SSC CHSL Tier 1 2025 Quantitative Aptitude Questions with Solutions

Explanation

Using the algebraic expansion of (a + b)³: x³ = (√3 + √5)³ = (√3)³ + (√5)³ + 3 × √3 × √5 × (√3 + √5) = 3√3 + 5√5 + 3√15(√3 + √5) = 3√3 + 5√5 + 3√45 + 3√75 = 3√3 + 5√5 + 9√5 + 15√3 = 18√3 + 14√5

Substituting the values of x³ and x into the expression x³ − 3x: x³ − 3x = (18√3 + 14√5) − 3(√3 + √5) = 18√3 + 14√5 − 3√3 − 3√5 = 15√3 + 11√5

Explanation

The total marked price of the 10 chairs is calculated by multiplying the quantity by the marked price of a single chair: Total Marked Price = 10 × 500 = Rs. 5000

The selling price of the set is Rs. 4200.

The discount amount is the difference between the total marked price and the selling price: Discount = 5000 - 4200 = Rs. 800

The discount percentage is calculated using the formula: Discount Percentage = (Discount / Total Marked Price) × 100 Discount Percentage = (800 / 5000) × 100 = 16%

Explanation

The volume of the displaced water in the cylindrical tank is equal to the volume of the fully immersed regular right pyramid.

The volume of the displaced water is calculated using the formula: V = π × R² × h

where R is the radius of the cylindrical tank and h is the rise in the water level. Given R = 8 cm and h = 22.5 - 20 = 2.5 cm, the volume is: V = π × 8² × 2.5 = 160π cm³

The volume of a regular right pyramid is calculated using the formula: V = ⅓ × Area of base × Height

The base of the pyramid is an equilateral triangle with side a = 16 cm. Its area is: Area of base = (√3/4) × a² = (√3/4) × 16² = 64√3 cm²

Let H be the perpendicular height of the pyramid. Equating the volume of the pyramid to the volume of the displaced water: ⅓ × 64√3 × H = 160π

Solving for H: H = (160π × 3) / (64√3) H = 480π / (64√3) H = 15π / (2√3) H = 5π√3/2 cm

Explanation

The slant height l of a regular right pyramid with a square base of side a and vertical height h is calculated using the Pythagorean theorem on the right triangle formed by the vertical height, the inradius of the base, and the slant height: l = √(h² + (a/2)²)

Substituting h = 24 cm and a = 14 cm: l = √(24² + (14/2)²) l = √(576 + 7²) l = √(576 + 49) l = √625 l = 25 cm

The total surface area (TSA) of the pyramid is the sum of the area of the square base and the lateral surface area of the four triangular faces: TSA = a² + 4 × (½ × a × l) TSA = a² + 2 × a × l

Substituting the values: TSA = 14² + 2 × 14 × 25 TSA = 196 + 700 TSA = 896 cm²

Explanation

An irrational number is a real number that cannot be expressed as a fraction p/q, where p and q are integers and q is not equal to 0. Consequently, when written in decimal form, its expansion continues infinitely without ever ending and without establishing any periodic pattern or sequence of digits that repeats. This is exemplified by well-known irrational numbers such as π, which is approximately 3.14159..., or √2, which is approximately 1.41421..., where the digits continue indefinitely without establishing a repeating cycle.

Explanation

Let the cost price of the second gadget be x. Since the cost price of the first gadget is 50% more than that of the second, its cost price is 1.5x.

The profit earned on the first gadget is 20% of 1.5x, which is 0.20 × 1.5x = 0.30x. The loss incurred on the second gadget is 15% of x, which is 0.15 × x = 0.15x.

The net gain is the difference between the profit and the loss: Net Gain = 0.30x - 0.15x = 0.15x

We are given that the net gain is Rs. 75: 0.15x = 75 x = 75 / 0.15 = 500

Thus, the cost price of the second gadget is Rs. 500, and the cost price of the first gadget is 1.5 × 500 = Rs. 750.

Explanation

Using the rule of alligation on the concentration of milk in the mixtures:

In the first container, the fraction of milk is M₁ = 5 / (5 + 4) = 5/9. In the second container, the fraction of milk is M₂ = 9 / (9 + 5) = 9/14. In the final mixture, the fraction of milk is M_f = 7 / (7 + 5) = 7/12.

