Quantitative Aptitude PYQs

Shortcut Trick

Factor out common term: tan²θ (tan²θ + 1)

Use identity: 1 + tan²θ = sec²θ

Substitute tan²θ = (sec²θ − 1)

Final Step: (sec²θ − 1) × sec²θ = sec⁴θ − sec²θ

∴ The correct answer is sec⁴θ − sec²θ.

Alternate Method

Given:

Expression: tan⁴θ + tan²θ

Formula Used:

Fundamental Trigonometric Identity: 1 + tan²θ = sec²θ

⇒ Expression = tan⁴θ + tan²θ

⇒ Taking tan²θ as common: tan²θ(tan²θ + 1)

⇒ From identity sec²θ = 1 + tan²θ, we have (tan²θ + 1) = sec²θ

⇒ Also, tan²θ = sec²θ − 1

⇒ Substituting these values: (sec²θ − 1) × sec²θ

⇒ Expanding the bracket: (sec²θ × sec²θ) − (1 × sec²θ)

⇒ Result = sec⁴θ − sec²θ

∴ The correct answer is sec⁴θ − sec²θ.

Additional Information

Standard Pythagorean Identities

There are three primary identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Reciprocal Relations

secθ = 1/cosθ and tanθ = sinθ/cosθ. Squaring these helps in converting between higher powers of different trigonometric ratios.

Algebraic Manipulations in Trigonometry

Always look for common factors like tan²θ or sin²θ to simplify complex powers into standard squared identities.

Shortcut Trick

Each additional side in a polygon adds 180° to the sum of interior angles.

Divide the total sum by 180° to find the value of (n − 2).

4500 ÷ 180 = 25

Number of sides (n) = 25 + 2 = 27

∴ The correct answer is 27.

Alternate Method

Given: Sum of interior angles = 4500°

Formula Used: Sum of interior angles of a polygon = (n − 2) × 180°

⇒ (n − 2) × 180 = 4500

⇒ n − 2 = 4500 ÷ 180

⇒ n − 2 = 25

⇒ n = 25 + 2

⇒ n = 27

∴ The correct answer is 27.

Additional Information

Exterior Angle Sum

The sum of the exterior angles of any convex polygon is always 360° regardless of the number of sides.

Regular Polygon Interior Angle

Each interior angle of a regular polygon is given by [(n − 2) × 180°] ÷ n.

Number of Diagonals

The number of diagonals in a polygon with n sides is calculated as [n × (n − 3)] ÷ 2.

Interior and Exterior Relation

At each vertex of a polygon, the sum of the interior angle and the corresponding exterior angle is 180°.

Shortcut Trick

Solve the nested expression from the innermost square root outwards.

Step 1: √(850 − 66) = √784 = 28

Step 2: √(1268 + 28) = √1296 = 36

Step 3: √(2061 − 36) = √2025 = 45

∴ The correct answer is 45.

Alternate Method

Given expression: √(2061 − √(1268 + √(850 − 66)))

Simplifying the innermost term:

⇒ 850 − 66 = 784

⇒ √784 = 28

Substituting back into the expression:

⇒ √(2061 − √(1268 + 28))

⇒ √(2061 − √1296)

Since 36² = 1296:

⇒ √(2061 − 36)

⇒ √2025

Since 45² = 2025:

⇒ 45

∴ The correct answer is 45.

Additional Information

Perfect Squares Ending in 5

To find the square of a number ending in 5 (n5), the result is [n × (n+1)] followed by 25. For example, 45² = [4 × 5]25 = 2025.

Order of Operations (VBODMAS)

In simplification problems with nested radicals or brackets, always evaluate from the innermost level to the outermost level.

Common Square Roots

Memorizing squares up to 50 is vital for competitive exams. √784 = 28 and √1296 = 36 are frequently appearing values.

Shortcut Trick

Successive Multiplier Method: MP × (100 − D)% × (100 + VAT)% = SP

x × (37/100) × (125/100) = 481

x × 0.37 × 1.25 = 481

x = 481 / 0.4625 = 1040

∴ The correct answer is 1,040.

