Quantitative Aptitude PYQs

Shortcut Trick

Ratio of investment of Preeti, Qadir and Reena = 2 : 8 : 13.

Total ratio units = 2 + 8 + 13 = 23 units.

Difference between Preeti and Reena = 13 − 2 = 11 units.

Value of 11 units = (Total Profit ÷ 23) × 11 = (87,193 ÷ 23) × 11.

Value = 3,791 × 11 = 41,701.

∴ The correct answer is ₹41,701.

Alternate Method

Given → Investment Ratio = 2 : 8 : 13 | Total Profit = ₹87,193.
Formulas: Profit Share ∝ Investment × Time | Profit% = (Profit ÷ CP) × 100

⇒ Since time is the same for all, Profit Ratio = Investment Ratio = 2 : 8 : 13.
⇒ Let the shares be 2x, 8x, and 13x respectively.
⇒ Total Profit = 2x + 8x + 13x = 23x = 87,193.
⇒ x = 87,193 ÷ 23 = 3,791.
⇒ Difference between Preeti and Reena = 13x − 2x = 11x.
⇒ Difference = 11 × 3,791 = 41,701.

∴ The correct answer is ₹41,701.

Additional Information

Partnership Basics

When the time period of investment is the same for all partners, the profit is distributed in the ratio of their investments.

Compound Partnership

If time periods are different, Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂).

Shortcut Trick

Ratio of Length : Breadth : Height = 3 : 2 :

1. Let common factor be x.

Product of ratios = 3 × 2 × 1 = 6. Given Volume = 10,368 cm³.

x³ = 10,368 ÷ 6 = 1,728 ⇒ x = ∛1,728 = 12 cm.

Total Surface Area (in ratio units) = 2 × (3×2 + 2×1 + 1×3) = 2 × 11 = 22 units.

Total Cost = TSA × Rate = (22 × x²) × 2 = 22 × 144 × 2 = ₹6,336.

∴ The correct answer is ₹6,336.

Alternate Method

Given: Volume of rectangular block = 10,368 cm³. Ratio of L : B : H = 3 : 2 :

1. Polishing rate = ₹2/cm².

Formula Used: Volume = L × B × H | Total Surface Area (TSA) = 2(LB + BH + HL)

⇒ Let length = 3x, breadth = 2x, and height = x.

⇒ Volume = 3x × 2x × x = 6x³

⇒ 6x³ = 10,368

⇒ x³ = 1,728 ⇒ x = 12

⇒ Dimensions: L = 36 cm, B = 24 cm, H = 12 cm

⇒ TSA = 2(36 × 24 + 24 × 12 + 12 × 36)

⇒ TSA = 2(864 + 288 + 432) = 2(1,584) = 3,168 cm²

⇒ Total Cost = Area × Rate = 3,168 × 2 = ₹6,336

∴ The correct answer is ₹6,336.

Additional Information

Volume of a Cuboid

The space occupied by a rectangular prism is calculated as Length × Breadth × Height.

Lateral Surface Area

Area of the four side walls is given by 2 × Height × (Length + Breadth).

Diagonal of a Cuboid

The longest rod that can be placed inside is √(L² + B² + H²).

Surface Area of a Cube

If L=B=H=a, then the Total Surface Area = 6a².

Shortcut Trick

Net percentage change = a + b + (a × b) ÷ 100

Here, markup percentage a = +85% and discount percentage b = −49%.

Net result = 85 − 49 + (85 × (−49)) ÷ 100

Net result = 36 − 41.65 = −5.65%.

Negative sign indicates a loss.

∴ The correct answer is 5.65%.

Alternate Method

Given: Marked Price (MP) is 85% above Cost Price (CP), Discount = 49%.

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

⇒ Let Cost Price (CP) be 100.

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

⇒ Selling Price (SP) = 185 × (100 − 49) ÷ 100 = 185 × 51 ÷ 100 = 94.35.

⇒ Loss = CP − SP = 100 − 94.35 = 5.65.

⇒ Loss Percentage = (5.65 ÷ 100) × 100 = 5.65%.

∴ The correct answer is 5.65%.

Additional Information

Relation between CP and MP

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

Markup Percentage

Markup% is the percentage by which the Marked Price is higher than the Cost Price: Markup% = (MP − CP) ÷ CP × 100.

