Quantitative Aptitude PYQs

Shortcut Trick

If CP of x articles = SP of y articles, then Profit% = [(x − y) ÷ y] × 100.

Given: x = 60 and y = 45.

Profit% = [(60 − 45) ÷ 45] × 100 = [15 ÷ 45] × 100.

Profit% = (1 ÷ 3) × 100 = 33.33%.

∴ The correct answer is 33.33%.

Alternate Method

Given → CP of 60 guavas = SP of 45 guavas.
Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100

⇒ 60 × CP = 45 × SP
⇒ SP ÷ CP = 60 ÷ 45 = 4 ÷ 3
⇒ Let CP = 3 units and SP = 4 units.
⇒ Profit = 4 − 3 = 1 unit.
⇒ Profit% = (1 ÷ 3) × 100 = 33.333...%
⇒ Rounded to 2 decimal places = 33.33%.

∴ The correct answer is 33.33%.

Additional Information

Profit and Loss on Article Quantity

When the cost price of a certain number of items equals the selling price of another number, the base for percentage calculation is always the number of items sold (SP quantity).

Rounding Off Rules

To round to 2 decimal places, look at the third decimal digit; if it is 5 or greater, round up the second digit, otherwise keep it as is.

Shortcut Trick

Total Successive Discount for 16%, 29% and 4% can be calculated using the Effective Discount formula.

Step 1: Discount for 16% and 29% ⇒ 16 + 29 − (16 × 29) ÷ 100 = 45 − 4.64 = 40.36%.

Step 2: Discount for 40.36% and 4% ⇒ 40.36 + 4 − (40.36 × 4) ÷ 100 = 44.36 − 1.6144 = 42.7456%.

Rounding off to two decimal places, we get 42.75%.

∴ The correct answer is 42.75%.

Alternate Method

Given → Successive Discounts: d₁ = 16%, d₂ = 29%, d₃ = 4%.
Formulas: Equivalent Discount = [1 − (1 − d₁/100) × (1 − d₂/100) × (1 − d₃/100)] × 100.

⇒ Let Marked Price (MP) = 100.
⇒ Price after 16% discount = 100 × (84/100) = 84.
⇒ Price after 29% discount = 84 × (71/100) = 59.64.
⇒ Price after 4% discount = 59.64 × (96/100) = 57.2544.
⇒ Total Discount = MP − Final SP = 100 − 57.2544 = 42.7456%.
⇒ Rounding to two decimal places = 42.75%.

∴ The correct answer is 42.75%.

Additional Information

Successive Discount Concept

When multiple discounts are applied one after another, the base for the subsequent discount is the reduced price from the previous step. Formula for two discounts: a + b − (ab/100).

Marked Price & Discount

Discount is always calculated on the Marked Price. SP = MP × (100 − D%)/100.

Shortcut Trick

Combine the profit sharing ratios: P : Q : R = (2 × 11) : (1 × 11) : (1 × 7) = 22 : 11 : 7.

Total units = 22 + 11 + 7 = 40 units.

Given 40 units = ₹25,000 → 1 unit = ₹625.

Share of R = 7 units = 7 × 625 = ₹4,375.

∴ The correct answer is ₹4375.

Alternate Method

Given:

Total profit = ₹25,000

Ratio P : Q = 2 : 1 and Q : R = 11 : 7

Calculations:

⇒ To equalize Q, multiply P : Q by 11: P : Q = 22 : 11

⇒ Combined Ratio P : Q : R = 22 : 11 : 7

⇒ Sum of ratio parts = 22 + 11 + 7 = 40

⇒ Share of R = (R's part / Total parts) × Total Profit

⇒ Share of R = (7 / 40) × 25000

⇒ Share of R = 7 × 625

⇒ Share of R = 4375

∴ The correct answer is ₹4375.

Additional Information

Compound Ratio

When two or more ratios are multiplied together, the result is a compound ratio. For P:Q and Q:R, the combined P:Q:R is found by making the common term (Q) equal.

Partnership Profit Distribution

Profit is distributed in the ratio of (Capital × Time). If time is constant, profit is shared directly in the ratio of investment/shares.

Ratio Proportion Property

If a : b = c : d, then product of extremes (a × d) equals product of means (b × c).

Shortcut Trick

Simplify the surds directly by extracting perfect square factors:

⇒ (√98 + √200 − 2√8)²

⇒ (7√2 + 10√2 − 4√2)²

⇒ (13√2)²

⇒ 169 × 2 = 338

∴ The correct answer is 338.