Alternate Method

Given: Marked Price (MP) = ₹x, Discount = 63%, VAT = 25%, Final Selling Price = ₹481

⇒ Discounted Price (DP) = x − 63% of x = 37% of x = 0.37x

⇒ Final SP = DP + VAT = 0.37x + 25% of 0.37x

⇒ 481 = 0.37x × (1 + 25/100)

⇒ 481 = 0.37x × 1.25

⇒ 481 = 0.4625x

⇒ x = 481 / 0.4625

⇒ x = (481 × 10000) / 4625

⇒ x = 1,040

∴ The correct answer is 1,040.

Additional Information

Marked Price and Discount

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

VAT/Sales Tax

Value Added Tax is a percentage added to the net selling price. Final Price = SP × (100 + VAT%)/100.

Successive Percentage Change

If an initial value x undergoes multiple percentage changes a% and b%, final value = x(1 + a/100)(1 + b/100).

Shortcut Trick

Effective rate for 2 years at 20% p.a. = 20 + 20 + (20 × 20)/100 = 44%

Total Amount percentage = 100% (Principal) + 44% (Interest) = 144%

Amount = 144% of ₹6,200 = 1.44 × 6200

Amount = ₹8,928

∴ The correct answer is ₹8,928.

Alternate Method

Given:

Principal (P) = ₹6,200

Rate (R) = 20% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 6200 × (1 + 20/100)²

⇒ A = 6200 × (120/100)²

⇒ A = 6200 × (1.2)²

⇒ A = 6200 × 1.44

⇒ A = 8928

∴ The correct answer is ₹8,928.

Additional Information

CI vs SI Difference for 2 Years

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

Successive Percentage Change

For two successive changes of x% and y%, the effective change is [x + y + (xy/100)]%.

Quarterly Compounding

When interest is compounded quarterly, the rate becomes R/4 and the time becomes 4n.

Shortcut Trick

72% of voters = 8640

1% of voters = 8640 ÷ 72 = 120

Total voters next year (8% increase) = 100% + 8% = 108%

Next year total = 120 × 108 = 12,960

∴ The correct answer is 12,960.

Alternate Method

Given: Cast votes = 8640 (72% of current total) | Growth = 8%.

Formula: Current Total = (Given Value ÷ Current Percentage) × 100.

⇒ Let total current eligible voters be V_c.

⇒ 0.72 × V_c = 8640

⇒ V_c = 8640 ÷ 0.72 = 12,000

⇒ Next year growth = 8% of 12,000

⇒ Growth = 0.08 × 12,000 = 960

⇒ Total eligible voters next year = 12,000 + 960 = 12,960

∴ The correct answer is 12,960.

Additional Information

Percentage Increase Formula

New Value = Old Value × (1 + Growth Rate ÷ 100). For an 8% increase, multiply by 1.08.

Base Value Concept

When a percentage of a quantity is known, divide the value by its percentage to find 1% of the base, then multiply by the desired target percentage.

Multiplying Factor (MF)

A growth of x% means MF = (100 + x) ÷ 100. A decrease of x% means MF = (100 − x) ÷ 100.

Shortcut Trick

Ratio of shares = 7 : 13 : 9

Difference between largest (13) and smallest (7) = 6 units

Given: 6 units = ₹58,326

1 unit = 58,326 ÷ 6 = ₹9,721

Total units = 7 + 13 + 9 = 29 units

Total profit = 29 × 9,721 = ₹2,81,909

∴ The correct answer is ₹2,81,909.

Alternate Method

Given:

Ratio of shares of three partners = 7 : 13 : 9

Difference between the smallest and largest share = ₹58,326

Formula:

Individual Share = (Individual Ratio Part ÷ Total Ratio Parts) × Total Profit

Let the shares of the three partners be 7x, 13x, and 9x.

⇒ Smallest share = 7x

⇒ Largest share = 13x

⇒ Difference = 13x − 7x = 6x

⇒ 6x = 58,326

⇒ x = 58,326 ÷ 6

⇒ x = 9,721

⇒ Total profit = 7x + 13x + 9x = 29x

⇒ Total profit = 29 × 9,721

⇒ Total profit = 2,81,909

∴ The correct answer is ₹2,81,909.

Additional Information

Partnership Profit Ratio

Profit is always distributed in the ratio of the product of Capital and Time: P₁ : P₂ = (C₁ × T₁) : (C₂ × T₂).

Simple Partnership

When investments of all partners are for the same duration, the profit is distributed simply in the ratio of their investments.

