SSC CHSL Tier 1 2022 Quantitative Aptitude Questions with Solutions

Explanation

Let the total amount of money Nakul initially had be x.

After spending 20% of his money on wheat flour, the remaining money is: 100% - 20% = 80% of x = 0.8x

He then spends 25% of this remaining money on cooking oils, which means he is left with 75% of the remaining money: 100% - 25% = 75% of 0.8x = 0.75 × 0.8x

Since the final remaining money is Rs.900, we set up the equation: 0.75 × 0.8x = 900

Using fractions for simpler calculation: (3/4) × (4/5) × x = 900 (3/5) × x = 900 x = 900 × (5/3) x = 300 × 5 x = 1500

Explanation

The simple interest (SI) on a principal sum P at an annual rate R for T years is given by the formula:

SI = (P × R × T) / 100

The difference in simple interest for 6 years and 5 years at an annual rate of 8% is equivalent to the simple interest accrued in 1 year (6 - 5 = 1 year).

Using the given difference of Rs. 26:

26 = (P × 8 × 1) / 100

Solving for P:

8 × P = 2600 P = 2600 / 8 P = 325

The principal sum is Rs. 325.

Explanation

For any two similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides.

Using the relation for the corresponding sides PQ and UV:

Perimeter(ΔPQR) / Perimeter(ΔUVW) = PQ / UV

Substituting the given values into the formula:

120 / 240 = 30 / UV

1/2 = 30 / UV

UV = 30 × 2 = 60 cm

Explanation

From the given trigonometric equations: cos(A + B) = 0 Since 0° ≤ A, B ≤ 90°, the sum A + B lies in the interval [0°, 180°]. The only angle in this interval that satisfies the equation is 90°. A + B = 90°

Similarly, we have: sin(A - B) = 0 Since 0° ≤ A, B ≤ 90°, the difference A - B lies in the interval [-90°, 90°]. The only angle in this interval that satisfies the equation is 0°. A - B = 0°

Adding the two equations: 2A = 90° A = 45°

Substituting A = 45° into the equation A - B = 0° gives: B = 45°

Explanation

By equating the volume of 24 solid hemispheres to the volume of the resulting right circular cylinder, we can find the radius of each hemisphere.

The volume of a hemisphere of radius r is (2/3) × π × r³. The volume of a cylinder of radius R and height H is π × R² × H.

For 24 hemispheres, the volume equation is: 24 × (2/3) × π × r³ = π × R² × H

Substituting R = 12 cm and H = 24 cm: 16 × π × r³ = π × 12² × 24

Dividing both sides by π: 16 × r³ = 144 × 24

Simplifying for r³: r³ = (144 × 24) / 16 r³ = 9 × 24 r³ = 216

Taking the cube root on both sides: r = ∛216 r = 6 cm

Explanation

The semi-perimeter s of a triangle with sides a = 7 cm, b = 9 cm, and c = 8 cm is calculated as:

s = (a + b + c) / 2 s = (7 + 9 + 8) / 2 = 12 cm

Using Heron's formula, the area of the triangle is:

Area = √(s(s - a)(s - b)(s - c)) Area = √(12 × (12 - 7) × (12 - 9) × (12 - 8)) Area = √(12 × 5 × 3 × 4) Area = √(12 × 5 × 12) Area = 12√5 sq. cm

Explanation

Using the fundamental trigonometric identities: sec² x - tan² x = 1 → (sec x - tan x)(sec x + tan x) = 1 cosec² y - cot² y = 1 → (cosec y - cot y)(cosec y + cot y) = 1

Given: sec x + tan x = 5 cosec y - cot y = 1/3

From these relations, we calculate: sec x - tan x = 1/5 = 0.2 cosec y + cot y = 1 / (1/3) = 3

We evaluate the expression (sec x + cosec y) - (tan x - cot y): (sec x + cosec y) - (tan x - cot y) = (sec x - tan x) + (cosec y + cot y)

Substituting the values: 0.2 + 3 = 3.2

Explanation

The perpendicular drawn from the center of a circle to a chord bisects the chord.

