Quantitative Aptitude PYQs

Shortcut Trick

When the distance is constant, the Average Speed = (2 × S₁ × S₂) ÷ (S₁ + S₂).

Average Speed = (2 × 9 × 45) ÷ (9 + 45)

Average Speed = 810 ÷ 54 = 15 km/hr.

∴ The correct answer is 15 km/hr.

Alternate Method

Given:

Speed to school (S₁) = 9 km/hr

Speed from school (S₂) = 45 km/hr

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Let the distance between home and school be 45 km (LCM of 9 and 45).

⇒ Time taken going (T₁) = 45 ÷ 9 = 5 hours

⇒ Time taken returning (T₂) = 45 ÷ 45 = 1 hour

⇒ Total Distance = 45 + 45 = 90 km

⇒ Total Time = 5 + 1 = 6 hours

⇒ Average Speed = 90 ÷ 6 = 15 km/hr

∴ The correct answer is 15 km/hr.

Additional Information

Average Speed (General Case)

It is the ratio of Total Distance traveled to the Total Time taken. Formula: V_avg = (d₁ + d₂ + ...) ÷ (t₁ + t₂ + ...)

Average Speed (Equal Time Intervals)

If a body travels at speed v₁ and v₂ for equal time intervals, the average speed is the Arithmetic Mean: (v₁ + v₂) ÷ 2.

Relative Speed

For two objects moving in the same direction, relative speed is |S₁ − S₂|. For opposite directions, it is (S₁ + S₂).

Shortcut Trick

Identify the minimum difference between any two numbers: 32 − 28 = 4 and 28 − 24 = 4.

The HCF must be a factor of this difference (4).

Check if 4 divides 32, 28, and 24 completely → Yes.

∴ The correct answer is 4.

Alternate Method

Given: Numbers are 32, 28, and 24.

Formula Used: Prime Factorization Method for finding Highest Common Factor (HCF).

⇒ Prime factors of 32 = 2 × 2 × 2 × 2 × 2 = 2⁵

⇒ Prime factors of 28 = 2 × 2 × 7 = 2² × 7

⇒ Prime factors of 24 = 2 × 2 × 2 × 3 = 2³ × 3

⇒ The HCF is the product of the lowest power of common prime factors.

⇒ Common prime factor is 2, and its lowest power is 2².

⇒ HCF = 2 × 2 = 4

∴ The correct answer is 4.

Additional Information

HCF Properties

The HCF of two or more numbers is the greatest number that divides each of them exactly. It is also known as GCD (Greatest Common Divisor).

Relationship between HCF and LCM

For two numbers a and b: HCF(a, b) × LCM(a, b) = a × b.

Division Method

To find HCF of large numbers, divide the larger by the smaller until the remainder is zero; the last divisor is the HCF.

Shortcut Trick

To find the age of the teacher when the average age increases, use the formula:

Teacher age = Old Average + (New Total Strength × Increase in Average)

Teacher age = 27 + (40 × 1) = 27 + 40 = 67

∴ The correct answer is 67 years.

Alternate Method

Given:

Number of students = 39

Initial average age = 27 years

Total members including teacher = 39 + 1 = 40

New average age = 28 years

Formula Used:

Total Sum = Average × Number of observations

Teacher age = (New Total Sum) − (Initial Total Sum)

Calculations:

⇒ Total age of 39 students = 39 × 27

⇒ Total age of 39 students = 1053 years

⇒ Total age including teacher = 40 × 28

⇒ Total age including teacher = 1120 years

⇒ Teacher age = 1120 − 1053

⇒ Teacher age = 67 years

∴ The correct answer is 67 years.

Additional Information

Net Deviation Method

The sum of deviations of all observations from their average is always zero. If the average increases by 1 for 40 people, the extra value brought by the new member must be 40 × 1.

Weighted Average Formula

Average_combined = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂), where n is the number of items and A is the average.

Replacement Rule

Age of new person = Age of replaced person + (Total count × Change in Average).