The ratio in which the two mixtures must be mixed is: Ratio = |M₂ - M_f| : |M₁ - M_f|

Calculating the absolute differences: |M₂ - M_f| = |9/14 - 7/12| = |54/84 - 49/84| = 5/84 |M₁ - M_f| = |5/9 - 7/12| = |20/36 - 21/36| = 1/36

Finding the ratio: Ratio = (5/84) : (1/36)

Multiplying both terms by their least common multiple, 252: Ratio = (5/84) × 252 : (1/36) × 252 Ratio = 15 : 7

Explanation

To find the value of angle A, we rewrite the equation by substituting sec A = 1/cos A:

4cos A + 2/cos A = 4√2

Let x = cos A. The equation becomes:

4x + 2/x = 4√2

Multiplying the entire equation by x to eliminate the fraction gives:

4x² - 4√2 x + 2 = 0

Dividing the entire equation by 2:

2x² - 2√2 x + 1 = 0

We can rewrite this quadratic equation as a perfect square:

(√2 x - 1)² = 0

Taking the square root on both sides:

√2 x - 1 = 0 x = 1/√2

Substituting x back as cos A:

cos A = 1/√2

Since A lies in the interval 0° < A < 90°, the angle whose cosine value is 1/√2 is 45°.

Explanation

A rational number is defined as any number that can be expressed in the form p/q, where p and q are integers and q ≠ 0. An irrational number, by definition, is a real number that cannot be expressed as a ratio of two integers. Since these two sets of numbers are mutually exclusive and completely disjoint, no rational number can ever be an irrational number.

Explanation

Daily wage of the man and the boy together is: Total wage ÷ Number of days = 960 ÷ 6 = Rs. 160

Wages are distributed in proportion to efficiency. Since the man is three times as efficient as the boy, the ratio of the man's daily wage to the boy's daily wage is 3 : 1.

Let the daily wage of the boy be x. The daily wage of the man is 3x.

3x + x = 160 4x = 160 x = 40

The daily wage of the boy is Rs. 40.

Explanation

Using the trigonometric identity sin² A = 1 - cos² A, we can substitute this into the given equation:

2(1 - cos² A) + √3 cos A - 2 = 0

Expanding and simplifying the equation:

2 - 2 cos² A + √3 cos A - 2 = 0 -2 cos² A + √3 cos A = 0 cos A (√3 - 2 cos A) = 0

This gives two possible solutions: cos A = 0 or cos A = √3/2.

If cos A = 0, then tan A is undefined.

If cos A = √3/2, we find the value of tan A using the relation:

tan A = sin A / cos A = √(1 - cos² A) / cos A

Substituting cos A = √3/2:

tan A = √(1 - 3/4) / (√3/2) = (½) / (√3/2) = 1/√3

Explanation

Profit is shared in proportion to the capital invested by each partner when the investment duration is equal.

The ratio of investments of X, Y, and Z is: 24,000 : 36,000 : 60,000 = 2 : 3 : 5

Sum of the ratio terms = 2 + 3 + 5 = 10

Y's share of the profit is calculated as: (3 / 10) × 60,000 = 18,000

Explanation

Curved surface area of a right circular cylinder is given by the formula: CSA = 2πrh

Volume of a right circular cylinder is given by the formula: V = πr²h

Equating the curved surface area and the volume: 2πrh = πr²h

Dividing both sides by πrh (where r ≠ 0 and h ≠ 0): r = 2

Explanation

The area of the portion of the square lying outside the inscribed circle is the difference between the area of the square and the area of the circle.

For a square of side s, the area is s². Since the circle is inscribed in the square, its diameter is equal to the side of the square, which means its radius r is s/2.

Given s = 14 cm: The radius of the circle r = 14 / 2 = 7 cm.

The area of the square is: 14² = 196 cm²

The area of the circle is: πr² = (22/7) × 7² = 154 cm²

The area of the portion of the square outside the circle is: 196 - 154 = 42 cm²

Explanation

The algebraic identity for the square of a trinomial is: (x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

By substituting x = a, y = -b, and z = c into the identity, we get: (a - b + c)² = a² + (-b)² + c² + 2(a(-b) + (-b)c + ca) (a - b + c)² = a² + b² + c² - 2(ab + bc - ca)

Substitute the given values of a² + b² + c² = 180 and ab + bc - ca = 44 into this equation: (a - b + c)² = 180 - 2(44) (a - b + c)² = 180 - 88 (a - b + c)² = 92

Explanation

The curved surface area of a cone with radius r and slant height l is given by the formula: CSA_cone = πrl

The curved surface area of a hemisphere with radius r is given by the formula: CSAₕemisphere = 2πr²

Since both solids have equal curved surface areas: πrl = 2πr²

Dividing both sides of the equation by πr gives: l = 2r

Explanation

The interest earned in the first year represents the simple interest on the principal amount P for one year.