Therefore, half the length of the chord is: 30 / 2 = 15 cm

In the right-angled triangle formed by the radius of the circle r, the perpendicular distance from the center to the chord 8 cm, and half the chord length 15 cm, we apply Pythagoras' theorem: r² = 15² + 8² r² = 225 + 64 r² = 289 r = √289 = 17 cm

Since the radius r of the circle is 17 cm, the diameter of the circle is: d = 2r = 2 × 17 = 34 cm

Explanation

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

According to the given condition, selling the article at 9/10 of its usual selling price yields a 20% profit: 9/10 × SP = 1.2 × CP

Rearranging the terms to find the ratio of the usual selling price to the cost price: SP / CP = 1.2 × 10 / 9 = 12 / 9 = 4/3

The profit percentage when the article is sold at its usual selling price is: Profit% = (SP - CP) / CP × 100 Profit% = (4/3 - 1) × 100 = 1/3 × 100 = 33.33%

Explanation

Rahul's daily work rate is 1/10 and Sona's daily work rate is 1/15.

Their combined daily work rate when working together is: 1/10 + 1/15 = 5/30 = 1/6

In 4 days, the fraction of the work they complete together is: 4 × 1/6 = 2/3

The fraction of the total work remaining is: 1 - 2/3 = 1/3

Explanation

Using the standard algebraic identity: (a + b)² - (a - b)² = 4ab

By substituting this identity into the numerator of the given expression: ((a + b)² - (a - b)²) / ab = 4ab / ab = 4

The terms ab cancel out, resulting in a constant value of 4.

Explanation

When three equal distances are covered at different speeds v₁, v₂, and v₃, the average speed of the entire journey is given by the harmonic mean formula:

Average Speed = 3 / (1/v₁ + 1/v₂ + 1/v₃)

Given the speeds are v₁ = 200 km/h, v₂ = 300 km/h, and v₃ = 600 km/h, substitute these values into the formula:

Average Speed = 3 / (1/200 + 1/300 + 1/600)

Find the common denominator for the terms in the denominator, which is 600:

1/200 + 1/300 + 1/600 = (3 + 2 + 1) / 600 = 6 / 600 = 1 / 100

Now, calculate the average speed:

Average Speed = 3 / (1/100) = 300 km/h

Explanation

The relation between the Selling Price (SP) and Marked Price (MP) after two successive discounts d₁% and d₂% is given by the formula:

SP = MP × (1 - d₁/100) × (1 - d₂/100)

Substituting the given values, SP = 560, d₁ = 30, and d₂ = 20:

560 = MP × (1 - 30/100) × (1 - 20/100)

560 = MP × 0.70 × 0.80

560 = MP × 0.56

MP = 560 ÷ 0.56 = 1000

Explanation

Let the shares of P, Q, and R be represented as 7x, 9x, and 4x respectively. The difference between the shares of P and R is given as Rs. 1500. This gives the relation 7x - 4x = 1500, which simplifies to 3x = 1500, or x = 500. The difference between the shares of P and Q is 9x - 7x = 2x. Substituting the value of x, the difference is 2 × 500 = 1000.

Explanation

The circumradius R of a triangle with sides a, b, and c is related to its area Δ by the formula R = abc / (4Δ). Rearranging this formula for the area of the triangle gives Δ = abc / (4R).

We are given that the square of the product of the three sides is 1024: (abc)² = 1024 abc = √1024 = 32

We are also given that the area of the circumcircle is 16π: πR² = 16π R² = 16 R = 4

Substituting the values of abc and R into the area formula: Δ = 32 / (4 × 4) Δ = 32 / 16 = 2 sq. units

Explanation

Given that sin θ - cos θ = 0, we can rewrite this equation as: sin θ = cos θ

Dividing both sides by cos θ (since cos θ ≠ 0): tan θ = 1

For acute angles, this gives θ = 45°.

Now, we substitute θ = 45° into the expression sin² θ + tan² θ: sin² 45° + tan² 45° = (1/√2)² + (1)² = ½ + 1 = 3/2

Explanation

The expansion of the cubic term is (a - b)³ = a³ - 3a²b + 3ab² - b³. Substituting this back into the expression yields (a³ - 3a²b + 3ab² - b³) - a³ + b³ = -3a²b + 3ab², which factors as -3ab(a - b).

Explanation

The angles subtended by the same arc of a circle at any points on the remaining part of the circumference are equal. Since A, B, P, and Q are points on the circumference of the circle, both angle AQB and angle APB are subtended by the same arc AB. When points P and Q lie in the same segment of the circle with respect to the chord AB, the inscribed angles are equal, meaning angle APB = angle AQB = 60°.