Shortcut Trick

कुल वर्तमान आयु = 42 वर्ष | 5 वर्ष बाद कुल आयु = 42 + (2 × 5) = 52 वर्ष

5 वर्ष बाद आयु का अनुपात (माता : पुत्री) = 3 : 1 | कुल अनुपात = 4

4 यूनिट = 52 → 1 यूनिट (पुत्री की 5 वर्ष बाद आयु) = 13 वर्ष

पुत्री की वर्तमान आयु = 13 − 5 = 8 वर्ष | माता की 5 वर्ष बाद आयु = 3 × 13 = 39 वर्ष

माता की 4 वर्ष बाद आयु = 39 − 1 = 38 वर्ष | अभीष्ट अनुपात = 8 : 38 = 4 : 19

∴ The correct answer is 4 : 19.

Alternate Method

दिया गया है: माता और पुत्री की वर्तमान आयु का योग = 42 वर्ष

सूत्र: अनुपात = मान 1 : मान 2

माना पुत्री की वर्तमान आयु = x वर्ष, तो माता की वर्तमान आयु = (42 − x) वर्ष

5 वर्ष बाद की स्थिति:

⇒ (42 − x + 5) = 3 × (x + 5)

⇒ 47 − x = 3x + 15

⇒ 4x = 32 ⇒ x = 8 वर्ष (पुत्री की वर्तमान आयु)

⇒ माता की वर्तमान आयु = 42 − 8 = 34 वर्ष

⇒ माता की 4 वर्ष बाद आयु = 34 + 4 = 38 वर्ष

⇒ अभीष्ट अनुपात = पुत्री (वर्तमान) : माता (4 वर्ष बाद) = 8 : 38

⇒ सरल करने पर = 4 : 19

∴ The correct answer is 4 : 19.

Additional Information

आयु योग नियम (Sum of Ages)

यदि n व्यक्तियों की वर्तमान आयु का योग S है, तो t वर्ष बाद उनकी आयु का योग S + (n × t) होगा।

आयु अंतर (Age Difference)

दो व्यक्तियों के बीच आयु का अंतर हमेशा स्थिर रहता है, चाहे वह वर्तमान हो, भविष्य हो या भूतकाल।

अनुपात परिवर्तन (Ratio Concept)

यदि A:B का वर्तमान अनुपात x:y है, तो k वर्ष बाद अनुपात (x+k):(y+k) होगा (जहाँ x और y वास्तविक मान हैं)।

Shortcut Trick

For any regular polygon, the sum of an interior angle and its corresponding exterior angle is always 180°.

Exterior angle = 180° − 156° = 24°

Number of sides (n) = 360° ÷ Exterior angle

n = 360 ÷ 24 = 15

∴ The correct answer is 15 sides.

Alternate Method

Given:

Interior angle of a regular polygon = 156°

Formula Used:

Interior angle of a regular polygon = [(n − 2) × 180°] ÷ n

Where n = number of sides of the polygon.

Calculations:

⇒ 156 = [(n − 2) × 180] ÷ n

⇒ 156n = 180n − 360

⇒ 180n − 156n = 360

⇒ 24n = 360

Shortcut Trick

Using the ratio method for successive changes:

Initial : Final ratio = (100 : 50) × (100 : 70) × (100 : 50) × (100 : 165)

⇒ Ratio = (2 : 1) × (10 : 7) × (2 : 1) × (20 : 33) = 800 : 231

⇒ Net decrease = (800 − 231) ÷ 800 × 100 = 569 ÷ 8 = 71.125%

∴ The correct answer is Decreases by 71.13%.

Alternate Method

Given: Successive changes are −50%, −30%, −50%, and +65%.

Formula Used: Final Price = Initial Price × (1 + r₁/100) × (1 + r₂/100) ...

Let the original price of fuel be 100.