First year interest (I₁) = P × r / 100 = 1,800

In the second year, the interest earned includes the interest on the principal plus the interest earned on the first year's interest.

Second year interest (I₂) = I₁ + (I₁ × r / 100)

Substitute the given values into the equation:

2,160 = 1,800 + (1,800 × r / 100)

360 = 18 × r

r = 20%

Using the rate of interest, the principal amount P is calculated as:

P × 20 / 100 = 1,800

P = 1,800 × 5 = 9,000

To find 50% of the principal amount:

50% of P = 9,000 × 0.5 = 4,500

Explanation

The volume V of a rectangular solid is given by the formula:

V = Base Area × Height

Given that the area of the base is 54 cm² and the height of the solid is 12 cm, the volume can be directly calculated by substituting these values into the formula:

V = 54 × 12 = 648 cm³

Thus, the volume of the solid is 648 cubic cm.

Explanation

Correct Answer: B

We can find the overall percentage profit or loss directly using the successive percentage change formula:

Net percentage change = a + b + ab/100

Here, the markup percentage (a) is +32% and the discount percentage (b) is -15%.

Substituting these values into the formula:

Net percentage change = 32 - 15 + (32 × (-15))/100 Net percentage change = 17 - 4.8 = 12.2%

Since the net percentage change is positive, the transaction resulted in a 12.2% profit. The actual cost price of the painting is not required to calculate the percentage profit.

Explanation

By the principle of inclusion-exclusion for two sets, the percentage of candidates who qualified in at least one of the two subjects is given by the formula:

P(R ∪ Q) = P(R) + P(Q) - P(R ∩ Q)

Here, P(R) represents the percentage of candidates who qualified in Reasoning, which is 55%.

P(Q) represents the percentage of candidates who qualified in Quantitative Aptitude, which is 65%.

P(R ∩ Q) represents the percentage of candidates who qualified in both subjects, which is 40%.

Substituting these values into the formula:

P(R ∪ Q) = 55% + 65% - 40%

P(R ∪ Q) = 120% - 40% = 80%

Explanation

Let the marks obtained in History be H.

The student scored 25% higher marks in English (E) than in History, which gives: E = H + 0.25H = 1.25H

The average of the marks in both subjects is 90: (E + H) / 2 = 90 E + H = 180

Substituting the value of E in terms of H into the equation: 1.25H + H = 180 2.25H = 180 H = 180 / 2.25 H = 80

Explanation

The ratio of profit sharing among partners in a business is determined by the formula: Profit = Capital × Time.

P invested Rs. 40,000 for 12 months. Q invested Rs. 60,000 for 12 months. R joined after 4 months, which means R invested Rs. 80,000 for 8 months (12 - 4 = 8).

The ratio of their profits at the end of one year is: P's profit : Q's profit : R's profit = (40,000 × 12) : (60,000 × 12) : (80,000 × 8) = 4,80,000 : 7,20,000 : 6,40,000

Dividing each part by 80,000 simplifies the ratio to: 6 : 9 : 8

Explanation

The correct average score is found using the average correction formula:

Correct Average = Incorrect Average + (Correct Value - Incorrect Value) / n

Using the given values: Incorrect Average = 64.5 Incorrect Value = 55 Correct Value = 75 Number of students (n) = 20

Substituting these values into the formula:

Correct Average = 64.5 + (75 - 55) / 20 Correct Average = 64.5 + 20 / 20 Correct Average = 64.5 + 1 Correct Average = 65.5

Explanation

Let the side length of the solid cube be a.

The total surface area of the original cube is given by the formula: Original Surface Area = 6a²

When the cube is cut into two equal cuboids by a plane passing through its mid-height, a single cut is made parallel to its base. This cut exposes two new identical surfaces, each having an area equal to the face of the cube, which is a².