Explanation

For a number to be divisible by 36, it must be divisible by both 4 and 9.

To be divisible by 4, the last two digits 5B must be divisible by 4. The only two-digit numbers starting with 5 that are divisible by 4 are 52 and 56. Therefore, B can be either 2 or 6.

To be divisible by 9, the sum of the digits must be a multiple of 9. Sum of digits = 7 + A + 4 + 2 + 5 + B = 18 + A + B

Since 18 is already a multiple of 9, the sum A + B must also be a multiple of 9. Since A and B are single-digit numbers, their sum can be either 9 or 18.

If B = 2, then A + 2 = 9, which gives A = 7. Here, the value of A - B is 7 - 2 = 5.

If B = 6, then A + 6 = 9, which gives A = 3. Here, the value of A - B is 3 - 6 = -3.

Explanation

Simple interest is calculated using the formula: SI = (P × R₁ × T₁) / 100

Substituting the given values: 4500 = (P × 6 × 4) / 100 P = (4500 × 100) / 24 = 18750

The principal sum is Rs. 18750.

For compound interest compounding annually for 2 years at a rate of 4% per annum, the effective interest rate can be found using the formula: Effective Rate = R₂ + R₂ + (R₂ × R₂) / 100 Effective Rate = 4 + 4 + (4 × 4) / 100 = 8.16%

Now, calculate the compound interest: CI = P × Effective Rate / 100 CI = 18750 × 8.16 / 100 = 1530

Explanation

When a new member is added to a group and the average of the group remains unchanged, the value of the new member's attribute must be exactly equal to the existing average.

Mathematically, the sum of the ages of the 14 friends is: 14 × 14 = 196 years

Let the age of the 15th friend be x. Since the average of all 15 friends remains 14 years, we set up the equation: (196 + x) / 15 = 14

Multiplying both sides by 15: 196 + x = 210 x = 210 - 196 x = 14

The age of the 15th friend is 14 years.

Explanation

Correct Answer: D

Let the length of the rectangular floor be L and its breadth be B.

According to the given condition, B = 3/5 L.

The area of a rectangle is given by the formula: Area = L × B

Substituting the given values into the formula: 60 = L × 3/5 L 60 = 3/5 L² L² = 60 × 5/3 L² = 100 L = 10 m

Now, calculating the breadth B: B = 3/5 × 10 = 6 m

The difference between the length and the breadth is: L - B = 10 - 6 = 4 m

Explanation

To find the total number of factors of 840 except 1 and itself, we first determine its prime factorization: 840 = 2³ × 3¹ × 5¹ × 7¹

The formula for the total number of factors of a number written in its prime factorized form p₁ᵃ × p₂ᵇ × p₃ᶜ × p₄ᵈ is: Total factors = (a + 1)(b + 1)(c + 1)(d + 1)

Substituting the exponents of the prime factors of 840: Total factors = (3 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 × 2 = 32

To find the number of factors excluding 1 and the number itself, we subtract these 2 factors from the total: Required factors = 32 - 2 = 30

Explanation

Let the speed of Ram be v km/hr. Since Mohan's speed is 10 km/hr more than Ram's, the speed of Mohan is v + 10 km/hr.

Since both cover the same distance, we use the formula: Distance = Speed × Time

For Ram: Distance = v × 8

For Mohan: Distance = (v + 10) × 4

Equating the two distances: 8v = 4 × (v + 10) 8v = 4v + 40 4v = 40 v = 10 km/hr

Thus, Ram's speed is 10 km/hr, and Mohan's speed is 10 + 10 = 20 km/hr. This makes statement I correct.

The sum of their speeds is 10 + 20 = 30 km/hr. This makes statement II correct.

Explanation

Let the cost price of the trouser be 100. Since the marked price is four times the cost price, the marked price is: MP = 4 × 100 = 400

To earn a profit of 64%, the selling price must be: SP = 100 + 64 = 164

The discount allowed on the marked price is: Discount = MP - SP = 400 - 164 = 236

The discount percentage is calculated as: Discount % = (Discount / MP) × 100 Discount % = (236 / 400) × 100 = 59%

Explanation

Let the original number be x.