⇒ Price after 1^st month = 100 × (1 − 0.50) = 50

⇒ Price after 2^nd month = 50 × (1 − 0.30) = 35

⇒ Price after 3^rd month = 35 × (1 − 0.50) = 17.5

⇒ Price after 4^th month = 17.5 × (1 + 0.65) = 17.5 × 1.65 = 28.875

⇒ Net percentage change = (Initial − Final) / Initial × 100

⇒ Percentage change = (100 − 28.875) ÷ 100 × 100 = 71.125%

∴ The correct answer is Decreases by 71.13%.

Additional Information

Successive Percentage Change

For two changes a% and b%, effective change = a + b + (ab/100). This can be extended to multiple changes.

Ratio Method for Percentage

Express each percentage change as a fraction (e.g., 50% decrease = 1/2). Final Value = Initial Value × (Product of multipliers).

Base Value Selection

Taking 100 as the initial base simplifies percentage calculations as the absolute change directly equals the percentage change.

Shortcut Trick

The unit digit of the edge length 45 is 5.

The Volume of a cube is (Edge)³, so its unit digit will be 5 × 5 × 5 = 125, which ends in 5.

Among the given options, only 91125 ends with the digit 5.

∴ The correct answer is 91125 m³.

Alternate Method

Given:

Edge length of the cube (a) = 45 m

Formula Used:

Volume of a cube = a³ (where a is the edge of the cube)

Calculations:

⇒ Volume = 45³

⇒ Volume = 45 × 45 × 45

⇒ Volume = 2025 × 45

⇒ Volume = 91125 m³

∴ The correct answer is 91125 m³.

Additional Information

Total Surface Area of a Cube

The total area of all six faces of the cube is given by 6a².

Diagonal of a Cube

The longest distance between two opposite vertices is calculated as a√3.

Lateral Surface Area

The area of the four side faces (excluding top and bottom) is 4a².

Shortcut Trick

Let the number be N.

Given: 20% × 10% × (3/4) × N = 882

(1/5) × (1/10) × (3/4) × N = 882

3N / 200 = 882

N = (882 × 200) / 3 = 294 × 200 = 58800

∴ The correct answer is 58800.

Alternate Method

Given: 20% of 10% of 3/4 of a number = 882

⇒ Let the number be x.

⇒ (20/100) × (10/100) × (3/4) × x = 882

⇒ (1/5) × (1/10) × (3/4) × x = 882

⇒ (3/200) × x = 882

⇒ x = (882 × 200) ÷ 3

⇒ x = 294 × 200

⇒ x = 58800

∴ The correct answer is 58800.

Additional Information

Percentage to Fraction Conversion

To simplify calculations, convert percentages to fractions: 20% = 1/5 and 10% = 1/10.

Successive Percentage

When multiple percentages are applied to a number, they are multiplied together as factors: x × a% × b%.

Base Change Rule

If a number is increased or decreased, the new base for the next percentage calculation is the resulting value from the previous step.

Shortcut Trick

Total amount to be divided after deductions = 2037 − (23 + 42 + 52) = 2037 − 117 = ₹1920.

Ratio of remaining shares = 14 : 19 : 15. Sum of ratios = 14 + 19 + 15 = 48 units.

48 units = ₹1920 ⇒ 1 unit = ₹40.

Tina remaining share = 19 units × 40 = ₹760.

Tina actual share = ₹760 + 42 = ₹802.

∴ The correct answer is ₹802.

Alternate Method

Given: Total amount = ₹2,037. Deductions = ₹23, ₹42, ₹52. Ratio = 14:19:15.

Formula: Actual Share = (Ratio Share × Remaining Total / Sum of Ratios) + Deduction

⇒ Total Deduction = 23 + 42 + 52 = ₹117

⇒ Remaining Amount = 2037 − 117 = ₹1920

⇒ Let shares be 14x, 19x, and 15x.

⇒ 14x + 19x + 15x = 1920

⇒ 48x = 1920 ⇒ x = 40

⇒ Tina remaining share = 19 × 40 = ₹760

⇒ Tina actual share = 760 + 42 = ₹802

∴ The correct answer is ₹802.