Ratio Unitary Method

If the difference between two parts is D and their ratio parts are a and b, then 1 unit = D ÷ |a − b|. Total value = (Sum of all ratio parts) × (Value of 1 unit).

Shortcut Trick

Marked Price (100%) = ₹2,000

Discount = 10%

Selling Price = 100% − 10% = 90%

SP = 90% of 2,000 = 0.9 × 2,000 = ₹1,800

∴ The correct answer is ₹1,800.

Alternate Method

Given: Marked Price (MP) = ₹2,000 | Discount % = 10%

Formula Used: Selling Price (SP) = MP − Discount | Discount = (Discount% / 100) × MP

⇒ Discount = (10 / 100) × 2,000

⇒ Discount = 0.1 × 2,000 = ₹200

⇒ SP = 2,000 − 200

⇒ SP = ₹1,800

∴ The correct answer is ₹1,800.

Additional Information

Marked Price and Discount

Marked Price is the price printed on an item. Discount is always calculated on the Marked Price unless stated otherwise. Formula: SP = MP × (100 − Discount%)/100.

Successive Discounts

If two successive discounts of a% and b% are given, the effective single discount is (a + b − ab/100)%.

Markup Percentage

Markup is the extra value added to the Cost Price to arrive at the Marked Price. Markup % = (MP − CP)/CP × 100.

Shortcut Trick

To compare ratios P = 5/2 and Q = 3/7, use the cross-multiplication method.

Multiply the numerator of P by the denominator of Q: 5 × 7 = 35.

Multiply the numerator of Q by the denominator of P: 3 × 2 = 6.

Since 35 > 6, the first ratio P is greater than the second ratio Q.

∴ The correct answer is P > Q.

Alternate Method

Given: P = 5:2 and Q = 3:7

Convert the ratios into their decimal equivalents for direct comparison.

⇒ Value of P = 5 ÷ 2

⇒ P = 2.5

⇒ Value of Q = 3 ÷ 7

⇒ Q ≈ 0.428

⇒ Comparing the values: 2.5 > 0.428

⇒ P > Q

∴ The correct answer is P > Q.

Additional Information

Ratio Comparison Rule

For two ratios a:b and c:d, if (a × d) > (b × c), then a:b > c:d. This is known as the cross-product method.

Inverse Ratio

The inverse ratio of a:b is b:a. For example, the inverse of P (5:2) is 2:5.

Compounded Ratio

The compounded ratio of a:b and c:d is calculated as (a × c) : (b × d). Here, the compounded ratio of P and Q is 15:14.

Shortcut Trick

Total Expenditure = 1120 + 915 = ₹2035

Total Number of Books = 52 + 47 = 99

Average Price per Book = Total Expenditure ÷ Total Books

Average = 2035 ÷ 99 = 20.555...

Average ≈ 20.56

∴ The correct answer is 20.56.

Alternate Method

Given:

Price of 52 books = ₹1,120

Price of 47 books = ₹915

Formula Used:

Average = (Total Sum of Observations) ÷ (Total Number of Observations)

Calculations:

⇒ Total books purchased by Keshav = 52 + 47 = 99

⇒ Total money spent by Keshav = 1120 + 915 = ₹2035

⇒ Average price per book = 2035 ÷ 99

⇒ Average price = 20.5555...

⇒ Rounding to two decimal places, we get 20.56

∴ The correct answer is 20.56.

Additional Information

Weighted Average

When groups have different sizes, use the formula A_w = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n is quantity and x is the value.

Rounding Rules

To round to 2 decimal places, look at the 3^rd decimal. If it is 5 or more, increase the 2^nd decimal by 1.

Unitary Method

To find the value of one item, divide the total value by the total number of items.

Shortcut Trick

Total % of votes = 100%

Votes for C = 100% − (18% + 43%) = 39%

Ranking: B (43%) > C (39%) > A (18%) ∴ Runner up is C

Winning Margin = 43% − 39% = 4%

4% units = 6,996 → 1% unit = 1,749

Total votes (100%) = 1,749 × 100 = 1,74,900

∴ The correct answer is 1,74,900.

Alternate Method

Given:

Votes of A = 18%

Votes of B = 43%

Winning margin (B over Runner up) = 6,996

Formula Used:

Percentage of value = (Part ÷ Total) × 100

⇒ Let total number of votes be X.