A successive decrease of 25%, 40%, and 20% translates to multiplying the original number by the corresponding remaining percentage factors: First decrease of 25% leaves 75%, which is 3/4. Second decrease of 40% leaves 60%, which is 3/5. Third decrease of 20% leaves 80%, which is 4/5.

Setting up the equation for the final value: x × (3/4) × (3/5) × (4/5) = 32,904

Simplifying the fraction multipliers: x × (9/25) = 32,904

Solving for x: x = (32,904 × 25) / 9 x = 3,656 × 25 x = 91,400

Explanation

The cost price (CP) of an item when sold at a profit is given by the formula CP = SP / (1 + P/100), and when sold at a loss, it is given by CP = SP / (1 - L/100), where SP is the selling price, P is the profit percentage, and L is the loss percentage.

Since both A and B sell their watches at the same selling price of Rs. 5,400, the SP cancels out when finding the ratio of their cost prices.

CP_A : CP_B = [1 / (1 + 10/100)] : [1 / (1 - 25/100)] CP_A : CP_B = [1 / 1.1] : [1 / 0.75] CP_A : CP_B = 0.75 : 1.1 CP_A : CP_B = 75 : 110 CP_A : CP_B = 15 : 22

Explanation

In a partnership business, the profit is shared in the ratio of the product of the investment amount and the time duration.

Profit ratio of X, Y, and Z is: Ratio = (Investment of X × Time of X) : (Investment of Y × Time of Y) : (Investment of Z × Time of Z) Ratio = (4000 × 3) : (6000 × 2) : (8000 × 4) Ratio = 12000 : 12000 : 32000 Ratio = 3 : 3 : 8

Sum of the ratio terms = 3 + 3 + 8 = 14 parts.

Since 14 parts correspond to the total profit of Rs. 56,000: Value of 1 part = 56000 / 14 = Rs. 4,000.

Y's share in the profit corresponds to 3 parts: Y's share = 3 × 4000 = Rs. 12,000.

Explanation

The total value of the stock is the sum of the product of quantity and average cost for each item category.

Value of Mobile Phones = 25 × 15000 = 3,75,000 Rupees Value of Cameras = 80 × 16000 = 12,80,000 Rupees Value of TVs = 54 × 55000 = 29,70,000 Rupees Value of Refrigerators = 41 × 27000 = 11,07,000 Rupees Value of ACs = 64 × 24000 = 15,36,000 Rupees

Total Value of Stock = 3,75,000 + 12,80,000 + 29,70,000 + 11,07,000 + 15,36,000 = 72,68,000 Rupees

Since 1 lakh is equal to 1,00,000, the total value in lakh rupees is: 72,68,000 ÷ 1,00,000 = 72.68 lakh rupees

Explanation

The co-function identity of trigonometric ratios states that sec θ = cosec(90° - θ).

Applying this identity to the given equation: sec 3A = cosec(A - 72°)

We can rewrite sec 3A as cosec(90° - 3A). Substituting this into the equation gives: cosec(90° - 3A) = cosec(A - 72°)

By equating the angles: 90° - 3A = A - 72°

Rearranging the terms to solve for A: 90° + 72° = A + 3A 162° = 4A A = 162° / 4 A = 40.5°

Explanation

The relationship between the number of taps and the time taken to fill a tank is inversely proportional, represented by the formula:

M₁ × T₁ = M₂ × T₂

Here, M₁ is 15 taps, T₁ is 36 minutes, and T₂ is 1 hour, which equals 60 minutes. Substituting these values into the formula to find the required number of taps M₂:

15 × 36 = M₂ × 60

540 = M₂ × 60

M₂ = 540 / 60

M₂ = 9

Explanation

The expression (299)² can be evaluated using the algebraic identity: (a - b)² = a² - 2ab + b²

By expressing 299 as (300 - 1), we can substitute a = 300 and b = 1 into the identity: (300 - 1)² = 300² - 2 × 300 × 1 + 1² = 90000 - 600 + 1 = 89401

Explanation

In a right-angled triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side, while the cosine is the ratio of the adjacent side to the hypotenuse.

