SSC CHSL Tier 1 2015 Quantitative Aptitude Questions with Solutions

Explanation

The internal surface area of a hemispherical bowl is given by the formula for the curved surface area of a hemisphere:

A = 2πr²

Here, the internal radius r is 6 cm and π is taken as 3.14.

Substituting these values into the formula:

A = 2 × 3.14 × 6² A = 2 × 3.14 × 36 A = 72 × 3.14 A = 226.08 cm²

Explanation

The speed of the first train (v1) is calculated by dividing the length of the train by the time it takes to pass a stationary km stone: v1 = 156 / 30 = 5.2 m/s

When two trains of equal length cross each other in opposite directions, their relative speed is the sum of their individual speeds (v1 + v2), and the total distance covered is the sum of their lengths: Total distance = 156 + 156 = 312 m

Using the relative speed relation, relative speed = total distance / time: v1 + v2 = 312 / 10 5.2 + v2 = 31.2 v2 = 26 m/s

To convert the speed of the second train from m/s to km/hr, multiply by 18/5: Speed of the second train = 26 × 18/5 = 93.6 km/hr

Explanation

Let the initial volume of water be 100 units.

When water freezes to ice, its volume increases by 10%: Volume of ice = 100 + 10 = 110 units

When this ice melts back into water, its volume decreases from 110 units to its original volume of 100 units. Decrease in volume = 110 - 100 = 10 units

The percentage decrease in volume is calculated relative to the volume of ice: Percentage decrease = (Decrease in volume / Volume of ice) × 100 Percentage decrease = (10 / 110) × 100 = 100/11 % = 9 1/11 %

Explanation

To simplify the given expression, first perform the multiplication inside the parentheses:

(3/15 a⁵ b⁶ c³) × (5/9 a b⁵ c⁴)

Multiply the numerical coefficients: (3/15) × (5/9) = (1/5) × (5/9) = 1/9

Multiply the corresponding variable terms by adding their exponents: a⁵ × a = a⁵⁺¹ = a⁶ b⁶ × b⁵ = b⁶⁺⁵ = b¹¹ c³ × c⁴ = c³⁺⁴ = c⁷

This yields: 1/9 a⁶ b¹¹ c⁷

Now, divide this result by the remaining term: (1/9 a⁶ b¹¹ c⁷) ÷ (10/27 a² b c³)

Divide the numerical coefficients: (1/9) ÷ (10/27) = (1/9) × (27/10) = 3/10

Divide the corresponding variable terms by subtracting their exponents: a⁶ ÷ a² = a⁶⁻² = a⁴ b¹¹ ÷ b = b¹¹⁻¹ = b¹⁰ c⁷ ÷ c³ = c⁷⁻³ = c⁴

Combining these parts gives the simplified expression: 3/10 a⁴ b¹⁰ c⁴

Explanation

Let the number of boys be x. Since each boy contributed as many rupees as there were boys, the contribution of each boy is ₹x.

The total amount raised is: Total Amount = x × x = x²

We are given that the total amount raised is ₹12,544: x² = 12544 x = √12544

We can find the square root by estimating the range. Since 110² = 12100 and 120² = 14400, the value of x must lie between 110 and 120. Since the units digit of 12544 is 4, the square root must end in either 2 or 8. Within this range, the only matching value is 112.

Verifying this: 112 × 112 = 12544

Explanation

The given equation is tan²(π/4) - cos²(π/3) - X sin(π/4) cos(π/4) tan(π/3) = 0.

Substitute the standard values of the trigonometric functions: tan(π/4) = 1 cos(π/3) = ½ sin(π/4) = 1/√2 cos(π/4) = 1/√2 tan(π/3) = √3

Substituting these values into the equation: 1² - (½)² - X × (1/√2) × (1/√2) × √3 = 0 1 - ¼ - X × ½ × √3 = 0 ¾ - (√3 / 2) X = 0 (√3 / 2) X = ¾ X = (¾) × (2 / √3) X = √3 / 2

Explanation

Let the side of the square ABCD be a. The diagonal AC of the square acts as the hypotenuse of the right-angled triangle ABC, which is given by Pythagoras theorem: AC = √(a² + a²) = a√2

According to the properties of similar triangles, the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. Since triangle QBC is similar to triangle PAC: Area of ΔQBC / Area of ΔPAC = (BC / AC)²

Substituting the values BC = a and AC = a√2 into the formula: Area of ΔQBC / Area of ΔPAC = (a / a√2)² = (1 / √2)² = 1/2

Explanation

Let the current ages of Sonali and Monali be 5x and 3x, respectively.