Shortcut Trick

Apply the algebraic identity directly: a² + b² = (a − b)² + 2ab

Square the difference and add twice the product: (9)² + 2(20)

81 + 40 = 121

∴ The correct answer is 121.

Alternate Method

Given:

Difference (a − b) = 9

Product (ab) = 20

Formula Used:

The square of a binomial difference is given by: (a − b)² = a² + b² − 2ab

Calculations:

Substituting the given values into the formula:

⇒ (9)² = a² + b² − 2 × 20

⇒ 81 = a² + b² − 40

⇒ a² + b² = 81 + 40

⇒ a² + b² = 121

∴ The correct answer is 121.

Additional Information

Square of Sum Identity

The value can also be found if the sum is known using: a² + b² = (a + b)² − 2ab.

Relationship between Sum and Difference

(a + b)² − (a − b)² = 4ab. This relates the sum, difference, and product of two numbers.

Difference of Squares

a² − b² = (a + b)(a − b). This is a fundamental factoring identity in algebra.

Shortcut Trick
Identify odd numbers between 415 and 428: 417, 419, 421, 423, 425, 427.
Eliminate numbers divisible by 3 (sum of digits): 417 (12), 423 (9).
Eliminate numbers divisible by 5: 425.
Check remaining: 419, 421, 427. Since 427 = 7 × 61, it is not prime.
Prime numbers: 419 and 421.
∴ The correct answer is 2.

Alternate Method
Given: Range is 415 < n < 428.
Numbers to check: 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427.

⇒ 417: 4+1+7 = 12 (Divisible by 3)
⇒ 419: Not divisible by 2, 3, 5, 7, 11, 13, 17, 19. (Prime)
⇒ 421: Not divisible by 2, 3, 5, 7, 11, 13, 17, 19. (Prime)
⇒ 423: 4+2+3 = 9 (Divisible by 3)
⇒ 425: Ends in 5 (Divisible by 5)
⇒ 427: 427 ÷ 7 = 61 (Divisible by 7)
∴ The correct answer is 2.

Additional Information
Prime Number Definition
A natural number greater than 1 that has no positive divisors other than 1 and itself.
Primality Test
To check if n is prime, test divisibility by primes up to √n. For 421, √421 ≈ 20.5, so check primes up to 19.
Divisibility Rule of 7
Double the last digit and subtract it from the rest: 427 → 42 − (7 × 2) = 28. Since 28 is divisible by 7, 427 is divisible by 7.

Shortcut Trick

In melting problems, Total Volume remains constant: R³ = r₁³ + r₂³ + r₃³.

⇒ 1.5³ = 0.75³ + 1³ + r₃³

⇒ 3.375 = 0.421875 + 1 + r₃³

⇒ r₃³ = 3.375 − 1.421875 = 1.953125 ⇒ r₃ = 1.25 cm.

⇒ Diameter of the third ball = 2 × 1.25 = 2.5 cm.

∴ The correct answer is 2.5 cm.

Alternate Method

Given:

Radius of large iron ball (R) = 1.5 cm

Radius of first smaller ball (r₁) = 0.75 cm

Radius of second smaller ball (r₂) = 1.0 cm

Formula Used:

Volume of a sphere = 4/3 × π × r³

Let the radius of the third smaller ball be r₃.

⇒ Total Volume = Volume₁ + Volume₂ + Volume₃

⇒ 4/3 × π × (1.5)³ = 4/3 × π × (0.75)³ + 4/3 × π × (1.0)³ + 4/3 × π × (r₃)³

⇒ 1.5³ = 0.75³ + 1.0³ + r₃³

⇒ 3.375 = 0.421875 + 1 + r₃³

⇒ 3.375 = 1.421875 + r₃³

⇒ r₃³ = 3.375 − 1.421875

⇒ r₃³ = 1.953125

⇒ r₃ = 1.25 cm

⇒ Diameter of the third ball = 2 × r₃ = 2 × 1.25 = 2.5 cm

∴ The correct answer is 2.5 cm.

Additional Information

Surface Area of Sphere

The total surface area of a sphere is given by 4 × π × r².