Given: tan Q = opposite / adjacent = 5/12

Using the Pythagorean theorem, the hypotenuse is calculated as: hypotenuse = √((opposite)² + (adjacent)²) hypotenuse = √(5² + 12²) hypotenuse = √(25 + 144) hypotenuse = √169 = 13

Using this value, the cosine of the angle Q is: cos Q = adjacent / hypotenuse = 12/13

Explanation

The intersection point of the perpendicular bisectors of the sides of a triangle is its circumcenter. Therefore, X is the circumcenter of triangle MNO.

According to the properties of the circumcenter, the angle subtended by any side of a triangle at the circumcenter is twice the angle subtended by that same side at the opposite vertex.

For the side NO, the opposite vertex is M, which means: ∠NXO = 2 × ∠NMO

Given that ∠NMO = 55°, substituting this value gives: ∠NXO = 2 × 55° = 110°

Explanation

To simplify the expression, multiply and divide the given product by (k + 1/k):

[(k + 1/k)(k - 1/k)(k² + 1/k²)(k⁴ + 1/k⁴)(k⁸ + 1/k⁸)(k¹⁶ + 1/k¹⁶)] / (k + 1/k)

Using the algebraic identity (a - b)(a + b) = a² - b² successively on the terms in the numerator:

(k + 1/k)(k - 1/k) = k² - 1/k²

(k² - 1/k²)(k² + 1/k²) = k⁴ - 1/k⁴

(k⁴ - 1/k⁴)(k⁴ + 1/k⁴) = k⁸ - 1/k⁸

(k⁸ - 1/k⁸)(k⁸ + 1/k⁸) = k¹⁶ - 1/k¹⁶

(k¹⁶ - 1/k¹⁶)(k¹⁶ + 1/k¹⁶) = k³² - 1/k³²

Substituting these simplified products back into the numerator of the expression yields:

(k³² - 1/k³²) / (k + 1/k)

Explanation

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Given the circumference is 58π cm:

2πr = 58π r = 29 cm

A perpendicular drawn from the centre of a circle to a chord bisects the chord. For a chord XY of length 42 cm, the perpendicular divides it into two equal segments, each of length:

42 / 2 = 21 cm

The perpendicular distance from the centre (d), the half-chord (21 cm), and the radius (29 cm) form a right-angled triangle. Applying Pythagoras' theorem:

r² = d² + 21² 29² = d² + 21² d² = 29² - 21² d² = (29 - 21)(29 + 21) d² = 8 × 50 d² = 400 d = 20 cm

Explanation

An angle subtended by a chord at the circumference of a circle is 90° if and only if the chord is the diameter of the circle. This is a fundamental property of circles (Thales' theorem).

Therefore, the diameter of the circle is equal to the length of the chord: Diameter = 40 cm

Since the radius is half of the diameter: Radius = Diameter / 2 Radius = 40 / 2 = 20 cm

Explanation

Using the standard speed formula:

Speed = Distance / Time

First, convert the distance and time into kilometers and hours to obtain the speed in kmph:

Distance = 1200 meters = 1200 / 1000 = 1.2 km Time = 10 minutes = 10 / 60 = 1/6 hours

Substituting these values into the formula:

Speed = 1.2 / (1/6) = 1.2 × 6 = 7.2 kmph

Explanation

Using the trigonometric co-function identity cot θ = tan(90° - θ), the given equation can be rewritten by expressing cot 2A in terms of tangent:

tan(90° - 2A) = tan(A - 48°)

Equating the angles:

90° - 2A = A - 48°

90° + 48° = A + 2A

138° = 3A

A = 138° / 3

A = 46°

Explanation

A tangent to a circle is perpendicular to the radius at the point of contact. Since PQ is a tangent touching the circle at Q and OQ is the radius, the angle OQP is 90°.

Taking the angle at the centre O, angle POQ, to be 75°, we consider the right-angled triangle OPQ. The sum of acute angles in a right-angled triangle is 90°.

angle OPQ + angle POQ = 90° angle OPQ + 75° = 90° angle OPQ = 15°

Explanation

For any two similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides. In the corresponding triangles RST and IJK, this relation is expressed as:

Perimeter(RST) / Perimeter(IJK) = RS / IJ

Substituting the given values into the formula:

64 / 56 = RS / 16

Solving for RS:

RS = (64 × 16) / 56

RS = 128 / 7 ≈ 18.28 cm

Rounding to the nearest whole number gives 18 cm.