Five years from now, their ages will be 5x + 5 and 3x + 5.

According to the given condition: (5x + 5) / (3x + 5) = 10 / 7

Cross-multiplying the equation: 7(5x + 5) = 10(3x + 5) 35x + 35 = 30x + 50 5x = 15 x = 3

Monali's current age is 3x = 3 × 3 = 9 years.

Explanation

For quarterly compounding, the annual interest rate is divided by 4, and the number of compounding periods is the total number of quarters.

Given: Principal (P) = ₹12000 Annual Rate = 20% Quarterly Rate (r) = 20% / 4 = 5% Time = 9 months = 3 quarters (n = 3)

The formula for the total accumulated amount (A) under compound interest is: A = P × (1 + r/100)ⁿ

Substituting the given values: A = 12000 × (1 + 5/100)³ A = 12000 × (1.05)³ A = 12000 × 1.157625 A = 13891.50

The compound interest (CI) is calculated by subtracting the principal from the total amount: CI = A - P CI = 13891.50 - 12000 = 1891.50

Explanation

Using the trigonometric identity sin²θ + cos²θ = 1, the given expression can be simplified by replacing 1 in the numerators.

For any angle θ, we have: 1 + 2 sin θ cos θ = sin²θ + cos²θ + 2 sin θ cos θ = (sin θ + cos θ)² 1 - 2 sin θ cos θ = sin²θ + cos²θ - 2 sin θ cos θ = (sin θ - cos θ)²

Substituting these identities into the expression gives: (sin 60° + cos 60°² / (sin 60° + cos 60°) + (sin 60° - cos 60°² / (sin 60° - cos 60°)

This simplifies directly to: (sin 60° + cos 60°) + (sin 60° - cos 60°) = 2 sin 60°

Since sin 60° = √3/2, substituting this value yields: 2 × (√3/2) = √3

Explanation

Starting from sinθ + cosθ = 3(sinθ − cosθ), collect terms to get 2sinθ = 4cosθ, so sinθ = 2cosθ. Since cosθ = √(1 − sin²θ), squaring gives sin²θ = 4(1 − sin²θ), so 5sin²θ = 4 and sin²θ = 4/5, which is the value asked for.

Explanation

Given the equation sin 2θ = √3/2, we know from standard trigonometric values that sin 60° = √3/2. By equating the angles, we get 2θ = 60°, which simplifies to θ = 30°.

Substituting this value of θ into the expression sin 3θ gives sin(3 × 30°) = sin 90°. Since the standard value of sin 90° is 1, the value of sin 3θ is 1.

Explanation

The volume of the largest right circular cone that can be carved out of a cube of edge a is obtained when the base of the cone is inscribed in one of the faces of the cube and its height is equal to the edge of the cube.

Therefore, the dimensions of the cone are: Radius, r = a/2 = 7/2 cm Height, h = a = 7 cm

The volume V of a cone is given by the formula: V = 1/3 × π × r² × h

Substituting the given values: V = 1/3 × 22/7 × (7/2)² × 7 V = 1/3 × 22/7 × 49/4 × 7 V = 539/6 V ≈ 89.8 cm³

Explanation

Let the first number be x and the second number be y. According to the given conditions, we can set up the following system of linear equations:

x + 2y = 8 x - y = 2

To find the values of x and y, subtract the second equation from the first:

(x + 2y) - (x - y) = 8 - 2 3y = 6 y = 2

Substitute the value of y into the second equation:

x - 2 = 2 x = 4

Thus, the first number is 4 and the second number is 2, both of which are positive whole numbers that satisfy the given conditions.

Explanation

To convert speed from kilometers per hour (km/hr) to meters per second (m/sec), multiply the given value by 5/18. This conversion factor is derived from converting 1 kilometer to 1000 meters and 1 hour to 3600 seconds, which simplifies to 1000/3600 = 5/18.

Speed in m/sec = 54 × 5/18 = 3 × 5 = 15 m/sec

Explanation

The relation between the incomes of two different years under a constant compound annual growth rate is given by the formula:

Income in 2012 = Income in 2010 × (1 + r/100)ⁿ

Here, the annual growth rate r = 20% and the time period n = 2 years (from 2010 to 2012).