⇒ Percentage of votes for C = 100% − (18% + 43%)

⇒ Percentage of votes for C = 100% − 61% = 39%

⇒ Comparison of votes: B (43%) > C (39%) > A (18%)

⇒ Since C is on second rank, B won the election over C.

⇒ Margin in percentage = 43% − 39% = 4%

⇒ According to question: 4% of X = 6,996

⇒ (4 ÷ 100) × X = 6,996

⇒ X = (6,996 × 100) ÷ 4

⇒ X = 1,749 × 100 = 1,74,900

∴ The correct answer is 1,74,900.

Additional Information

Percentage Difference

When comparing two percentages of the same base, the difference in their percentage values directly represents the difference in their absolute values relative to the base.

Total Votes Calculation

In election problems, Total Votes = Valid Votes + Invalid Votes. If not specified, all votes are considered valid and distributed among candidates.

Successive Percentage Formula

For two successive changes of a% and b%, the effective change is given by: [a + b + (ab ÷ 100)]%.

Shortcut Trick

Successive Discount Formula = (a + b − ab/100)%

Here a = 29 and b = 28

⇒ Equivalent Discount = (29 + 28 − (29 × 28)/100)%

⇒ 57 − 812/100 = 57 − 8.12

⇒ 48.88%

∴ The correct answer is 48.88%.

Alternate Method

Given:

First discount (d₁) = 29%

Second discount (d₂) = 28%

Formula Used:

Selling Price (SP) = Marked Price (MP) × (1 − d₁/100) × (1 − d₂/100)

⇒ Let Marked Price (MP) = 100

⇒ Price after first discount = 100 − (29% of 100) = 71

⇒ Second discount amount = 28% of 71 = (28/100) × 71

⇒ Second discount amount = 19.88

⇒ Final Selling Price (SP) = 71 − 19.88 = 51.12

⇒ Total Discount = MP − SP = 100 − 51.12 = 48.88

⇒ Single Equivalent Discount % = (48.88 / 100) × 100 = 48.88%

∴ The correct answer is 48.88%.

Additional Information

Successive Percentage Change

The net percentage change for two successive changes of x% and y% is given by the formula: (x + y + xy/100)%. For discounts, values of x and y are taken as negative.

Three Successive Discounts

For three discounts a%, b%, and c%, the single equivalent discount is found by calculating the equivalent of any two first, and then using that result with the third discount.

Relation between MP and SP

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

Shortcut Trick

Total amount to be saved = Target amount − Initial savings

Total savings required = ₹21,000 − ₹12,000 = ₹9,000

Number of weeks = Total savings required ÷ Weekly savings

Number of weeks = 9,000 ÷ 1,500 = 6

∴ The correct answer is 6 weeks.

Alternate Method

Given:

Initial savings = ₹12,000

Target amount = ₹21,000

Weekly savings rate = ₹1,500

Formula:

Total Amount = Initial Savings + (Weekly Savings × Number of Weeks)

Let the number of weeks be "n"

⇒ 21,000 = 12,000 + (1,500 × n)

⇒ 21,000 − 12,000 = 1,500n

⇒ 9,000 = 1,500n

⇒ n = 9,000 ÷ 1,500

⇒ n = 6

∴ The correct answer is 6 weeks.

Additional Information

Arithmetic Progression (A.P.)

This problem follows an A.P. where the first term a = 12,000 + 1,500 (after 1 week), the common difference d = 1,500, and the n^th term is 21,000.

Linear Equation Modeling

Any situation involving a fixed starting value and a constant rate of change can be modeled by y = mx + c, where c is the initial value and m is the rate.

Time and Savings Relation

Time = (Required Amount − Initial Amount) ÷ Savings per unit time. This logic is also used in Simple Interest where Interest = Principal × Rate × Time.

Shortcut Trick

Initial Income : Expenditure = 12 : 7

New Income = 12 × (100 + 40)% = 12 × 140

New Expenditure = 7 × (100 + 50)% = 7 × 150

New Ratio = (12 × 140) : (7 × 150) = 1680 : 1050

Simplifying by dividing by 210 ⇒ 8 : 5

∴ The correct answer is 8 : 5.

Alternate Method

Given: Initial Ratio of Income to Expenditure = 12 : 7

Formula: New Value = Old Value × [ (100 + Increase%) / 100 ]

⇒ Let Ratnesh’s monthly income = 1200 and expenditure = 700.