The total surface area of the two resulting cuboids combined is: New Surface Area = 6a² + 2a² = 8a²

The increase in total surface area is: Increase = 8a² - 6a² = 2a²

The percentage increase in the total surface area is calculated as: Percentage Increase = (Increase / Original Surface Area) × 100% Percentage Increase = (2a² / 6a²) × 100% = (1/3) × 100% ≈ 33.33%

Explanation

To find the overall percentage profit or loss, we can use the weighted average method. Since the cost price of each bag is the same, we can use the number of bags as weights.

The shopkeeper sells 25 bags at a 12% profit and the remaining 15 bags at an 8% loss. The ratio of the two quantities of bags is 25 to 15, which simplifies to 5 to 3.

Using the weighted average formula:

Overall percentage = (5 × 12 + 3 × (-8)) / (5 + 3)

Overall percentage = (60 - 24) / 8

Overall percentage = 36 / 8 = 4.5%

Since the resulting value is positive, the shopkeeper makes an overall profit of 4.5%.

Explanation

For Scheme A, the simple interest earned on the investment is calculated using the formula: SI = P × R × T / 100

Substituting P = ₹15,000, R = 10%, and T = 3 years: SI = 15000 × 10 × 3 / 100 = ₹4,500

The total amount received from Scheme A (A₁) is: A₁ = P + SI = 15000 + 4500 = ₹19,500

For Scheme B, this amount of ₹19,500 is invested for 2 years at 5% p.a. compounded annually. The final compound interest amount (A₂) is calculated using the formula: A₂ = P₂ × (1 + R₂/100)ⁿ

Substituting P₂ = ₹19,500, R₂ = 5%, and n = 2 years: A₂ = 19500 × (1 + 5/100)² A₂ = 19500 × (1.05)² A₂ = 19500 × 1.1025 A₂ = ₹21,498.75

Explanation

Let the number of Rs. 10, Rs. 5, and Rs. 2 coins in the box be 4x, 3x, and 2x respectively.

The total value of these coins is calculated as: Total Value = (10 × 4x) + (5 × 3x) + (2 × 2x) Total Value = 40x + 15x + 4x Total Value = 59x

Given that the total amount in the box is Rs. 1,180, we can write: 59x = 1180 x = 1180 ÷ 59 x = 20

The number of Rs. 5 coins is 3x: Number of Rs. 5 coins = 3 × 20 = 60

Explanation

In a partnership, when the investment duration is the same for all partners, the profits are distributed in the ratio of their initial investments.

The ratio of the investments of A and B is: Ratio = 24,000 : 36,000 = 2 : 3

Let the profit share of A be 2x and that of B be 3x.

The difference between their profit shares is: 3x - 2x = x

According to the question, B receives Rs. 1200 more than A, which means: x = 1200

The total profit is the sum of the profit shares of A and B: Total Profit = 2x + 3x = 5x

Substituting the value of x: Total Profit = 5 × 1200 = 6000

Thus, the total profit is Rs. 6000.

Explanation

The given equation is sin θ + sin² θ = 1.

By rearranging the terms, we get: sin θ = 1 - sin² θ

Using the fundamental trigonometric identity sin² θ + cos² θ = 1, we know that: 1 - sin² θ = cos² θ

Therefore: sin θ = cos² θ

Squaring both sides of this equation yields: sin² θ = cos⁴ θ

We need to find the value of cos² θ + cos⁴ θ. Substituting the values of cos² θ and cos⁴ θ in terms of sin θ into this expression gives: cos² θ + cos⁴ θ = sin θ + sin² θ

Since it is given that sin θ + sin² θ = 1, we have: cos² θ + cos⁴ θ = 1

Explanation

To find the number of perfect squares n² between 5000 and 15000, we find the range of the integer n such that: 5000 < n² < 15000

Taking the square root of the inequality: √5000 < n < √15000

Calculating the approximate square roots: √5000 ≈ 70.71 √15000 ≈ 122.47

Since n must be an integer, the values of n range from the first integer greater than 70.71 to the last integer less than 122.47. Smallest integer n = 71 Largest integer n = 122

To find the total number of integers in this range, we use the formula: Number of terms = (Largest term - Smallest term) + 1 Number of terms = 122 - 71 + 1 = 52

Explanation

Using the trigonometric identity cos(90° − p) = sin p, the given equation simplifies to:

sin p × sin p = 1/4 sin²p = 1/4

Since 0° < p < 90°, taking the positive square root gives:

sin p = 1/2

This yields p = 30°.

