Search Previous Year Questions

Shortcut Trick

Total Monthly Cost = Daily Units × Rate × Number of Days

Total Monthly Cost = 12 × 8 × 31

Total Monthly Cost = 96 × 31 = ₹2,976

∴ The correct answer is ₹2,976.

Alternate Method

Given:

Daily consumption of electricity = 12 units

Cost per unit = ₹8

Total duration = 31-day month

Formula Used:

Total Payment = (Units per day × Total days) × Rate per unit

⇒ Total units consumed in 31 days = 12 × 31

⇒ Total units consumed = 372 units

⇒ Total payment = 372 × 8

⇒ Total payment = ₹2,976

∴ The correct answer is ₹2,976.

Additional Information

Unitary Method

A technique for solving problems by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Total Expenditure Formula

Total Expenditure = Price × Consumption. If consumption is given as a daily rate, multiply by the number of days in the specific month.

Electricity Units (kWh)

1 Unit of electricity is equivalent to 1 kiloWatt-hour (kWh). The total bill is the product of Total Units × Slab Rate.

Shortcut Trick

Percentage difference between the two values = 45% − 20% = 25%

According to the question, this 25% corresponds to 48.

To find the total number (100%), we multiply by 4:

100% = 48 × 4 = 192

∴ The correct answer is 192.

Alternate Method

Given:

First percentage of the number = 45%

Second percentage of the same number = 20%

Numerical difference between them = 48

Formula Used:

Number = (Given Difference ÷ Percentage Difference) × 100

Calculations:

⇒ Let the required number be x.

⇒ 45% of x − 20% of x = 48

⇒ (45 − 20)% of x = 48

⇒ 25% of x = 48

⇒ (25 ÷ 100) × x = 48

⇒ x ÷ 4 = 48

⇒ x = 48 × 4

⇒ x = 192

∴ The correct answer is 192.

Additional Information

Percentage to Fraction Conversion

Always remember common fractional equivalents for faster calculation: 20% = 1/5, 25% = 1/4, 40% = 2/5, 50% = 1/2, and 75% = 3/4.

Net Percentage Change

When a number is changed by two successive percentages a% and b%, the net percentage change is given by the formula: (a + b + (a × b) ÷ 100)%.

Base Value Concept

Percentage calculations are always relative to a base value (100%). If the base increases, the absolute value of the percentage also increases proportionally.

Shortcut Trick

Net percentage change for a decrease of x% followed by an increase of x% is always a decrease of (x²/100)%.

Step 1: Net change for −30% and +30% = −(30²/100) = −9%.

Step 2: Apply successive change formula for −9% and +20%: a + b + (ab/100).

⇒ −9 + 20 + (−9 × 20)/100 = 11 − 1.8 = 9.2%.

Since the result is positive, it is an increase.

∴ The correct answer is 9.2% increase.

Alternate Method

Given: First year decrease = 30%, Second year increase = 30%, Third year increase = 20%.

Formula: Final Value = Initial Value × (1 ± r₁/100) × (1 ± r₂/100) × (1 ± r₃/100)

⇒ Let the initial value of the investment be 100.

⇒ Value after the first year = 100 − 30% of 100 = 70.

⇒ Value after the second year = 70 + 30% of 70 = 70 + 21 = 91.

⇒ Value after the third year = 91 + 20% of 91 = 91 + 18.2 = 109.2.

⇒ Overall percentage change = (Final Value − Initial Value) ÷ Initial Value × 100

⇒ Net change = (109.2 − 100) ÷ 100 × 100 = 9.2%.

∴ The correct answer is 9.2% increase.

Additional Information

Successive Percentage Formula

For two successive changes of a% and b%, the effective net change is given by (a + b + ab/100)%.

Fraction Method for Multi-Step Changes

Convert percentages to fractions (e.g., 20% = 1/5). For an increase, multiply by (1 + 1/5) = 6/5; for a decrease, multiply by (1 − 1/5) = 4/5.

Inverse Percentage Change

If a value increases by r%, it must decrease by [r/(100 + r)] × 100% to return to the original value.

Shortcut Trick

Assume all 400 questions are correct: 400 × 4 = 1600 marks.

Actual score = 1280 marks; Difference = 1600 − 1280 = 320 marks.

Loss per wrong/unattempted question = 4 (marks not gained) + 1 (penalty) = 5 marks.

Number of wrong/unattempted questions = 320 ÷ 5 = 64.