Additional Information

Ratio and Proportion

Ratio is a comparison of two quantities of the same kind. If a sum S is divided in ratio a:b:c, the shares are [a/(a+b+c)]×S, [b/(a+b+c)]×S, and [c/(a+b+c)]×S respectively.

Inverse Variation

When two quantities are such that an increase in one leads to a decrease in the other, they are in inverse proportion (x × y = k).

Shortcut Trick

(1/3)^-2 = 9 and (1/2)^-3 = 8

{9 − 8} ÷ (1/4)^-2 = 1 ÷ 16 = 1/16

(-3/2)⁴ × (5/3)⁴ = [(−5/2)]⁴ = 625/16

Total = 1/16 + 625/16 = 626/16

∴ Answer = 313/8

Alternate Method

Given:

{ (1/3)^-2 − (1/2)^-3 } ÷ (1/4)^-2 + { (−3/2)⁴ × (5/3)⁴ }

Formula Used:

a⁻ⁿ = 1/aⁿ, (a/b)ⁿ × (c/d)ⁿ = [(ac)/(bd)]ⁿ

Calculation:

{ (1/3)-2 − (1/2)-3 } ÷ (1/4)-2 + { (−3/2)4 × (5/3)4 }

⇒ (3² − 2³) ÷ 4² + [ (−3/2 × 5/3)⁴ ]

⇒ (9 − 8) ÷ 16 + (−5/2)⁴

⇒ 1 ÷ 16 + 625/16

⇒ 626/16

⇒ 313/8

∴ The correct answer is 313/8.

Additional Information

Negative Powers

a⁻ⁿ = 1/aⁿ

Power Multiplication

(a/b)ⁿ × (c/d)ⁿ = [(ac)/(bd)]ⁿ

Even Power

Negative base becomes positive when power is even

Shortcut Trick

Loss of 5% means SP₁ is 95% of CP.

Gain of 5% means SP₂ must be 105% of CP.

Using the unitary method: 95% ⇒ ₹1805.

1% ⇒ 1805 ÷ 95 = ₹19.

105% ⇒ 19 × 105 = ₹1995.

∴ The correct answer is ₹ 1995.

Alternate Method

Given: Selling Price (SP₁) = ₹1805, Loss% = 5%, Required Gain% = 5%.

Formulas: CP = [SP × 100] ÷ [100 − Loss%], SP = [CP × (100 + Gain%)] ÷ 100.

⇒ First, find the Cost Price (CP): CP = [1805 × 100] ÷ (100 − 5) = [1805 × 100] ÷ 95.

⇒ CP = 19 × 100 = ₹1900.

⇒ Now, find the New Selling Price (SP₂) for 5% gain: SP₂ = [1900 × (100 + 5)] ÷ 100.

⇒ SP₂ = [1900 × 105] ÷ 100 = 19 × 105.

⇒ SP₂ = ₹1995.

∴ The correct answer is ₹ 1995.

Additional Information

Relation between SP and CP

When Profit occurs, SP = CP + Profit. When Loss occurs, SP = CP − Loss. CP is always considered 100% in percentage calculations.

Direct Ratio Method

If CP is constant, SP₁ ÷ (100 − L%) = SP₂ ÷ (100 + G%). This helps in solving questions involving change in profit/loss percentages quickly.

Shortcut Trick

The relationship between Cost Price (CP) and Marked Price (MP) is given by the ratio:

CP : MP = (100 − Discount%) : (100 + Profit%)

Given: Discount = 65% and Profit = 82%.

CP : MP = (100 − 65) : (100 + 82) = 35 : 182.

Dividing both sides by 7: 35 ÷ 7 : 182 ÷ 7 = 5 : 26.

∴ The correct answer is 5 : 26.

Alternate Method

Formulas: SP = CP × (100 + Profit%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100

⇒ Let CP be 100.

⇒ SP = 100 + 82% of 100 = 182.

⇒ SP is also equal to MP × (100 − 65) ÷ 100 = MP × 35 ÷ 100.