Substituting the given values into the formula:

26,64,000 = Income in 2010 × (1 + 20/100)² 26,64,000 = Income in 2010 × (1.2)² 26,64,000 = Income in 2010 × 1.44 Income in 2010 = 26,64,000 ÷ 1.44 Income in 2010 = 18,50,000

Explanation

The formula for the length of a direct common tangent to two circles with radii r₁ and r₂ and distance between their centers d is given by:

PQ = √(d² - (r₂ - r₁)²)

Substituting the given values, where d = 13 cm, r₁ = 3 cm, and r₂ = 8 cm:

PQ = √(13² - (8 - 3)²) PQ = √(169 - 5²) PQ = √(169 - 25) PQ = √144 PQ = 12 cm

Explanation

Let the Cost Price be ₹100. Since the goods are marked 20% higher than the cost price, the Marked Price is: Marked Price = 100 × (1 + 20/100) = ₹120

A discount of 5% is allowed on the Marked Price, so the Selling Price is: Selling Price = 120 × (1 - 5/100) = 120 × 0.95 = ₹114

The profit percentage is calculated using the formula: Profit % = ((Selling Price - Cost Price) / Cost Price) × 100 Profit % = ((114 - 100) / 100) × 100 = 14%

Alternatively, applying the successive percentage formula where a is the markup percentage (+20%) and b is the discount percentage (-5%): Net profit % = a + b + ab/100 Net profit % = 20 - 5 + (20 × (-5))/100 = 15 - 1 = 14%

Explanation

Since AB = BC = K, the triangle has two equal sides, making it an isosceles triangle.

Applying the Pythagorean theorem to check the relationship between the sides: AB² + BC² = K² + K² = 2K²

Also: AC² = (√2 K)² = 2K²

Since AB² + BC² = AC², the converse of the Pythagorean theorem holds true, proving that the triangle has a right angle at vertex B. Therefore, the triangle is both right-angled and isosceles, making it a right isosceles triangle.

Explanation

To find the smallest five-digit number divisible by 12, 18, and 21, we first find the Least Common Multiple (LCM) of the given numbers.

The prime factorizations of the numbers are 12 = 2² × 3, 18 = 2 × 3², and 21 = 3 × 7.

LCM(12, 18, 21) = 2² × 3² × 7 = 252

The smallest five-digit number is 10000. Dividing 10000 by 252 yields 39 with a remainder of 172. To find the smallest five-digit multiple of 252, we multiply 252 by the next higher integer, 40: 252 × 40 = 10080

Explanation

Using the direct proportional relation between selling prices under different profit or loss percentages:

New Selling Price = Initial Selling Price × (100 + Gain%) / (100 - Loss%)

Substituting the given values into the formula:

New Selling Price = 450 × (100 + 20) / (100 - 20) New Selling Price = 450 × 120 / 80 New Selling Price = 450 × 3/2 New Selling Price = 675

This directly yields the required selling price to achieve a 20% gain.

Explanation

Summing the three given equations: A + B = 120 B + C = 130 C + A = 140

We get: 2(A + B + C) = 120 + 130 + 140 2(A + B + C) = 390 A + B + C = 195

To find the score of C, substitute the value of A + B from the first equation into this combined equation: 120 + C = 195 C = 195 - 120 C = 75

Explanation

Since α + β = 90°, we have β = 90° - α.

From trigonometric complementary angle identities, we know: tan β = tan(90° - α) = cot α sin β = sin(90° - α) = cos α

Substituting these into the given expression: (tan α / tan β) + sin² α + sin² β = (tan α / cot α) + sin² α + cos² α

Since cot α = 1/tan α and sin² α + cos² α = 1, the expression simplifies to: tan² α + 1

Using the standard identity 1 + tan² α = sec² α, we obtain sec² α.

Explanation

The point of intersection of the direct common tangent with the line joining the centers of two circles is known as the external center of similitude. According to the property of circles, this point divides the line segment joining the centers of the circles externally in the ratio of their respective radii.

Let the radii of the two circles be r₁ and r₂. Here, r₁ = 5 cm and r₂ = 3 cm. Therefore, the ratio in which the direct common tangent divides the line joining the centers externally is r₁ : r₂, which equals 5 : 3.