Now, substitute p = 30° into the required expression:

cot²2p + cos²3p = cot²(2 × 30°) + cos²(3 × 30°) = cot²60° + cos²90°

Substituting the standard trigonometric values cot 60° = 1/√3 and cos 90° = 0:

(1/√3)² + 0² = 1/3 + 0 = 1/3

Explanation

The average speed of a journey is given by the formula:

Average Speed = Total Distance ÷ Total Time

The total distance is 300 km, and the overall average speed is 50 km/h.

The journey is split into three equal parts of 100 km each: Time taken for the first 100 km at 50 km/h: t₁ = 100 / 50 = 2 hours

Time taken for the next 100 km at 40 km/h: t₂ = 100 / 40 = 2.5 hours

Time taken for the remaining 100 km at x km/h: t₃ = 100 / x hours

The total time is: Total Time = t₁ + t₂ + t₃ = 2 + 2.5 + 100/x = 4.5 + 100/x hours

Using the average speed formula: 50 = 300 / (4.5 + 100/x)

4.5 + 100/x = 300 / 50 4.5 + 100/x = 6 100/x = 1.5 x = 100 / 1.5 = 200/3 = 66 2/3 km/h

Explanation

The difference between compound interest and simple interest for a period of 2 years is given by the formula P(R/100)². Substituting P = Rs. 25,000 and R = 12% into the formula yields 25000 * (12/100)² = 25000 * 0.0144 = Rs. 360.

Explanation

Average speed of a journey is given by the formula: Average Speed = Total Distance ÷ Total Time

First, the distance covered by train is 60% of 600 km, which is: d₁ = 0.60 × 600 = 360 km

The time taken by train at a speed of 75 km/h is: t₁ = 360 ÷ 75 = 4.8 hours

The remaining distance covered by bus is 40% of 600 km, which is: d₂ = 0.40 × 600 = 240 km

The time taken by bus at a speed of 50 km/h is: t₂ = 240 ÷ 50 = 4.8 hours

The total time for the entire journey is: T = t₁ + t₂ = 4.8 + 4.8 = 9.6 hours

Using the average speed formula: Average Speed = 600 ÷ 9.6 = 62.5 km/h

Explanation

Using the weighted average formula, the percentage of alcohol in the final mixture is calculated as (2 * 30 + 3 * x) / (2 + 3) = 24. Solving the equation 60 + 3x = 120 gives 3x = 60, which yields x = 20.

Explanation

The final price after successive discounts of d₁% and d₂% on the marked price is given by the formula: Final Price = Marked Price × (1 - d₁/100) × (1 - d₂/100)

Given that the marked price is Rs. 40,000, the first discount is 20%, and the additional cash discount is 5%: Final Price = 40,000 × (1 - 0.20) × (1 - 0.05) Final Price = 40,000 × 0.80 × 0.95 Final Price = 32,000 × 0.95 Final Price = 30,400

Explanation

The relation between the selling price, marked price, and discount percentage is given by the formula:

Marked Price = Selling Price / (1 - Discount/100)

Substituting the given values into the formula:

Marked Price = 1710 / (1 - 5/100) Marked Price = 1710 / 0.95 Marked Price = 1800

Explanation

Using the mixture and alligation method, the ratio of the number of initial students to the number of new students is determined by the differences between their individual average ages and the combined average age.

Difference for initial students: |18 - 17.6| = 0.4 Difference for new students: |16 - 17.6| = 1.6

The ratio of the number of initial students to the number of new students is 1.6 : 0.4, which simplifies to 4 : 1.

Since the initial number of students is 100, representing 4 parts of the ratio, 1 part represents the number of new students:

100 ÷ 4 = 25

Explanation

The percentage of students who like English or Hindi or both is calculated using the set union formula:

Percentage = E + H - (E ∩ H)

Substituting the given percentages:

Percentage = 60% + 50% - 35% = 75%

The remaining percentage of students who do not like English or Hindi is:

Remaining percentage = 100% - 75% = 25%

For a total of 1000 surveyed students, the number of remaining students is:

Remaining students = 25% of 1000 = 250

Among these 250 students, 20% prefer Sanskrit, which means the remaining 80% have no preference for any of the three subjects.

