to complete the work is: Time = Total Work / Combined Efficiency = 210/73 days = 2 64/73 days

Explanation

To find the ratio A : C, compound the given ratios A : B and B : C using the formula:

A/C = (A/B) × (B/C)

Substituting the given values into the formula:

A/C = (5/8) × (7/8) = (5 × 7) / (8 × 8) = 35/64

This yields the ratio:

A : C = 35 : 64

Explanation

Percentage Increase = (Increase in Price / Original Price) × 100

The original cost price of the item is ₹2,500 and the increased cost price is ₹3,000.

The absolute increase in price is: 3,000 - 2,500 = ₹500

Substituting these values into the formula: Percentage Increase = (500 / 2,500) × 100 Percentage Increase = 1/5 × 100 = 20%

Explanation

Let the total votes cast be V. Since there are only two candidates, and A received 33% of the total votes, the remaining votes went to B.

B's vote share = 100% - 33% = 67%

The margin of victory for B is the difference between B's votes and A's votes: 67% - 33% = 34% of the total votes

According to the question, this difference is 55,522 votes: 34% of V = 55,522 1% of V = 55,522 ÷ 34 = 1,633

To find the total number of votes received by B, we multiply this unit value by B's vote percentage: B's votes = 67 × 1,633 = 1,09,411

Explanation

The mean is calculated using the formula:

Mean = ∑(f × x) / ∑f

where x represents the age in years and f represents the number of children (frequency).

∑(f × x) = (6 × 8) + (7 × 3) + (8 × 7) + (9 × 2) + (10 × 20) ∑(f × x) = 48 + 21 + 56 + 18 + 200 = 343

The total number of children is: ∑f = 8 + 3 + 7 + 2 + 20 = 40

Mean = 343 / 40 = 8.575 years

The mode is the value that appears most frequently in the data set. Here, the highest frequency is 20, which corresponds to the age of 10 years.

Mode = 10 years

The absolute difference between the mean and the mode is: Difference = 10 - 8.575 = 1.425 years

Explanation

Using the BODMAS rule, simplify the operations inside each parenthesis first:

First term: (36 ÷ 6) ÷ 3 = 6 ÷ 3 = 2

Second term: (18 ÷ 9) × 4 = 2 × 4 = 8

Third term: (12 ÷ 6) × (5 ÷ 2) = 2 × 2.5 = 5

Combine these evaluated terms according to the arithmetic operations:

2 + 8 - 5 = 10 - 5 = 5

Explanation

The angle formed by the intersection of the internal angle bisectors of two angles of a triangle at the incenter is given by the relation:

Angle = 90° + A/2

where A is the third angle opposite to the side containing the bisected angles.

In this isosceles triangle, the angle between the equal sides is A = 40°. Substituting this value into the formula:

Angle = 90° + 40°/2 = 90° + 20° = 110°

Explanation

To find the combined ratio A:B:C, the term representing B must be equal in both individual ratios.

The given ratios are: A:B = 3:7 B:C = 2:5

The value corresponding to B is 7 in the first ratio and 2 in the second ratio. To make them equal, find the least common multiple of 7 and 2, which is 14.

Multiply both terms of the ratio A:B by 2: A:B = (3 × 2) : (7 × 2) = 6:14

Multiply both terms of the ratio B:C by 7: B:C = (2 × 7) : (5 × 7) = 14:35

Since the value for B is now common, combine the ratios directly: A:B:C = 6:14:35

Explanation

Number of girls = Total strength - Number of boys Number of girls = 640 - 400 = 240

The ratio of girls to boys is: Girls : Boys = 240 : 400

Dividing both terms by their greatest common divisor, 80: 240 ÷ 80 = 3 400 ÷ 80 = 5

This gives the simplified ratio of 3:5.

Explanation

The volume of a cone is given by the formula V = (1/3) × π × r² × h, where r is the radius and h is the height.