Explanation

The cost price of one dozen oranges is ₹10 and the selling price of one dozen oranges is ₹12.

The formula for gain is: Gain = Selling Price - Cost Price Gain = 12 - 10 = ₹2

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

Substituting the values into the formula: Gain % = (2 / 10) × 100 = 20%

Explanation

Outer circumference of the circular track = 2πR = 528 m, where R is the outer radius.

Using π = 22/7: 2 × (22/7) × R = 528 R = (528 × 7) / 44 R = 84 m

Since the track is 14 m wide everywhere, the inner radius r is: r = R - 14 = 84 - 14 = 70 m

The area of the track is the difference between the outer and inner circular areas: Area = π(R² - r²) = π(R - r)(R + r) Area = (22/7) × (84 - 70) × (84 + 70) Area = (22/7) × 14 × 154 Area = 44 × 154 = 6776 sq. m

The cost of levelling the track at the rate of ₹10 per sq. m is: Cost = 6776 × 10 = ₹67760

Explanation

The given series is: S = 2³ + 4³ + ... + 20³

This can be rewritten by factoring out 2³ from each term: S = (2 × 1)³ + (2 × 2)³ + ... + (2 × 10)³ S = 2³(1³ + 2³ + ... + 10³)

Substituting the given value of 1³ + 2³ + ... + 10³ = 3025: S = 8 × 3025 S = 24200

Explanation

The surface area of a sphere is given by the formula 4πr², where r is the radius of the sphere.

Using the given surface area: 4πr² = 616 4 × (22/7) × r² = 616 88/7 × r² = 616 r² = (616 × 7) / 88 r² = 7 × 7 = 49 r = 7 cm

The volume of a sphere is given by the formula 4/3 πr³.

Substituting r = 7 cm into the volume formula: Volume = 4/3 × (22/7) × 7³ Volume = 4/3 × 22 × 49 Volume = 4312 / 3 Volume = 1437 ⅓ cm³

Explanation

The remaining quantity of milk after n replacement operations is given by the formula: Remaining milk = Initial quantity × (1 - Quantity replaced / Initial quantity)ⁿ

Here, the initial quantity of milk is 60 litres, the quantity replaced each time is 12 litres, and the operation is performed n = 2 times.

Remaining milk = 60 × (1 - 12/60)² Remaining milk = 60 × (1 - 1/5)² Remaining milk = 60 × (4/5)² Remaining milk = 60 × 16/25 Remaining milk = 12 × 16/5 = 38.4 litres

Since the total volume of the mixture remains 60 litres, the quantity of water in the final mixture is: Water = 60 - 38.4 = 21.6 litres

The ratio of milk and water in the resultant mixture is: Milk : Water = 38.4 : 21.6 Milk : Water = 384 : 216 Dividing both terms by 24 gives the simplified ratio of 16:9.

Explanation

The given equation is: (2a - 1)² + (4b - 3)² + (4c + 5)² = 0

Since the sum of squares of real numbers is always non-negative, the sum can only be zero if each individual term is zero. This gives: 2a - 1 = 0 which means a = ½ 4b - 3 = 0 which means b = ¾ 4c + 5 = 0 which means c = -5/4

Adding the values of a, b, and c gives: a + b + c = 2/4 + 3/4 - 5/4 = 0

We use the algebraic identity: a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

Since a + b + c = 0, the numerator becomes: a³ + b³ + c³ - 3abc = 0 × (a² + b² + c² - ab - bc - ca) = 0

Since a² + b² + c² is a positive non-zero quantity, dividing the numerator by this term yields: (a³ + b³ + c³ - 3abc) / (a² + b² + c²) = 0

Explanation

Let the list price of the house be LP. The selling price is given as y, and the discount rate is x%.