Alternate Method

Given:

(√98 + √200 − 2√8)²

Calculations:

Break down each radical into its simplest form by factoring out perfect squares:

⇒ √98 = √(49 × 2) = 7√2

⇒ √200 = √(100 × 2) = 10√2

⇒ 2√8 = 2 × √(4 × 2) = 2 × 2√2 = 4√2

Substitute the simplified values back into the given expression:

⇒ (7√2 + 10√2 − 4√2)²

Combine the like terms:

⇒ (17√2 − 4√2)²

⇒ (13√2)²

Square the combined term:

⇒ 13² × (√2)²

⇒ 169 × 2 = 338

∴ The correct answer is 338.

Additional Information

Simplification of Surds

A surd is simplified by identifying and extracting the largest perfect square factor from under the root: √(a² × b) = a√b.

Addition and Subtraction of Surds

Only like surds (surds having the exact same irrational part) can be added or subtracted directly: a√x + b√x = (a + b)√x.

BODMAS Rule

Always simplify the expressions inside the Brackets first before applying higher order operations like exponentiation (Order).

Shortcut Trick

When distance is constant, Speed is inversely proportional to Time.

Speed Ratio (Usual : New) = 4 : 3 → Time Ratio (Usual : New) = 3 : 4.

Difference in time units = 4 − 3 = 1 unit.

Given, 1 unit = 20 minutes.

Usual time = 3 units = 3 × 20 = 60 minutes.

∴ The correct answer is 60 min.

Alternate Method

Given: New speed = 3/4 of Usual speed. Delay = 20 minutes.

Formula Used: Usual Time = [Numerator / (Denominator − Numerator)] × Delay (when speed is reduced to n/d of usual speed).

⇒ Let usual speed be S and usual time be T.

⇒ Distance (D) = S × T

⇒ New speed = 3/4 S, New time = T + 20

⇒ D = (3/4 S) × (T + 20)

⇒ S × T = 3/4 S × (T + 20)

⇒ T = 3/4(T + 20)

⇒ 4T = 3T + 60

⇒ T = 60 minutes

∴ The correct answer is 60 min.

Additional Information

Inverse Relation of Speed and Time

For a fixed distance, if speed becomes a/b of its original value, time becomes b/a of its original value. The change in time is |b/a − 1| × original time.

Average Speed Formula

If a person covers equal distances at speeds x and y, the average speed for the whole journey is (2xy) / (x + y).

Relative Speed

When two objects move in the same direction, relative speed is (S₁ − S₂). In opposite directions, it is (S₁ + S₂).

Shortcut Trick

Combined efficiency (P+Q) = 1/10 per hour

Efficiency of P = 1/20 per hour

Efficiency of Q = 1/10 − 1/20 = 1/20 per hour

Time for Q to fill 1/4^th cistern = (1/4) ÷ (1/20) = 5 hours

∴ The correct answer is 5 hours.

Alternate Method

Given:

Time taken by P and Q = 10 hours

Time taken by P alone = 20 hours

Calculations:

⇒ Efficiency of Q = (Efficiency of P+Q) − (Efficiency of P)

⇒ Efficiency of Q = 2 − 1 = 1 unit/hour

⇒ One-fourth of the total work = 20 ÷ 4 = 5 units

⇒ Time taken by Q alone = 5 ÷ 1 = 5 hours

∴ The correct answer is 5 hours.

Additional Information

Pipes and Cisterns Efficiency

The efficiency of a pipe is inversely proportional to the time taken to fill the tank. Total Work = Time taken × Efficiency.

Combined Work Formula

If two pipes A and B fill a tank in x and y hours respectively, they together fill it in (xy) ÷ (x + y) hours.

Negative Work (Inlet/Outlet)

Inlet pipes perform positive work (+), while outlet pipes (leaks) perform negative work (−) on the cistern capacity.

Shortcut Trick

Required number = LCM(20, 98, 35, 21) × k + Remainder

LCM(20, 98, 35, 21) = 1470 × 4 = 5880

Desired number must be of form 5880k + 5

For k = 1, Number = 5880 + 5 = 5885

Number to be added = 5885 − 5023 = 862

∴ The correct answer is 862.

Alternate Method

Given: Divisors are 20, 98, 35, 21 and remainder is 5.