Substituting the given values of radius r = 3.5 cm (which can be written as 7/2 cm) and height h = 4 cm: V = (1/3) × π × (7/2)² × 4 V = (1/3) × π × (49/4) × 4 V = (49/3) × π cm³

Let N be the number of cones obtained. The total volume of the melted sphere must be equal to the combined volume of all the recast cones: 3136π = N × (49/3) × π

Canceling π from both sides: 3136 = N × 49/3 N = (3136 × 3) / 49 N = 64 × 3 N = 192

Explanation

According to the triangle inequality theorem, the length of any side of a triangle must be strictly greater than the absolute difference of the other two sides and strictly less than their sum. For a triangle with sides of length a, b, and c, this relationship is expressed as:

|a - b| < c < a + b

Substituting the given side lengths of 25 cm and 19 cm into the inequality for the third side y:

|25 - 19| < y < 25 + 19

6 < y < 44

Explanation

Let the number be x. The given condition states that 20% of 35% of this number is 240.8. This relation is expressed as:

0.20 × 0.35 × x = 240.8

Multiplying the decimal coefficients:

0.07 × x = 240.8

Solving for x:

x = 240.8 ÷ 0.07 x = 3440

Now, calculate 18% of this number:

18% of 3440 = 0.18 × 3440 18% of 3440 = 619.2

Explanation

To find the marks obtained by Ram in Botany, calculate 95% of the maximum marks of 200: Ram's Botany marks = 95% of 200 = (95 / 100) × 200 = 190

To find the marks obtained by Karn in Botany, calculate 80% of the maximum marks of 200: Karn's Botany marks = 80% of 200 = (80 / 100) × 200 = 160

Comparing the two scores: Difference = 190 - 160 = 30

Since 190 is greater than 160, Ram's marks in Botany are 30 more than Karn's marks.

Explanation

The volume of a sphere of radius r is given by the formula V = 4/3 πr³.

The diameter of the larger sphere is 18 cm, which gives a radius R of 9 cm. The diameter of each smaller paper ball is 2 cm, which gives a radius r of 1 cm.

The number of small paper balls that can be made from the larger sphere is equal to the ratio of their volumes:

Number of balls = Volume of larger sphere ÷ Volume of smaller sphere

Number of balls = (4/3 π R³) ÷ (4/3 π r³) = R³ ÷ r³

Substituting the values into the relation:

Number of balls = 9³ ÷ 1³ = 729 ÷ 1 = 729

Explanation

The speed of the thief (Vₜ) is calculated using the distance they covered and the time taken before being caught: Vₜ = 6 km / 0.5 hours = 12 km/h

Since the speed of the thief is 4/5 times the speed of the policeman (Vₚ): Vₜ = (4/5) × Vₚ 12 = (4/5) × Vₚ Vₚ = 15 km/h

The relative speed of the policeman with respect to the thief is: Relative Speed = Vₚ - Vₜ = 15 - 12 = 3 km/h

The initial distance between them is the distance covered by the policeman relative to the thief in the given time of 30 minutes (0.5 hours): Initial Distance = Relative Speed × Time = 3 km/h × 0.5 hours = 1.5 km

Explanation

The given side lengths of the triangle are 6 cm, 8 cm, and 10 cm. These lengths satisfy the Pythagorean relation:

6² + 8² = 36 + 64 = 100 = 10²

This confirms that the triangle is right-angled, where the sides of lengths 6 cm and 8 cm are the perpendicular legs (base and height) and the side of length 10 cm is the hypotenuse.

The area of a right-angled triangle is given by the formula:

Area = ½ × base × height

Substituting the values:

Area = ½ × 6 × 8 = 24 cm²

Explanation

Let the selling price of one item be s.

The selling price of 22 items is 22s. The gain earned on selling these 22 items is equal to the selling price of 6 items, which is 6s.

Using the standard profit relation: Cost Price = Selling Price - Gain The cost price of 22 items = 22s - 6s = 16s

The formula for gain percentage is: Gain% = (Gain / Cost Price) × 100

Substituting the values into the formula: Gain% = (6s / 16s) × 100 Gain% = 3/8 × 100 Gain% = 37.5% = 37 ½%

Explanation

Let the three angles of the triangle be A, B, and C. The sum of the angles in a triangle is 180°.

When 17° is decreased from each of the three angles, the sum of the new angles is: 180° - (3 × 17°) = 180° - 51° = 129°

The ratio of these decreased angles is 3:4:7. Let the decreased angles be 3x, 4x, and 7x. 3x + 4x + 7x = 129° 14x = 129° x = 129°/14

The greatest decreased angle is represented by the largest ratio term, 7x: 7x = 7 × (129°/14) = 129°/2 = 64.5°

To find the greatest original angle, add back the 17° that was removed: 64.5° + 17° = 81.5°

To convert this angle from degrees to radians, multiply by π/180: 81.5° × (π/180) = (163/2) × (π/180) = 163π/360

Explanation

The relation between Cost Price (CP) and Marked Price (MP) is determined by the formula: CP × (100 + Profit%) = MP × (100 - Discount%)

Substituting the given initial values: CP × (100 + 90) = MP × (100 - 20) CP × 190 = MP × 80 MP/CP = 19/8

When the discount is changed to 40%, the new Selling Price (SP) is: New SP = MP × (100 - 40)% = MP × 0.6

Substituting MP/CP = 19/8 into the equation: New SP = (19/8) × CP × 0.6 = 1.425 × CP

The new profit percentage is: New Profit% = ((New SP - CP) / CP) × 100% = (1.425 - 1) × 100% = 42.5%

Explanation

Let the original price of the electronic watch be P.