The formula relating the selling price, list price, and discount percentage is: Selling Price = List Price × (1 - Discount/100)

Substituting the given values into this relation: y = LP × (1 - x/100) y = LP × ((100 - x)/100)

Rearranging the terms to solve for the list price: LP = 100y / (100 - x)

Explanation

From the first given equation, we have: a + 1/b = 1 a = (b - 1)/b 1/a = b/(b - 1)

From the second given equation, we have: b + 1/c = 1 1/c = 1 - b c = 1/(1 - b) = -1/(b - 1)

Adding the expressions for c and 1/a: c + 1/a = -1/(b - 1) + b/(b - 1) c + 1/a = (b - 1)/(b - 1) c + 1/a = 1

Alternatively, assuming a convenient value like b = 2: a + 1/2 = 1, which means a = 1/2 2 + 1/c = 1, which means c = -1

Substituting these values: c + 1/a = -1 + 1/(1/2) = -1 + 2 = 1

Explanation

Using the work equivalence formula:

(M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

where M is the number of women, D is the number of days, and W is the work done (length of the road).

Substituting the given values: M₁ = 20, D₁ = 10, W₁ = 100 M₂ = 10, W₂ = 50

We get: (20 × 10) / 100 = (10 × D₂) / 50

Simplifying the equation: 2 = D₂ / 5 D₂ = 10

Explanation

Convert the percentage 83 1/3% into a fraction: 83 1/3% = 250/3% = (250 / 3) × (1 / 100) = 5/6

Now, calculate 83 1/3% of 90: 5/6 × 90 = 75

Let the required number be x. According to the question, 60% of x is equal to 75: 60% × x = 75 3/5 × x = 75 x = 75 × 5/3 x = 25 × 5 x = 125

Explanation

Since the mixture is sold at the cost price of pure milk, the profit is solely due to the addition of free water. The relationship between the profit percentage, water, and milk is given by:

Profit % = (Volume of water / Volume of milk) × 100

Given a profit of 25%:

25 = (Volume of water / Volume of milk) × 100

Volume of water / Volume of milk = 25 / 100 = 1 / 4

This yields a ratio of water to milk of 1:4.

Explanation

Using the algebraic identity (x - 1/x)³ = x³ - 1/x³ - 3(x - 1/x), we substitute the given value of x - 1/x = 2. This gives 2³ = x³ - 1/x³ - 3(2), which simplifies to 8 = x³ - 1/x³ - 6, and thus x³ - 1/x³ = 14.

Explanation

Based on the pie chart, the percentage distribution of students who are members of the clubs is: Members of both clubs = 75% Members of football club only = 15% Members of cricket club only = 5%

To find the percentage of students who are not members of any club, we first calculate the total percentage of students who are members of at least one club: 75% + 15% + 5% = 95%

Subtracting this from the total student population of 100% gives: 100% - 95% = 5%

Explanation

The total surface area of a right circular cylinder is given by the formula:

Total Surface Area = 2πr(h + r)

where r is the radius of the base and h is the height of the cylinder.

Substituting the given values, r = 7 cm, h = 20 cm, and taking π ≈ 22/7:

Total Surface Area = 2 × (22/7) × 7 × (20 + 7)

Total Surface Area = 2 × 22 × 27

Total Surface Area = 44 × 27

Total Surface Area = 1188 cm²

Explanation

To convert speed from metres per second (m/s) to kilometres per hour (km/h), multiply the speed value by 18/5.

Given that the car travels 20 metres in one second, its speed is 20 m/s.

Using the conversion formula: Speed in km/h = 20 × 18/5 = 4 × 18 = 72 km/h.

Explanation

Let the side of the square be s. The area of the square is s² = 4, which gives s = 2.

The diagonal of a square is given by d = s√2. Substituting s = 2, the diagonal is d = 2√2.

The radius r of the circle is equal to this diagonal, so r = 2√2.

The area of the circle is calculated using the formula A = πr². Substituting r = 2√2 yields A = π × (2√2)² = 8π.

Explanation

Let the cost price of the article be ₹100. Since the article is sold at a profit of 25%, the initial selling price is ₹125.

When the selling price is doubled, the new selling price becomes 2 × ₹125 = ₹250.

With the cost price remaining at ₹100, the new profit earned is ₹250 - ₹100 = ₹150.

The new profit percentage is calculated as (New Profit / Cost Price) × 100, which gives (150 / 100) × 100 = 150%.

Explanation

Using the algebraic identity for the difference of squares: x² - y² = (x + y)(x - y)

Let the two numbers be x and y. We are given: x + y = 37 x² - y² = 185

Substituting these values into the formula: 185 = 37 × (x - y)

Solving for the difference of the two numbers (x - y): x - y = 185 / 37 = 5

Explanation

Let the total work be the Least Common Multiple of the individual days taken by A, B, and C, which is the LCM of 10, 12, and 15, representing 60 units of work.