⇒ 182 = MP × 35 ÷ 100 ⇒ MP = (182 × 100) ÷ 35 = 520.

⇒ Ratio CP : MP = 100 : 520 = 10 : 52 = 5 : 26.

∴ The correct answer is 5 : 26.

Additional Information

Marked Price & Discount

The price at which an article is listed is the Marked Price (MP). Discount is always calculated on the MP.

Profit on Cost Price

Profit or loss is always calculated on the Cost Price (CP) unless otherwise stated.

Shortcut Trick

Ratio of Time = 1 : 1.5 = 2 : 3

Using weighted average: Average Speed = (S₁×T₁ + S₂×T₂) ÷ (T₁ + T₂)

52 = (70×2 + p×3) ÷ 5

260 = 140 + 3p ⇒ 3p = 120 ⇒ p = 40

∴ The correct answer is 40 km/hr.

Alternate Method

Given: Speed 1 = 70 km/hr, Time 1 = 1 hr, Speed 2 = p km/hr, Time 2 = 1.5 hr, Avg Speed = 52 km/hr.

Formula Used: Total Distance = Average Speed × Total Time

⇒ Total Distance = (70 × 1) + (p × 1.5) = 70 + 1.5p

⇒ Total Time = 1 + 1.5 = 2.5 hours

⇒ Average Speed = Total Distance ÷ Total Time

⇒ 52 = (70 + 1.5p) ÷ 2.5

⇒ 52 × 2.5 = 70 + 1.5p

⇒ 130 = 70 + 1.5p

⇒ 1.5p = 60

⇒ p = 60 ÷ 1.5 = 40

∴ The correct answer is 40 km/hr.

Additional Information

Average Speed Formula

Average Speed = Total Distance ÷ Total Time. It is not the simple arithmetic mean of speeds unless times are equal.

Harmonic Mean Case

If a car covers two equal distances at speeds x and y, then the average speed = 2xy ÷ (x + y).

Weighted Average Property

The average speed always lies between the minimum and maximum individual speeds of the journey segments.

Shortcut Trick

Total Work = LCM(12, 15, 20) = 60 units.

Efficiencies: (A+B) = 5, (B+C) = 4, (C+A) = 3.

2(A+B+C) = 5+4+3 = 12 → (A+B+C) = 6.

Efficiency of B = (A+B+C) − (C+A) = 6 − 3 = 3.

Efficiency of C = (A+B+C) − (A+B) = 6 − 5 = 1.

Ratio of Days = Inverse Ratio of Efficiency = 1 : 3.

∴ The correct answer is 1:3.

Alternate Method

Given: (A+B) = 12 days, (B+C) = 15 days, (C+A) = 20 days.

Formula Used: Efficiency = Total Work ÷ Time; Time ∝ 1 ÷ Efficiency.

⇒ 2(A + B + C) = 5 + 4 + 3 = 12

⇒ Efficiency of (A + B + C) = 6

⇒ Efficiency of B = (A + B + C) − (A + C) = 6 − 3 = 3 units/day

⇒ Efficiency of C = (A + B + C) − (A + B) = 6 − 5 = 1 unit/day

⇒ Days taken by B = 60 ÷ 3 = 20 days

⇒ Days taken by C = 60 ÷ 1 = 60 days

⇒ Ratio of days (B : C) = 20 : 60 = 1 : 3

∴ The correct answer is 1:3.

Additional Information

Inverse Relation Rule

For a constant amount of work, the time taken is inversely proportional to the efficiency of the worker (Time₁/Time₂ = Efficiency₂/Efficiency₁).

Combined Work Formula

If individuals work in pairs, the total efficiency is half the sum of paired efficiencies: (A+B+C) = [(A+B) + (B+C) + (C+A)] ÷ 2.

LCM Method

Taking the Least Common Multiple of time periods as the total work simplifies calculation by avoiding fractions.