The relationship between the original price and the final price after successive percentage changes is expressed as: Final Price = P × (1 - Decrease%) × (1 + Increase%)

Substituting the given values into the equation: 7,650 = P × (1 - 0.25) × (1 + 0.50) 7,650 = P × 0.75 × 1.5 7,650 = P × (3/4) × (3/2) 7,650 = P × 9/8

Solving for P: P = 7,650 × 8/9 P = 850 × 8 P = 6,800

Explanation

The total simple interest rate for successive years is the sum of the individual annual rates, which is R = r₁ + r₂.

Substituting the given values: R = 8% + 6% = 14%

The total simple interest earned over the 2 years is calculated as: Interest = Principal × R Interest = 36,000 × 14/100 = 5,040

The total amount due at the end of 2 years is the sum of the principal and the interest: Amount = Principal + Interest Amount = 36,000 + 5,040 = 41,040

Explanation

The time taken by two individuals working together to complete a piece of work can be calculated using the formula:

T = (a × b) / (a + b)

Here, a represents the time taken by A working alone, which is 4 days, and b represents the time taken by B working alone, which is 12 days.

Substituting these values into the formula:

T = (4 × 12) / (4 + 12) T = 48 / 16 T = 3 days

Explanation

The volume of a cylindrical cup is calculated using the formula V = πr²h, where r is the radius of the base and h is the height of the liquid.

The diameter of the cup is 7 cm, which gives a radius r of 7/2 cm, and the height of the tea is 4 cm.

Calculating the volume of tea in a single cup: V = (22/7) × (7/2)² × 4 V = (22/7) × (49/4) × 4 V = 22 × 7 V = 154 cm³

The total volume of tea required daily for 180 patients is: Total volume = 154 × 180 = 27720 cm³

Converting cubic centimeters to litres, where 1000 cm³ equals 1 litre: Total volume in litres = 27720 ÷ 1000 = 27.72 litres

Explanation

Let the present ages of Ravi and Kavya be R and K respectively.

Four years ago, their ages were R - 4 and K - 4. According to the first condition: R - 4 = 4(K - 4) R - 4 = 4K - 16 R - 4K = -12

Seven years from now, their ages will be R + 7 and K + 7. According to the second condition: R + 7 = 3(K + 7) R + 7 = 3K + 21 R - 3K = 14

Subtracting the first equation from the second equation: (R - 3K) - (R - 4K) = 14 - (-12) K = 26

Substituting K = 26 into the second equation: R - 3(26) = 14 R - 78 = 14 R = 92

The present age of Ravi is 92 years and the present age of Kavya is 26 years.

The sum of their present ages is: 92 + 26 = 118 years

Explanation

Let the total monthly salary of Ram be S.

The total percentage of salary spent by Ram on food, house rent, entertainment, and conveyance is: Total expenditure = 30% + 10% + 7% + 6% = 53%

The savings percentage is the remaining portion of his salary: Savings = 100% - 53% = 47%

Given that his savings at the end of the month are ₹1,880, we can set up the relation: 47% of S = 1,880 (47 / 100) × S = 1,880 S = (1,880 × 100) ÷ 47 S = 40 × 100 S = 4,000

Explanation

The formula for the length of the transverse common tangent between two circles is given by √(d² - (r₁ + r₂)²), where d is the distance between the centres of the circles, and r₁ and r₂ are their radii.

Given: Distance between centres (d) = 25 cm Radius of the first circle (r₁) = 7 cm Radius of the second circle (r₂) = 4 cm

Substituting these values into the formula: Length of transverse common tangent = √(25² - (7 + 4)²) Length of transverse common tangent = √(625 - 11²) Length of transverse common tangent = √(625 - 121) Length of transverse common tangent = √504 Length of transverse common tangent = √(36 × 14) Length of transverse common tangent = 6√14 cm

Explanation

Let the cost price of 1 unit of weight of goods be ₹1. For a nominal true weight of 100 units, the true cost price is ₹100.