The work efficiencies per day for each person are: Efficiency of A = 60 ÷ 10 = 6 units Efficiency of B = 60 ÷ 12 = 5 units Efficiency of C = 60 ÷ 15 = 4 units

Let the total number of days taken to complete the entire work be x.

A left 5 days before completion, meaning A worked for (x - 5) days. B left 2 days after A, meaning B worked for (x - 5 + 2) = (x - 3) days. C worked for the entire duration of x days.

We can set up the equation for the total work done: 6 × (x - 5) + 5 × (x - 3) + 4 × x = 60 6x - 30 + 5x - 15 + 4x = 60 15x - 45 = 60 15x = 105 x = 7

Explanation

Let the length and width of the rectangular carpet be l and w respectively.

The perimeter of the carpet is given by the formula: 2(l + w) = 46 l + w = 23

The area of the carpet is: l × w = 120

The length of the diagonal d is related to the sides by the Pythagorean theorem: d² = l² + w²

Using the algebraic identity (l + w)² = l² + w² + 2lw, we can substitute the known values: 23² = d² + 2(120) 529 = d² + 240 d² = 529 - 240 d² = 289 d = √289 = 17

Explanation

Given the equation: 4 sin²θ - 1 = 0

We can solve for sin²θ: 4 sin²θ = 1 sin²θ = 1/4

Since the angle θ is in the first quadrant (0° < θ < 90°), sin θ must be positive: sin θ = 1/2

This corresponds to: θ = 30°

Now, we substitute θ = 30° into the expression cos²θ + tan²θ: cos 30° = √3/2 cos² 30° = (√3/2)² = 3/4

tan 30° = 1/I√3 tan² 30° = (1/√3)² = 1/3

Adding these two values together: cos² 30° + tan² 30° = 3/4 + 1/3 To add these fractions, we find a common denominator, which is 12: (3 × 3)/12 + (1 × 4)/12 = 9/12 + 4/12 = 13/12

Explanation

The formula for the curved surface area of a right circular cylinder of radius r and height H is given by 2πrH.

Equating this standard formula to the given curved surface area of 4πrh:

2πrH = 4πrh

Dividing both sides by 2πr:

H = 2h

Thus, the height of the cylinder is 2h units.

Explanation

Let R be the age of the retired teacher, N be the age of the new teacher, and n be the total number of teachers.

The relationship between the change in average age and the ages of the replaced and new members is given by the formula: Change in average = (N - R) / n

Here, the number of teachers (n) is 10, the age of the new teacher (N) is 25, and the average age reduces by 3 years, which represents a change of -3.

Substituting these values into the relation: -3 = (25 - R) / 10 -30 = 25 - R R = 25 + 30 R = 55

The age of the retired teacher is 55 years.

Explanation

Using the successive percentage change formula, the net profit or loss percentage when a price is increased by a% and then decreased by b% is given by:

Net percentage change = a - b - ab/100

Here, the cost price is increased by 10% to set the marked price (a = 10), and a discount of 10% is given on the marked price (b = 10).

Net percentage change = 10 - 10 - (10 × 10)/100 = -1%

The negative sign indicates a net loss of 1%.

Explanation

Let L be the length of the train and v be its speed. When a train crosses a bridge, the total distance traveled is the sum of the length of the train and the length of the bridge.

For the first bridge of length 500 m, the train takes 100 seconds: L + 500 = 100v

For the second bridge of length 250 m, the train takes 60 seconds: L + 250 = 60v

Subtracting the second equation from the first equation: (L + 500) - (L + 250) = 100v - 60v 250 = 40v v = 25/4 m/s

Substituting the value of v into the second equation: L + 250 = 60 × (25/4) L + 250 = 15 × 25 L + 250 = 375 L = 125 m

Explanation

The formula for the total amount A at the end of 2 years with successive annual compound interest rates r₁ and r₂ is:

A = P × (1 + r₁/100) × (1 + r₂/100)

Given: P = ₹ 25000 r₁ = 4% r₂ = 5%

Substituting these values into the formula:

A = 25000 × (1 + 4/100) × (1 + 5/100) A = 25000 × (104/100) × (105/100) A = 250 × 1.04 × 105 A = 260 × 105 A = 27300