Formula: Required Number = LCM(Divisors) × k + Remainder

⇒ Prime factorization of divisors:

⇒ 20 = 2² × 5

⇒ 98 = 2 × 7²

⇒ 35 = 5 × 7

⇒ 21 = 3 × 7

⇒ LCM = 2² × 5 × 7² × 3 = 4 × 5 × 49 × 3 = 2940

⇒

Note:

Rechecking LCM(20, 98, 35, 21): 20=4×5, 98=2×49, 35=5×7, 21=3×7. LCM = 4 × 5 × 49 × 3 = 2940.

⇒ Next number after 5023 in the form 2940k + 5:

⇒ For k = 2: 2940 × 2 + 5 = 5880 + 5 = 5885

⇒ Number to be added = 5885 − 5023 = 862

∴ The correct answer is 862.

Additional Information

LCM Method for Remainders

When the remainder is the same for all divisors, the general form is (LCM × k) + Remainder.

LCM Calculation

LCM is the product of the highest powers of all prime factors present in the given numbers.

Natural Numbers

Natural numbers are positive integers starting from 1 {1, 2, 3, ...}.

Shortcut Trick

Total Distance = Sum of lengths = 297 + 243 = 540 m.

Relative Speed (Opposite) = 42 + 66 = 108 km/hr.

Convert to m/sec: 108 × (5/18) = 30 m/sec.

Time = 540 ÷ 30 = 18 sec.

∴ The correct answer is 18 sec.

Alternate Method

Given: Length of Train 1 (L₁) = 297 m, Length of Train 2 (L₂) = 243 m, Speed 1 (S₁) = 42 km/hr, Speed 2 (S₂) = 66 km/hr.

Formula Used: Time = (L₁ + L₂) ÷ (S₁ + S₂)

⇒ Total Length = 297 + 243 = 540 m

⇒ Relative Speed = 42 + 66 = 108 km/hr

⇒ Speed in m/sec = 108 × (5/18) = 6 × 5 = 30 m/sec

⇒ Time taken = 540 ÷ 30

⇒ Time taken = 18 sec

∴ The correct answer is 18 sec.

Additional Information

Relative Speed in Opposite Direction

When two objects move in opposite directions, their relative speed is the sum of their individual speeds: V_rel = V₁ + V₂.

Unit Conversion

To convert km/hr to m/sec, multiply by 5/18. To convert m/sec to km/hr, multiply by 18/5.

Crossing Distance

When two trains cross each other completely, the total distance covered is always the sum of the lengths of both trains (L₁ + L₂).

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Shortcut Trick

In any quadrilateral ABCD, the angle formed by the bisectors of two adjacent angles (say ∠C and ∠D) is equal to half the sum of the other two angles (∠A and ∠B).

∠DOC = (∠A + ∠B) ÷ 2

∠DOC = (88° + 81°) ÷ 2

∠DOC = 169° ÷ 2 = 84.5°

∴ The correct answer is 84.5°.

Alternate Method

Given: ∠A = 88°, ∠B = 81° in quadrilateral ABCD. CO and DO are angle bisectors of ∠C and ∠D respectively.

Formula Used: Sum of interior angles of a quadrilateral = 360° | Sum of angles in a triangle = 180°.

Calculations:

⇒ In quadrilateral ABCD, &ang

Shortcut Trick

Ratio change: (7 : 6) → (8 : 7). Both parts increase by 1 unit.

This 1 unit increase corresponds to the 8-year time gap.

⇒ 1 unit = 8 years.

Present age of B = 6 units = 6 × 8 = 48 years.

∴ The correct answer is 48 years.

Alternate Method

Given: Ratio of present ages of A and B is 7 : 6. After 8 years, the ratio becomes 8 : 7.

Let the present ages of A and B be 7x and 6x.

⇒ (7x + 8) ÷ (6x + 8) = 8 ÷ 7

⇒ 7 × (7x + 8) = 8 × (6x + 8)

⇒ 49x + 56 = 48x + 64

⇒ 49x − 48x = 64 − 56

⇒ x = 8

⇒ Present age of B = 6x = 6 × 8 = 48 years.

∴ The correct answer is 48 years.

Additional Information

Age Difference Property

The difference between the ages of two persons remains constant regardless of how many years pass.

Ratio Balancing

If the differences between ratio parts are not equal, multiply the ratios by the difference of the other ratio to balance the units.