Properties of Melting

When one solid object is melted and recast into other shapes, the total volume remains invariant (constant), assuming no material loss.

Hemisphere Formulas

Volume of hemisphere = 2/3 × π × r³ and Total Surface Area = 3 × π × r².

Shortcut Trick

Total deduction = 19 + 9 + 13 = ₹41.

Remaining amount = 8200 − 41 = ₹8159.

Ratio of remaining shares = 12 : 19 : 10 (Total units = 41).

1 unit = 8159 ÷ 41 = ₹199.

Difference (B − C) = (19 − 10) units + (deduction difference) = 9 × 199 + (9 − 13) = 1791 − 4 = ₹1787.

∴ The correct answer is ₹1787.

Alternate Method

Given: Total = ₹8,200. Deductions for A, B, C are ₹19, ₹9, ₹13 respectively. Ratio of remaining parts = 12 : 19 : 10.

⇒ Let remaining shares be 12x, 19x, and 10x.

⇒ (12x + 19) + (19x + 9) + (10x + 13) = 8200

⇒ 41x + 41 = 8200

⇒ 41x = 8159

⇒ x = 8159 ÷ 41 = 199

⇒ B's original share = 19x + 9 = 19 × 199 + 9 = 3781 + 9 = ₹3790

⇒ C's original share = 10x + 13 = 10 × 199 + 13 = 1990 + 13 = ₹2003

⇒ Difference = 3790 − 2003 = ₹1787

∴ The correct answer is ₹1787.

Additional Information

Ratio Distribution with Constants

When specific amounts are deducted or added to shares, first adjust the total sum and then divide the adjusted sum in the given ratio.

Difference between Shares

Difference = (Ratio Difference × Value per unit) ± (Difference between constants).

Shortcut Trick

Relative Speed when moving towards each other = Sum of speeds = 23 + 89 = 112 km/hr.

Time = Distance ÷ Relative Speed = 28 ÷ 112 = 1/4 hours.

In minutes = 1/4 × 60 = 15 minutes.

∴ The correct answer is 15 min.

Alternate Method

Given:

Distance between engines = 28 km

Speed of engine 1 (S₁) = 23 km/hr

Speed of engine 2 (S₂) = 89 km/hr

Formula Used:

Time = Distance ÷ Relative Speed

Relative Speed (Opposite Direction) = S₁ + S₂

Calculations:

⇒ Relative Speed = 23 + 89 = 112 km/hr

⇒ Time (in hours) = 28 ÷ 112

⇒ Time = 1/4 hours

⇒ Time (in minutes) = (1/4) × 60

⇒ Time = 15 min

∴ The correct answer is 15 min.

Additional Information

Relative Speed Concept

When two objects move in opposite directions, their relative speed is the sum of their individual speeds (S₁ + S₂). When they move in the same direction, it is the difference (|S₁ − S₂|).

Time Conversion

To convert time from hours to minutes, multiply the value by 60. To convert km/hr to m/s, multiply by 5/18.

Meeting Time Rule

The Meeting Time is the initial distance between the objects divided by the relative speed, provided they start at the same time.

Shortcut Trick

The angle formed by the bisectors of two adjacent angles in a quadrilateral is equal to half the sum of the other two angles.

∴ ∠TES = (∠Q + ∠R) ÷ 2

⇒ ∠TES = (74° + 39°) ÷ 2

⇒ ∠TES = 113° ÷ 2 = 56.5°

∴ The correct answer is 56.5°.

Alternate Method

Given: In quadrilateral QRST, ∠Q = 74° and ∠R = 39°. SE and TE are angle bisectors of ∠S and ∠T respectively.

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

In quadrilateral QRST:

⇒ ∠Q + ∠R + ∠S + ∠T = 360°

⇒ 74° + 39° + ∠S + ∠T = 360°

⇒ 113° + ∠S + ∠T = 360°

⇒ ∠S + ∠T = 360° − 113° = 247°

Since SE and TE are bisectors:

Shortcut Trick

Total Work = LCM of 12, 20, and 36 = 180 units.

Efficiency of A + B + C = 180 ÷ 12 = 15 units/day.

Efficiency of A = 180 ÷ 20 = 9 units/day | Efficiency of C = 180 ÷ 36 = 5 units/day.