⇒ New Income = 1200 + (40 / 100) × 1200 = 1200 + 480 = 1680

⇒ New Expenditure = 700 + (50 / 100) × 700 = 700 + 350 = 1050

⇒ New Ratio = 1680 : 1050

⇒ Dividing both sides by 210: 1680/210 : 1050/210

⇒ New Ratio = 8 : 5

∴ The correct answer is 8 : 5.

Additional Information

Income-Expenditure Relationship

Total Income = Expenditure + Savings. If income increases more than expenditure, savings increase.

Percentage Change in Ratios

If ratio is a : b and terms increase by x% and y% respectively, new ratio = a(100+x) : b(100+y).

Effective Change in Savings

Change in Savings = New Income − New Expenditure. It can be expressed as a percentage of original savings.

Shortcut Trick

In an isosceles trapezium, height (h) = √[slant² − ((a−b)/2)²]

h = √[13² − ((20−10)/2)²] = √(169 − 25) = √144 = 12 cm

Area = 1/2 × (Sum of parallel sides) × h

Area = 1/2 × (20 + 10) × 12 = 15 × 12 = 180 cm²

∴ The correct answer is 180 cm².

Alternate Method

Given:

Parallel sides (a, b) = 20 cm, 10 cm

Non-parallel sides (c) = 13 cm each (Isosceles Trapezium)

Formula Used:

Area of Trapezium = 1/2 × (Sum of parallel sides) × Height

Pythagoras Theorem: h² + base² = hypotenuse²

⇒ Let the height be h. Since it is an isosceles trapezium, the perpendiculars from the top vertices divide the base into segments: 5 cm, 10 cm, and 5 cm.

⇒ Base of the right-angled triangle formed at the side = (20 − 10) ÷ 2 = 5 cm

⇒ In the right-angled triangle, height (h) = √(13² − 5²)

⇒ h = √(169 − 25) = √144 = 12 cm

⇒ Area of Trapezium = 1/2 × (20 + 10) × 12

⇒ Area = 1/2 × 30 × 12

⇒ Area = 15 × 12 = 180 cm²

∴ The correct answer is 180 cm².

Additional Information

Isosceles Trapezium Properties

In an isosceles trapezium, non-parallel sides are equal, base angles are equal, and diagonals are equal in length.

Cyclic Quadrilateral Property

Every isosceles trapezium is a cyclic quadrilateral, meaning all its vertices lie on a single circle.

Median of a Trapezium

The median (mid-segment) joins the midpoints of non-parallel sides; Median length = (a + b) ÷ 2.

Shortcut Trick

For 2 years, the effective compound interest rate is calculated using the formula: x + y + (xy/100)%

Effective Rate = 15 + 15 + (15 × 15)/100 = 30 + 2.25 = 32.25%

Total Amount = 100% (Principal) + 32.25% (Interest) = 132.25%

Required Amount = 8400 × 132.25% = 84 × 132.25 = 11109

∴ The correct answer is ₹11,109.

Alternate Method

Given: Principal (P) = ₹8,400, Rate (R) = 15% per annum, Time (n) = 2 years.

Formula Used: Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 8400 × (1 + 15/100)²

⇒ A = 8400 × (1 + 3/20)²

⇒ A = 8400 × (23/20) × (23/20)

⇒ A = 8400 × 529 / 400

⇒ A = 21 × 529

⇒ A = 11109

∴ The correct answer is ₹11,109.

Additional Information

Compound Interest vs Simple Interest for 2 Years

The difference between CI and SI for 2 years is given by the formula: Difference = P × (R/100)².

Effective Rate of Interest

For a rate of R% compounded annually for 2 years, the net effective rate is 2R + R²/100 %.

Compounding Frequency

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

Shortcut Trick

Total New Price = 6 × [(860 × 1.05) + (2900 × 1.10)]

New Price of 1 Faucet = 860 + 43 = ₹903

New Price of 1 Wash Basin = 2900 + 290 = ₹3190

Total for 6 sets = 6 × (903 + 3190) = 6 × 4093 = ₹24,558

∴ The correct answer is ₹24,558.