Future and Past Ages

If current age is x, age 'n' years hence is (x + n) and age 'n' years ago was (x − n).

Shortcut Trick

Rahul's share = (Total − Difference) ÷ 2

Rahul's share = (50 − 16) ÷ 2

Rahul's share = 34 ÷ 2 = 17

∴ The correct answer is ₹17.

Alternate Method

Given:

Total amount (Amit + Rahul) = ₹50

Difference (Amit − Rahul) = ₹16

Let the amount with Rahul be ₹x.

Amount with Amit = ₹(x + 16).

⇒ x + (x + 16) = 50

⇒ 2x + 16 = 50

⇒ 2x = 50 − 16

⇒ 2x = 34

⇒ x = 34 ÷ 2

⇒ x = 17

∴ The correct answer is ₹17.

Additional Information

Linear Equations in One Variable

An equation which can be written in the form ax + b = 0, where a and b are real numbers and a ≠ 0.

Sum and Difference Method

If (A + B) = S and (A − B) = D, then the larger value A = (S + D) ÷ 2 and the smaller value B = (S − D) ÷ 2.

Verification

Rahul has ₹17, Amit has 17 + 16 = ₹33. Total = 17 + 33 = ₹50. The condition is satisfied.

Shortcut Trick

For third proportional, use the relation: b² = a × c

Here, a = 64, b = Z, and c = 4.

⇒ Z² = 64 × 4 = 256

⇒ Z = √256 = 16

∴ The correct answer is 16.

Alternate Method

Given: First number (a) = 64, Second number (b) = Z, Third proportional (c) = 4.

Formula Used: If a, b, and c are in continued proportion, then a : b = b : c.

⇒ 64 ÷ Z = Z ÷ 4

⇒ Z × Z = 64 × 4

⇒ Z² = 256

⇒ Z = √256

⇒ Z = 16

∴ The correct answer is 16.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b).

Fourth Proportional

If a : b = c : d, then d is the fourth proportional, calculated as d = (b × c) ÷ a.

Duplicate Ratio

The duplicate ratio of a : b is a² : b².

Shortcut Trick

Successive percentage formula: Net Change = a + b + (a × b) ÷ 100.

Here, a = +85% (Mark-up) and b = −20% (Discount).

Profit% = 85 − 20 + (85 × (−20)) ÷ 100.

Profit% = 65 − (1700 ÷ 100) = 65 − 17 = 48%.

∴ The correct answer is 48%.

Alternate Method

Given: Marked Price (MP) = 85% above Cost Price (CP), Discount = 20%.
Formulas: MP = CP × (100 + Mark-up%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100 | Profit% = (SP − CP) ÷ CP × 100.

⇒ Let the Cost Price (CP) be 100 units.

⇒ Marked Price (MP) = 100 + 85% of 100 = 185 units.

⇒ Selling Price (SP) = 185 − 20% of 185 = 185 − 37 = 148 units.

⇒ Profit = SP − CP = 148 − 100 = 48 units.

⇒ Profit Percentage = (48 ÷ 100) × 100 = 48%.

∴ The correct answer is 48%.

Additional Information

Mark-up and Discount Relationship

Profit% is the net result of the Mark-up percentage and the Discount percentage applied sequentially on the CP.

Selling Price Formula

SP can be directly calculated as: SP = CP × (1 + Mark-up%) × (1 − Discount%).

Shortcut Trick
Total Volume = 33 + 43 + 53 = 27 + 64 + 125 = 216 cm3
New Edge = √3216 = 6 cm
Initial Area = 6 × (32 + 42 + 52) = 6 × 50 = 300 cm2
New Area = 6 × 62 = 6 × 36 = 216 cm2
Percentage Decrease = [(300 − 216) ÷ 300] × 100 = 28%
∴ The correct answer is 28% decrease.
Alternate Method
Given:
Edges of three cubes = 3 cm, 4 cm, 5 cm
Formula Used:
Volume of cube = a3
Total Surface Area (TSA) of cube = 6a2
Percentage change = [(Initial Value − Final Value) ÷ Initial Value] × 100