Shortcut Trick

Selling Price = Marked Price × (100 − Discount%) ÷ 100

SP = 2,400 × (100 − 16) ÷ 100

SP = 2,400 × (84 ÷ 100) = 24 × 84

SP = 2,016

∴ The correct answer is ₹2,016.

Alternate Method

Given: Marked Price (MP) = ₹2,400, Discount Percentage = 16%.

Formulas: Discount = MP × (Discount% ÷ 100) | Selling Price (SP) = MP − Discount

⇒ Discount Amount = 2,400 × (16 ÷ 100)

⇒ Discount Amount = 24 × 16 = ₹384

⇒ Selling Price = 2,400 − 384

⇒ Selling Price = ₹2,016

∴ The correct answer is ₹2,016.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on the label. Discount is always calculated on the Marked Price unless otherwise specified.

Profit/Loss vs. Discount

While Discount is the reduction from the Marked Price, Profit or Loss is determined by the difference between the Selling Price and the Cost Price.

Shortcut Trick

For divisibility by 72, the number must be divisible by 8 and 9.

Check 8: Last three digits 47x must be divisible by 8 ⇒ x = 2.

Check 9: Sum of digits (8+3+y+5+4+7+2) = 29 + y must be divisible by 9 ⇒ y = 7.

Required value: x² + y² = 2² + 7² = 4 + 49 = 53.

∴ The correct answer is 53.

Alternate Method

Given: Number 83y547x is divisible by 72.

Formula Used: Divisibility by 72 requires divisibility by 8 (co-prime factor 1) and 9 (co-prime factor 2).

Step 1: Divisibility by 8

⇒ The last three digits 47x must be divisible by 8.

⇒ 472 ÷ 8 = 59 (remainder 0).

⇒ x = 2.

Step 2: Divisibility by 9

⇒ The sum of digits 8 + 3 + y + 5 + 4 + 7 + 2 must be divisible by 9.

⇒ 29 + y must be divisible by 9.

⇒ The nearest multiple of 9 after 29 is 36.

⇒ 29 + y = 36 ⇒ y = 7.

Step 3: Final Calculation

⇒ Sum of squares = x² + y²

⇒ 2² + 7² = 4 + 49 = 53.

∴ The correct answer is 53.

Additional Information

Divisibility Rule of 8

A number is divisible by 8 if the last three digits are divisible by 8 or are zeros.

Divisibility Rule of 9

A number is divisible by 9 if the sum of all its digits is divisible by 9.

Composite Divisibility

To check divisibility by a composite number like 72, break it into co-prime factors (8 and 9) and check for each.

Shortcut Trick

Net deviation of first 7 numbers from Average 92: (−62) + (−60) + (−46) + (−11) + (+18) + (−19) + (−72) = −252.

To maintain the overall average, the remaining 6 numbers must compensate for this loss.

Average compensation required = 252 ÷ 6 = +42.

Average of remaining numbers = 92 + 42 = 134.

∴ The correct answer is 134.

Alternate Method

Given: Total numbers = 13 | Average = 92 | First 7 numbers = 30, 32, 46, 81, 110, 73, 20.

Formula Used: Sum = Average × Number of terms | Average = Sum ÷ Number of terms.

⇒ Total sum of 13 numbers = 13 × 92 = 1196

⇒ Sum of first 7 numbers = 30 + 32 + 46 + 81 + 110 + 73 + 20 = 392

⇒ Sum of remaining 6 numbers = 1196 − 392 = 804

⇒ Average of remaining 6 numbers = 804 ÷ 6 = 134

∴ The correct answer is 134.

Additional Information

Deviation Method for Averages

The sum of deviations of all observations from their mean is always zero. This is used to find missing values or averages of subgroups quickly.

Weighted Average Formula

If two groups have sizes n₁, n₂ and averages A₁, A₂, then Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Effect of Change in Values

If every number in a set is increased or decreased by a constant k, the average of the set also increases or decreases by k.