Alternate Method

Given:

Price of faucet = ₹860

Price of wash basin = ₹2900

Increase in faucet price = 5%

Increase in wash basin price = 10%

Calculations:

⇒ New price of 1 faucet = 860 + (5/100 × 860) = 860 + 43 = ₹903

⇒ New price of 1 wash basin = 2900 + (10/100 × 2900) = 2900 + 290 = ₹3190

⇒ New price of 6 faucets = 6 × 903 = ₹5418

⇒ New price of 6 wash basins = 6 × 3190 = ₹19140

⇒ Total price = 5418 + 19140 = ₹24558

∴ The correct answer is ₹24,558.

Additional Information

Percentage Increase

New Value = Original Value × (1 + Rate/100). For a 5% increase, multiply by 1.05.

Distributive Property

To find the cost of multiple sets, use n × (Price A + Price B) which is equal to (n × Price A) + (n × Price B).

Successive Changes

If a price increases by x% and then y%, the effective increase is [x + y + (xy/100)]%.

Shortcut Trick

Assume all 363 children are girls, total amount = 363 × 6 = ₹2,178.

Difference from actual amount = 2,443 − 2,178 = ₹265.

Difference between a boy's share and a girl's share = 7 − 6 = ₹1.

Number of boys = Total Difference ÷ Share Difference = 265 ÷ 1 = 265.

∴ The correct answer is 265 boys.

Alternate Method

Given: Total children = 363, Total amount = ₹2,443, Girl's share = ₹6, Boy's share = ₹7.

⇒ Let the number of boys be x and the number of girls be (363 − x).

⇒ Total Amount = (Number of girls × 6) + (Number of boys × 7)

⇒ 2,443 = 6(363 − x) + 7x

⇒ 2,443 = 2,178 − 6x + 7x

⇒ 2,443 − 2,178 = x

⇒ x = 265

∴ The correct answer is 265 boys.

Additional Information

Alligation Method

This problem can also be solved using alligation by finding the average share per child (2,443 ÷ 363) and placing it in the center of the cross diagram.

Linear Equations in Two Variables

Standard algebraic approach: B + G = 363 and 7B + 6G = 2443. Multiply the first by 6 and subtract from the second to find B.

Unitary Method Logic

The surplus amount beyond the minimum guaranteed share (₹6 per child) is entirely attributed to the extra ₹1 given to each boy.

Shortcut Trick

Net discount % = a + b − (a × b) ÷ 100

Net discount = 20 + 30 − (20 × 30) ÷ 100 = 50 − 6 = 44%

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

SP = 7750 × (100 − 44) ÷ 100 = 7750 × 0.56 = 4340

∴ The correct answer is ₹4,340.

Alternate Method

Given → Marked Price (MP) = ₹7,750, Discount₁ (d₁) = 20%, Discount₂ (d₂) = 30%.
Formulas: SP = MP × (100 − d₁)% × (100 − d₂)%

⇒ Price after 1^st discount = 7750 × (80 ÷ 100) = 6200
⇒ Final Selling Price = 6200 × (70 ÷ 100)
⇒ SP = 62 × 70 = 4340

∴ The correct answer is ₹4,340.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on an item. Discount is always calculated on the Marked Price to arrive at the Selling Price.

Successive Discount

When a series of discounts are applied, the second discount is calculated on the value remaining after the first discount. Formula: SP = MP × (1 − d₁/100) × (1 − d₂/100).

Shortcut Trick

Total Provision = Men × Days = 1200 × 13

New Men = 1200 + 360 = 1560

New Days = (1200 × 13) ÷ 1560

New Days = 15600 ÷ 1560 = 10

∴ The correct answer is 10 days.

Alternate Method

Given:

Initial Men (M₁) = 1200

Initial Days (D₁) = 13

Increase in Men = 360

Final Men (M₂) = 1200 + 360 = 1560

Formula Used:

M₁D₁ = M₂D₂

Calculations:

⇒ 1200 × 13 = 1560 × D₂

⇒ D₂ = (1200 × 13) ÷ 1560

⇒ D₂ = 15600 ÷ 1560

⇒ D₂ = 10

∴ The correct answer is 10 days.

Additional Information

Inverse Proportion

When the number of men increases, the number of days provisions last decreases proportionally: M₁ × D₁ = M₂ × D₂.

Chain Rule

The general formula is (M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂, where M is men, D is days, H is hours, and W is work/provisions.

Ratio Method

Ratio of Men = 1200 : 1560 = 10 : 13. Therefore, ratio of Days = 13 : 10. Since 13 units = 13 days, 10 units = 10 days.