⇒ Total Volume of three cubes = 33 + 43 + 53
⇒ Total Volume = 27 + 64 + 125 = 216 cm3
⇒ Volume of the new single cube = 216 cm3
⇒ Edge of new cube (A) = √3216 = 6 cm
⇒ Initial Total Surface Area = 6 × (32 + 42 + 52)
⇒ Initial TSA = 6 × (9 + 16 + 25) = 6 × 50 = 300 cm2
⇒ New Total Surface Area = 6 × 62 = 6 × 36 = 216 cm2
⇒ Change in Area = 300 − 216 = 84 cm2
⇒ Percentage change = (84 ÷ 300) × 100
⇒ Percentage change = 28%
∴ The correct answer is 28% decrease.
Additional Information
Melting and Recasting Rule
When multiple solid objects are melted and formed into a single object, the total volume remains constant, although the surface area usually changes.
Cube Properties
For a cube with side 'a', Lateral Surface Area (LSA) = 4a2 and the longest diagonal = a√3.
Percentage Change Logic
If the final value is less than the initial value, the change is always a percentage decrease. In this problem, 216 < 300, hence a decrease.

Shortcut Trick

Total Capacity (LCM of 12, 24) = 24 units.

Efficiency: A = +2, B = −1. Net efficiency (A+B) = +1.

Work done by A in 4 mins = 4 × 2 = 8 units.

Remaining work = 24 − 8 = 16 units.

Time for remaining part = 16 ÷ 1 = 16 minutes.

∴ The correct answer is 16 minutes.

Alternate Method

Given: Pipe A fills for 4 minutes, then B is opened.

⇒ Work done by Pipe A in first 4 minutes = Efficiency × Time

⇒ 2 × 4 = 8 units

⇒ Remaining capacity to be filled = Total Work − Work Done

⇒ 24 − 8 = 16 units

⇒ When both pipes are open, Combined Efficiency = 2 + (−1) = 1 unit/min

⇒ Time taken to fill remaining tank = Remaining capacity ÷ Combined Efficiency

⇒ 16 ÷ 1 = 16 minutes

∴ The correct answer is 16 minutes.

Additional Information

Inlet and Outlet Pipes

An inlet pipe fills the tank (positive work), while an outlet pipe empties it (negative work).

Net Efficiency

If Pipe A fills in x hours and Pipe B empties in y hours, the net work per hour is (1/x − 1/y).

Remaining Work Concept

Always subtract the initial work done by the first pipe(s) from the total capacity before calculating time for the second phase.

Shortcut Trick

Numbers divisible by both 4 and 3 must be divisible by their LCM.

LCM of (4, 3) = 12.

Number of terms = Greatest Integer of (Upper Limit ÷ LCM).

Number of terms = [200 ÷ 12] = 16.66...

Taking the integer part, we get 16.

∴ The correct answer is 16.

Alternate Method

Given: Upper limit = 200, Divisors = 4 and 3.

Formula: Numbers divisible by both a and b are divisible by LCM(a, b).

⇒ LCM(4, 3) = 12

⇒ The sequence is an Arithmetic Progression (AP): 12, 24, 36, ..., 192

⇒ Here, First term (a) = 12, Common difference (d) = 12, Last term (l) = 192

⇒ l = a + (n − 1)d

⇒ 192 = 12 + (n − 1) × 12

⇒ 180 = (n − 1) × 12

⇒ 15 = n − 1

⇒ n = 16

∴ The correct answer is 16.

Additional Information

LCM Concept

To find numbers divisible by multiple divisors, always use their Least Common Multiple (LCM) as the effective divisor.

Arithmetic Progression (AP)

The number of terms n in an AP can be found using n = [(Last Term − First Term) ÷ Difference] + 1.

Divisibility of Range

If finding numbers between x and y, use [ (y−1) ÷ d ] − [ x ÷ d ] for exclusive boundaries.

Shortcut Trick

Assume an Assumed Mean as 50.

Find deviations from 50: +14, −39, +16, +48, −25, −33, 0, +25, +12.

Sum of deviations = 115 − 97 = +18.

Average deviation = 18 ÷ 9 = +2.

Arithmetic Mean = Assumed Mean + Average Deviation = 50 + 2 = 52.

∴ The correct answer is 52.

Alternate Method

Given: Observations = 64, 11, 66, 98, 25, 17, 50, 75, 62 and Total number of observations (n) = 9.

Formula Used: Arithmetic Mean = (Sum of all observations) ÷ (Total number of observations)

⇒ Sum = 64 + 11 + 66 + 98 + 25 + 17 + 50 + 75 + 62

⇒ Sum = 468

⇒ Arithmetic Mean = 468 ÷ 9

⇒ Arithmetic Mean = 52

∴ The correct answer is 52.