Shortcut Trick

Required percentage = (Value 1 ÷ Value 2) × 100

Value 1 = 1/30, Value 2 = 2/70 = 1/35

Percentage = (1/30 ÷ 1/35) × 100 = (35/30) × 100 = (7/6) × 100

7/6 × 100 = 1.1666... × 100 = 116.67%

∴ The correct answer is 116.67%.

Alternate Method

Given: First fraction = 1/30, Second fraction = 2/70

Formula Used: Percentage = (Part/Whole) × 100

Calculations:

⇒ Let 1/30 be x% of 2/70.

⇒ 1/30 = (x/100) × (2/70)

⇒ 1/30 = (x/100) × (1/35)

⇒ x = (35/30) × 100

⇒ x = (7/6) × 100

⇒ x = 700/6 = 116.666...

⇒ Rounding off to two decimal places, x = 116.67

∴ The correct answer is 116.67%.

Additional Information

Fraction to Percentage Conversion

To convert any fraction a/b to a percentage, multiply it by 100 and add the % symbol.

Reciprocal Fraction Values

1/6 is approximately 16.67%. Therefore, 7/6 can be calculated as 100% + 16.67% = 116.67%.

Rounding Off Rules

If the third decimal digit is 5 or greater, increase the second decimal digit by 1. Here, 116.666... becomes 116.67.

Shortcut Trick

Total days from 6 February 2023 to 20 April 2023 = 22 (Feb) + 31 (Mar) + 20 (Apr) = 73 days.

Time in years = 73 ÷ 365 = 1/5 year.

Interest for 1 year = 7% of ₹2,000 = ₹140.

Simple Interest for 1/5 year = 140 ÷ 5 = ₹28.

∴ The correct answer is ₹28.

Alternate Method

Given:

Principal (P) = ₹2,000

Rate (R) = 7% per annum

Time Calculation:

February (non-leap year) = 28 − 6 = 22 days

March = 31 days

April = 20 days

⇒ Total Days = 22 + 31 + 20 = 73 days

⇒ Time (T) = 73/365 year = 1/5 year

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ SI = (2000 × 7 × 1/5) ÷ 100

⇒ SI = (2000 × 7) ÷ (100 × 5)

⇒ SI = 14000 ÷ 500

⇒ SI = 140 ÷ 5

⇒ SI = ₹28

∴ The correct answer is ₹28.

Additional Information

Simple Interest (SI) Formula

Interest remains constant every year and is calculated only on the principal amount: SI = (P × R × T) ÷ 100.

Day Calculation Rule

While calculating the number of days, usually the day of deposit is excluded and the day of withdrawal is included.

Standard Conversions

In interest problems, 73 days is exactly 1/5 of a year (365 ÷ 73 = 5), and 146 days is 2/5 of a year.

Leap Year Check

If the year is divisible by 4, it is a leap year (29 days in Feb), otherwise, it has 28 days.

Shortcut Trick

Combined Efficiency = (Total Work ÷ A) + (Total Work ÷ B) + (Total Work ÷ C)

Using LCM (2, 24, 8) = 24 as Total Work.

Combined Efficiency = 12 + 1 + 3 = 16 units/day.

Time for twice the work = (2 × 24) ÷ 16 = 48 ÷ 16 = 3 days.

∴ The correct answer is 3 days.

Alternate Method

Given:

Time taken by A = 2 days

Time taken by B = 24 days

Time taken by C = 8 days

Calculations:

⇒ Total Work (LCM of 2, 24, 8) = 24 units

⇒ Combined efficiency of A + B + C = 12 + 1 + 3 = 16 units/day

⇒ Total work to be done = 2 × 24 = 48 units

⇒ Time taken = 48 ÷ 16 = 3 days

∴ The correct answer is 3 days.

Additional Information

Total Work Formula

Total Work = Efficiency × Time. If work is doubled, the time taken at constant efficiency also doubles.

Combined Efficiency

When individuals work together, their individual efficiencies are added to find the net rate of work.

Work and Wages

Wages are generally distributed in the ratio of efficiency or the ratio of work done by each individual.