Since the vendor makes a profit of 35% on the transaction, the selling price of this nominal quantity is: 100 × (1 + 35/100) = ₹135

The vendor uses a weight that is 19% less than the true weight. Thus, the quantity actually delivered is: 100 × (1 - 19/100) = 81 units

The actual cost price of the delivered quantity to the vendor is ₹81.

Using the net gain formula: Net Gain % = ((Selling Price - Actual Cost Price) / Actual Cost Price) × 100 Net Gain % = ((135 - 81) / 81) × 100 Net Gain % = (54 / 81) × 100 Net Gain % = (2 / 3) × 100 Net Gain % = 66.67%

Explanation

Let Sonu's land be 100 units.

Since Raju has 15% more land than Sonu: Raju's land = 100 + 15 = 115 units

Since Ramu has 25% more land than Sonu: Ramu's land = 100 + 25 = 125 units

The ratio of land owned by Raju and Ramu is: Raju's land : Ramu's land = 115 : 125

Dividing both terms by their greatest common divisor, which is 5: 115 ÷ 5 : 125 ÷ 5 = 23 : 25

Explanation

Let the number of days required by Q to finish the work be x days. P takes half of the time required by Q, which is x/2 days.

The daily work rate of Q is 1/x and the daily work rate of P is 2/x.

Together, their combined daily work rate is: 2/x + 1/x = 3/x

Since they together can finish the work in 36 days, their combined daily work rate is also equal to 1/36. Equating the two expressions: 3/x = 1/36

Solving for x: x = 3 × 36 = 108

Explanation

Correct Answer: C

The expression is 8 + 1, which equals 9.

Dividing 9 by 7 gives a quotient of 1 and a remainder: 9 = 7 × 1 + 2

Using modular arithmetic, we can also find the remainder by evaluating each term modulo 7: 8 ≡ 1 (mod 7) 1 ≡ 1 (mod 7)

Adding these terms gives: 8 + 1 ≡ 1 + 1 ≡ 2 (mod 7)

Thus, the remainder when 8 + 1 is divided by 7 is 2.

Explanation

The number of valid votes obtained by candidate B can be calculated using the direct formula:

Valid votes of B = Total votes polled × (1 - Invalid vote fraction) × (1 - Fraction of valid votes for A)

Given: Total votes polled = 8,750 Invalid vote fraction = 20% = 0.20 Fraction of valid votes for A = 63% = 0.63

Since candidate A received 63% of the valid votes, candidate B received the remaining 37% (1 - 0.63 = 0.37) of the valid votes.

Substituting these values into the formula:

Valid votes of B = 8,750 × (1 - 0.20) × (1 - 0.63) Valid votes of B = 8,750 × 0.80 × 0.37 Valid votes of B = 7,000 × 0.37 Valid votes of B = 2,590

Explanation

The formula for Simple Interest is: SI = (P × R × T) / 100

where SI is the simple interest, P is the principal amount, R is the rate of interest per annum, and T is the time in years.

Substituting the given values into the formula: 1,093.50 = (2,430 × R × 3) / 100

1,093.50 = 72.90 × R

R = 1,093.50 / 72.90

R = 15%

Explanation

The area of a sector of a circle with radius r and arc length l is given by the formula:

Area = ½ × r × l

Substituting the given values r = 48 cm and l = 15 cm into the formula:

Area = ½ × 48 × 15 Area = 24 × 15 Area = 360 cm²

Explanation

The relationship between distance, speeds, and the difference in time is given by the formula:

Distance = (Product of Speeds / Difference of Speeds) × Total Time Difference

The two speeds are v₁ = 3 km/h and v₂ = 4 km/h.

The total time difference is the sum of being late by 30 minutes and being early by 30 minutes: Total Time Difference = 30 minutes + 30 minutes = 60 minutes = 1 hour

Substituting the values into the formula: Distance = (3 × 4 / (4 - 3)) × 1 = 12 km

Explanation

The relationship between the number of workers and the days required to complete a work is represented by the formula:

W₁ × D₁ = W₂ × D₂

Here, W₁ = 55, D₁ = 16, and D₂ = 10. Let W₂ be the total number of workers required to finish the work in 10 days.

Substituting the given values into the formula:

55 × 16 = W₂ × 10 880 = W₂ × 10 W₂ = 880 / 10 W₂ = 88

To find the number of additional workers required, subtract the initial number of workers from the total number of workers needed:

88 - 55 = 33