Number of correct questions = 400 − 64 = 336.

∴ The correct answer is 336.

Alternate Method

Given:

Total questions = 400

Marks for correct answer = +4

Marks for wrong/unattempted = −1

Total score obtained = 1280

Formula Used:

Total Score = (Number of Correct Answers × Marks per Correct) − (Number of Incorrect Answers × Negative Marks)

Calculations:

Let the number of correctly answered questions be C.

Let the number of wrong or unattempted questions be W.

⇒ C + W = 400 --- (i)

⇒ 4C − 1W = 1280 --- (ii)

Adding equations (i) and (ii):

⇒ (C + W) + (4C − W) = 400 + 1280

⇒ 5C = 1680

⇒ C = 1680 ÷ 5

⇒ C = 336

∴ The correct answer is 336.

Additional Information

Net Negative Marking Effect

For every wrong answer, the net loss is the sum of the positive marks and the penalty (e.g., 4 + 1 = 5). This is used in the "Assumption Method" to find the total incorrect count.

Accuracy Calculation

Accuracy % = (Number of Correct Answers ÷ Total Questions Attempted) × 100. In this case, since unattempted also carry a penalty, the base is the total 400 questions.

Alligation Method

This can be solved by comparing the average marks per question (1280 ÷ 400 = 3.2) against the individual marks (+4 and −1) to find the ratio of correct to wrong questions.

Shortcut Trick

Multiplying factor for 2 years = Amount ÷ Principal = 1.1025

Multiplying factor for 1 year = √1.1025 = 1.05

Rate of interest = (1.05 − 1) × 100 = 0.05 × 100 = 5%

∴ The correct answer is 5%.

Alternate Method

Given:

Time (n) = 2 years

Amount (A) = 1.1025 × Principal (P)

Formula Used:

A = P(1 + r/100)ⁿ

Calculations:

⇒ 1.1025 × P = P(1 + r/100)²

⇒ 1.1025 = (1 + r/100)²

⇒ √1.1025 = 1 + r/100

⇒ 1.05 = 1 + r/100

⇒ r/100 = 1.05 − 1

⇒ r/100 = 0.05

⇒ r = 5%

∴ The correct answer is 5%.

Additional Information

Successive Percentage Rule

For two years, if the annual rate is r%, the effective rate is given by r + r + (r × r)/100.

Amount for n years

When interest is compounded annually, the total amount after n years is A = P(1 + r/100)ⁿ.

Multiplying Factor

If a sum grows by r% every year, it is multiplied by (1 + r/100) each year. For 2 years, the factor is (1 + r/100)².

Shortcut Trick

Assume an Assumed Mean of 360.

Calculate deviations: (320−360), (400−360), (360−360), (340−360), (380−360)

Net Deviation = (−40) + (+40) + (0) + (−20) + (+20) = 0

Average = Assumed Mean + (Net Deviation ÷ Total Flats) = 360 + (0 ÷ 5) = 360

∴ The correct answer is 360 units.

Alternate Method

Given: Monthly consumption of five flats are 320, 400, 360, 340, and 380 units.

Formula Used: Average = Sum of all observations ÷ Total number of observations

⇒ Total Consumption = 320 + 400 + 360 + 340 + 380

⇒ Total Consumption = 1800 units

⇒ Number of Flats = 5

⇒ Average = 1800 ÷ 5

⇒ Average = 360 units

∴ The correct answer is 360 units.

Additional Information

Arithmetic Mean

It is the most common measure of central tendency, calculated as Σx ÷ n, where Σx is the sum of values and n is the count.

Properties of Mean

The sum of deviations of a set of observations from their arithmetic mean is always zero.

Combined Average

If two groups have sizes n₁, n₂ and averages a₁, a₂, then the combined average is (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Shortcut Trick

Net profit % on 1^st half = 60 − 25 − (60 × 25) ÷ 100 = 20%

Net profit % on 2^nd half = 80 − 30 − (80 × 30) ÷ 100 = 26%

Since both halves are equal in quantity, average profit is calculated.

Overall Profit % = (20% + 26%) ÷ 2 = 23%

∴ The correct answer is 23%.

Alternate Method

Given:

Initial markup percentage = 60%

Revised markup percentage for second half = 80%

Discount on first half = 25% | Discount on second half = 30%

Formula Used:

SP = CP × (100 + Markup %)/100 × (100 − Discount %)/100

Overall Profit % = [(Total SP − Total CP) ÷ Total CP] × 100

Let the total quantity be 2 units and cost price of each unit be 100.