Additional Information

Properties of Arithmetic Mean

The algebraic sum of deviations of a set of observations from their arithmetic mean is always zero (Σ(x − Mean) = 0).

Combined Mean Formula

If two groups have sizes n₁, n₂ and means x₁, x₂, the Combined Mean = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Effect of Change in Origin and Scale

If every observation is increased by a constant k, the mean increases by k. If multiplied by k, the mean is multiplied by k.

Shortcut Trick

Use the algebraic identity: (2A + B)² = (4A² + B²) + 4AB.

Substitute the given values directly: (2A + B)² = 24 + 4(4).

⇒ (2A + B)² = 24 + 16 = 40.

⇒ 2A + B = ±√40 = ±2√10.

∴ The correct answer is ±2√10.

Alternate Method

Given:

4A² + B² = 24

AB = 4

Formula Used:

The standard expansion of the square of a sum: (x + y)² = x² + y² + 2xy

Calculations:

⇒ We need to find the value of 2A + B. Let us square this expression.

⇒ (2A + B)² = (2A)² + B² + 2 × (2A) × (B)

⇒ (2A + B)² = 4A² + B² + 4AB

⇒ Now, substitute the values 4A² + B² = 24 and AB = 4 into the equation:

⇒ (2A + B)² = 24 + 4 × 4

⇒ (2A + B)² = 24 + 16

⇒ (2A + B)² = 40

⇒ Taking the square root on both sides:

⇒ 2A + B = ±√40

⇒ 2A + B = ±√(4 × 10)

⇒ 2A + B = ±2√10

∴ The correct answer is ±2√10.

Additional Information

Algebraic Identity (a + b)²

The identity (a + b)² = a² + 2ab + b² is used to expand the square of a binomial or to find the sum of terms when their squares and product are known.

Algebraic Identity (a − b)²

The identity (a − b)² = a² − 2ab + b² helps in finding the difference between terms using similar logic.

Nature of Square Roots

In algebra, if x² = k (where k > 0), then x has two possible values: +√k and −√k, often written as ±√k.

Shortcut Trick

Salary is always 100%.

Savings = 35% ⇒ Expenditure = 100% − 35% = 65%.

Monthly Expenditure = 65% of ₹7,420.

Monthly Expenditure = 0.65 × 7420 = ₹4,823.

∴ The correct answer is ₹4,823.

Alternate Method

Given: Monthly Salary = ₹7,420 and Savings Percentage = 35%.

Formula Used: Expenditure = Total Salary − Savings

⇒ Monthly Savings = 35% of 7,420

⇒ Monthly Savings = (35 ÷ 100) × 7420

⇒ Monthly Savings = 0.35 × 7420 = ₹2,597

⇒ Monthly Expenditure = 7,420 − 2,597

⇒ Monthly Expenditure = ₹4,823

∴ The correct answer is ₹4,823.

Additional Information

Percentage Change

To find the percentage change, use the formula: (Change ÷ Original Value) × 100.

Successive Percentage

If a value is changed by a% and then by b%, the net change is [a + b + (ab ÷ 100)]%.

Base Change Rule

If A is x% more than B, then B is [x ÷ (100 + x)] × 100% less than A.

Shortcut Trick

The effective rate of compound interest for 2 years at 10% per annum = 10 + 10 + (10 × 10 / 100) = 21%.

Total Amount = Principal (100%) + Interest (21%) = 121% of the Principal.

Amount = 121% of ₹1,000 = 1.21 × 1000 = ₹1,210.

∴ The correct answer is ₹1,210.

Alternate Method

Given:

Principal (P) = ₹1,000

Rate (R) = 10% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 1000 × (1 + 10/100)²

⇒ A = 1000 × (110/100)²

⇒ A = 1000 × (11/10) × (11/10)

⇒ A = 1000 × (121 / 100)

⇒ A = 10 × 121

⇒ A = ₹1,210

∴ The correct answer is ₹1,210.

Additional Information

Effective Interest Rate

For two successive years with rate R%, the effective Compound Interest rate is R + R + (R×R/100)%.

CI and SI Difference

The difference between Compound Interest and Simple Interest for 2 years is given by P(R/100)².

Compounding Period

If interest is compounded half-yearly, the rate becomes R/2 and the time period becomes 2n.