Explanation

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle and π is approximately 22/7.

Substituting the given radius of 10.5 cm into the formula:

C = 2 × (22/7) × 10.5

C = 2 × 22 × 1.5

C = 66 cm

Explanation

To find the number of integers between 201 and 401 that are divisible by 5 but not by 4, we consider the integers in the range [202, 400].

First, we find the count of numbers in this range that are divisible by 5, denoted as N(5). The first term is 205, the last term is 400, and the common difference is 5. N(5) = (400 - 205)/5 + 1 = 195/5 + 1 = 40

Next, we find the count of numbers in this range that are divisible by both 5 and 4, which means they are divisible by their least common multiple, LCM(5, 4) = 20. We denote this count as N(20). The first term is 220, the last term is 400, and the common difference is 20. N(20) = (400 - 220)/20 + 1 = 180/20 + 1 = 10

Subtracting the numbers divisible by 20 from those divisible by 5 gives the count of numbers divisible by 5 but not by 4: N = N(5) - N(20) = 40 - 10 = 30

Explanation

According to the BODMAS rule, the operations are performed in the order of division, multiplication, and then addition.

First, evaluate the division: (7/3) ÷ (7/6) = (7/3) × (6/7) = 2

Next, multiply the result with the first term: (3/2) × 2 = 3

Then, add the remaining fraction: 3 + 1/4 = 13/4

This simplifies the given equation to: 13/4 = 1/x

Taking the reciprocal on both sides yields: x = 4/13

Explanation

Under compound interest compounding annually, the relationship between the final amount A and the principal P is given by the formula:

A = P(1 + r/100)ᵗ

Given that the sum becomes 1.96 times of itself in 2 years, we substitute the values:

1.96P = P(1 + r/100)²

Dividing both sides by P:

1.96 = (1 + r/100)²

Taking the square root of both sides:

1.4 = 1 + r/100

r/100 = 0.4

r = 40

This gives the annual rate of interest as 40%.

Explanation

The saving for each year is calculated using the formula Saving = Income - Expenditure.

Saving for year A = 350 - 150 = 200 Saving for year B = 250 - 100 = 150 Saving for year C = 200 - 150 = 50 Saving for year D = 400 - 100 = 300 Saving for year E = 150 - 75 = 75

Total saving across all five years = 200 + 150 + 50 + 300 + 75 = 775

The average saving is the total saving divided by the number of years: Average saving = 775 ÷ 5 = 155

Explanation

Using the work equivalence formula M₁ × D₁ = M₂ × D₂ for the remaining portion of the work:

The remaining work is equivalent to 8 boys working for the remaining 24 days (48 days - 24 days = 24 days).

After 2 boys leave, the number of remaining boys is 6 (8 - 2 = 6).

Let D be the number of days required by the remaining 6 boys to complete this remaining work.

8 × 24 = 6 × D

D = (8 × 24) / 6

D = 32 days.

Explanation

In a cyclic quadrilateral, the sum of opposite angles is 180°. Since angle M and angle O are opposite angles:

∠M + ∠O = 180°

We are given the relation:

2∠O = 3∠M ∠O = (3/2)∠M

Substituting this into the angle sum equation:

∠M + (3/2)∠M = 180°

(5/2)∠M = 180°

∠M = 180° × 2/5 = 72°

Explanation

When the cost price of each item is equal, the overall profit or loss percentage is simply the arithmetic mean of the individual profit and loss percentages.

Here, the cost price of each of the three spectacles is Rs.4,000.

The individual transactions are: First spectacle: +30% profit Second spectacle: -10% loss Third spectacle: -10% loss

Using the average formula for overall percentage: Overall profit percentage = (30% - 10% - 10%) / 3 Overall profit percentage = 10% / 3 = 3.33%

Explanation

The average sale for five months is given by the formula: Average sale = Total sale / Number of months

To get an average sale of Rs.9,000 over 5 months, the total sale required for all 5 months is: Total sale = 9,000 × 5 = 45,000

The sum of the sales for the first 4 months is: Sum of sales = 10,000 + 7,500 + 8,000 + 10,500 = 36,000

The required sale in the fifth month is the difference between the total sale required for 5 months and the sum of the sales of the first 4 months: Fifth month sale = 45,000 - 36,000 = 9,000