⇒ Total Cost Price = 2 × 100 = 200

⇒ Selling Price of 1^st unit = 100 × (160/100) × (75/100) = 120

⇒ Selling Price of 2^nd unit = 100 × (180/100) × (70/100) = 126

⇒ Total Selling Price = 120 + 126 = 246

⇒ Total Profit = 246 − 200 = 46

⇒ Overall Profit Percentage = (46 ÷ 200) × 100 = 23%

∴ The correct answer is 23%.

Additional Information

Net Percentage Change

When a value changes by x% and then by y%, the net percentage change is given by the formula x + y + (xy ÷ 100). In profit-loss, markup is positive and discount is negative.

CP, MP, and Profit Relationship

The ratio of Marked Price to Cost Price can be directly calculated as MP ÷ CP = (100 + Profit %) ÷ (100 − Discount %).

Successive Discounts

If two successive discounts of d₁% and d₂% are given, the single equivalent discount is (d₁ + d₂ − d₁d₂ ÷ 100)%.

Shortcut Trick

The difference between a 12% Loss and an 8% Profit is 12% + 8% = 20%.

Given that this 20% difference is equal to ₹84.

20% of Cost Price (CP) = ₹84.

100% (Total CP) = 84 × 5 = ₹420.

∴ The correct answer is ₹420.

Alternate Method

Given:

Initial Loss = 12%

New Profit = 8%

Increase in Selling Price (SP) = ₹84

Formula Used:

SP = CP × (100 ± Profit/Loss)%

Calculations:

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

⇒ Initial Selling Price (SP₁) = 100 − 12 = 88 units.

⇒ New Selling Price (SP₂) = 100 + 8 = 108 units.

⇒ Difference in Selling Price = 108 − 88 = 20 units.

⇒ 20 units = ₹84.

⇒ 1 unit = 84 ÷ 20 = ₹4.2.

⇒ 100 units (CP) = 4.2 × 100 = ₹420.

⇒ Therefore, the Cost Price of the article is ₹420, which corresponds to Option 2.

∴ The correct answer is ₹420.

Additional Information

Profit and Loss on Cost Price

Unless stated otherwise, profit or loss percentage is always calculated on the Cost Price (CP). Formula: Profit % = (Profit ÷ CP) × 100.

Relation between CP and SP

If there is a profit of P%, then SP = CP × (100 + P)/100. If there is a loss of L%, then SP = CP × (100 − L)/100.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount. MP = CP + Markup.

Shortcut Trick

The Volume of a cylinder is calculated using the formula πr²h.

Since π = 22/7, the final result must be a multiple of 11.

Checking the options for divisibility by 11: In 4158, the sum of digits at odd positions (4+5=9) minus the sum of digits at even positions (1+8=9) is 0.

Thus, 4158 is the only option that satisfies the divisibility rule of 11.

∴ The correct answer is 4158 cm³.

Alternate Method

Given:

Radius (r) = 7 cm

Height (h) = 27 cm

π = 22/7

Formula Used:

Volume of a Cylinder = π × r² × h

Calculations:

⇒ Volume = (22/7) × 7 × 7 × 27

⇒ Volume = 22 × 7 × 27

⇒ Volume = 154 × 27

⇒ Volume = 4158 cm³

∴ The correct answer is 4158 cm³.

Additional Information

Curved Surface Area (CSA) of a Cylinder

The area of the curved surface only, excluding the top and bottom circles, is given by 2πrh.

Total Surface Area (TSA) of a Cylinder

The total area including the two circular bases and the curved surface: 2πr(h + r).

Volume of a Cone

If a cone has the same base radius and height as the cylinder, its volume is exactly one-third: (1/3)πr²h.

Given:

((3⁵ × 6⁴ × 4³) ÷ (3² × 6² × 4¹))

Formula used:

The Law of Exponents for division states: a^m ÷ aⁿ = a^m−n

Calculation:

Subtracting the powers of the terms with the same base:

⇒ 3⁵⁻² × 6⁴⁻² × 4³⁻¹

⇒ 3³ × 6² × 4²

Evaluating the exponential values:

⇒ 27 × 36 × 16

⇒ 972 × 16

⇒ 15552

∴ The correct answer is option (1).