No preference = 80% of 250 = 0.80 × 250 = 200

Explanation

The total work done is the product of the daily work rate and the number of working days: Work = Rate × Time

Since the total work to be completed remains constant, the required daily work rate is inversely proportional to the number of working days: Rate ∝ 1 / Time

Let the original number of days be Tₒld and the new number of days actually worked due to strikes be Tₙew. Tₙew = 75% of Tₒld = 0.75 Tₒld

Using the inverse relationship: Rₙew / Rₒld = Tₒld / Tₙew = Tₒld / (0.75 Tₒld) = 1 / 0.75 = 4/3

The percentage increase in the daily work rate is: Percentage Increase = ((Rₙew - Rₒld) / Rₒld) × 100% Percentage Increase = (4/3 - 1) × 100% = 1/3 × 100% = 33.33%

Explanation

Correct Answer: D

A perfect square cannot end with an odd number of zeros. The number 750 ends with a single zero, which mathematically prevents it from being a perfect square.

Furthermore, the square root of 750 is √750 ≈ 27.386, which is not an integer. The consecutive integers 27 and 28 have squares of 27² = 729 and 28² = 784. Since 750 lies strictly between these two consecutive perfect squares, it is not a perfect square.

Explanation

The overall profit or loss percentage on identical items depends only on the number of items and their respective profit or loss rates, making the total cost of ₹7,500 redundant for this calculation.

Using the weighted average formula: Overall Percentage = (n₁ × r₁ + n₂ × r₂) / (n₁ + n₂)

Here, n₁ = 3 chairs with a gain rate r₁ = +20%, and n₂ = 2 chairs with a loss rate r₂ = -10%.

Substituting the values into the formula: Overall Percentage = (3 × 20 + 2 × (-10)) / (3 + 2) Overall Percentage = (60 - 20) / 5 Overall Percentage = 40 / 5 Overall Percentage = 8%

Since the result is positive, it represents an overall profit of 8%.

Explanation

Using the algebraic identity: a³ - b³ = (a - b)³ + 3ab(a - b)

Substitute the given values (a - b) = 6 and (a³ - b³) = 936 into the formula: 936 = 6³ + 3ab(6)

Simplify and solve for ab: 936 = 216 + 18ab 18ab = 720 ab = 40

Explanation

In a right-angled triangle formed by the ladder, the wall, and the ground, the length of the ladder represents the hypotenuse (h), which is 50 m.

The vertical height (y) of the wall where the ladder touches is given by: y = h × sin θ = 50 × (48/50) = 48 m

Using the Pythagorean theorem, the horizontal distance (x) of the foot of the ladder from the wall is: x² + y² = h² x² + 48² = 50² x² + 2304 = 2500 x² = 2500 - 2304 x² = 196 x = √196 = 14 m

Explanation

In a business partnership, profits are shared in the same ratio as the investments of the partners when the time period is constant.

Investment ratio of P to Q = 3 : 7

Let the shares of P and Q in the profit be 3x and 7x respectively.

The share of Q is given as ₹1400.

7x = 1400 x = 200

The total profit is the sum of P's and Q's shares: Total profit = 3x + 7x = 10x

Substituting the value of x: Total profit = 10 × 200 = 2000

Explanation

When the time period of investment is the same for all partners, the profit sharing ratio is directly proportional to the ratio of their investments.

Total investment = X's investment + Y's investment + Z's investment Total investment = 15,000 + 25,000 + 10,000 = 50,000

Y's percentage share of the total profit = (Y's investment / Total investment) × 100 Y's percentage share of the total profit = (25,000 / 50,000) × 100 = 50%

Explanation

Using the volume conservation method, let the total volume of the container be V.

Initially, the ratio of liquid A to liquid B is 7 : 5, which means the fraction of liquid A in the mixture is 7/12.

When 9 liters of the mixture is removed and replaced by 9 liters of liquid B, the total volume of the mixture remains V. The quantity of liquid A in the new mixture is entirely due to the remaining V - 9 liters of the original mixture.

The fraction of liquid A in the final mixture is 7 / (7 + 9) = 7/16.

Equating the quantity of liquid A before and after the replacement: (V - 9) × 7/12 = V × 7/16

Dividing both sides by 7: (V - 9) / 12 = V / 16

Cross-multiplying to solve for V: 16(V - 9) = 12V 4(V - 9) = 3V 4V - 36 = 3V V = 36 liters

The total initial volume of the mixture was 36 liters.

The initial quantity of liquid A is: 36 × 7/12 = 21 liters