Efficiency of B = 15 − (9 + 5) = 1 unit/day.

Time taken by B = 180 ÷ 1 = 180 days.

∴ The correct answer is 180 days.

Alternate Method

Given: Time taken by (A+B+C) = 12 days, A = 20 days, C = 36 days.

Formula Used: Efficiency = Total Work ÷ Time taken

⇒ Efficiency of (A + B + C) = Efficiency of A + Efficiency of B + Efficiency of C

⇒ 15 = 9 + Efficiency of B + 5

⇒ Efficiency of B = 15 − 14 = 1 unit/day

⇒ Time taken by B alone = Total Work ÷ Efficiency of B

⇒ Time taken by B = 180 ÷ 1 = 180 days

∴ The correct answer is 180 days.

Additional Information

Combined Efficiency Rule

The total work done by multiple individuals working together is the sum of their individual efficiencies. Total Efficiency = E₁ + E₂ + E₃.

Work & Time Relation

Time is inversely proportional to efficiency when the work remains constant. Time = Work ÷ Efficiency.

Pipes & Cisterns Analogy

This problem follows the same logic as three pipes filling a tank, where the combined rate is the sum of individual rates.

Shortcut Trick

Option Verification Method:

Check which pair satisfies Sum = 54 and LCM = 195.

Option (2): 39 + 15 = 54. Factors of 39 = 3 × 13; Factors of 15 = 3 × 5.

LCM(39, 15) = 3 × 13 × 5 = 195. This satisfies both conditions.

∴ The correct answer is 39, 15.

Alternate Method

Given: Sum of numbers = 54, LCM = 195.

Formula Used: HCF of two numbers is always a factor of their sum and their LCM.

⇒ Let the numbers be 3a and 3b, where a and b are co-prime.

⇒ Sum: 3a + 3b = 54 ⇒ a + b = 18

⇒ LCM: 3 × a × b = 195 ⇒ ab = 65

⇒ We need two numbers whose sum is 18 and product is 65. The factors of 65 are 1, 5, 13, 65.

⇒ Clearly, a = 13 and b = 5 (since 13 + 5 = 18 and 13 × 5 = 65).

⇒ First number = 3 × 13 = 39.

⇒ Second number = 3 × 5 = 15.

∴ The correct answer is 39, 15.

Additional Information

Product Rule

For any two numbers x and y, x × y = HCF(x,y) × LCM(x,y).

HCF property

The Highest Common Factor (HCF) must divide both the sum and the Least Common Multiple (LCM) of the numbers.

Co-prime Numbers

Numbers are co-prime if their HCF is 1. In the method above, a and b must be co-prime to ensure 3 is the highest factor.

Shortcut Trick

Time taken by A, B, and C working together to complete the original work = 3 ÷ 3 = 1 day.

To complete twice the same work, the time taken will be doubled.

Time taken = 1 day × 2 = 2 days.

∴ The correct answer is 2 days.

Alternate Method

Given:

Time taken by A = 3 days

Time taken by B = 3 days

Time taken by C = 3 days

Formula Used:

Efficiency = Total Work ÷ Time Taken

Combined Efficiency = Efficiency of A + Efficiency of B + Efficiency of C

Time Taken = Total Work ÷ Combined Efficiency

Calculations:

⇒ Total original work = 3 units

⇒ Combined efficiency of A, B and C = 1 + 1 + 1 = 3 units/day

⇒ New work to be completed = 2 × Total original work = 2 × 3 = 6 units

⇒ Time taken to do twice the work = 6 ÷ 3 = 2 days

∴ The correct answer is 2 days.

Additional Information

Time and Work Relation

Time taken is directly proportional to the amount of work done if the efficiency remains constant. If work is multiplied by n, the time taken is also multiplied by n.

Combined Efficiency Formula

For three individuals with time periods T₁, T₂, and T₃, their combined work rate is (1/T₁) + (1/T₂) + (1/T₃).

Shortcut Trick

Excess runs scored in 16^th inning = 111 − 94 = 17.

This excess is distributed over the total 16 innings to find the increase in average.

Increase in average = 17 ÷ 16 = 1.0625.

Rounding 1.0625 to the nearest whole number gives 1.

∴ The correct answer is 1.

Alternate Method

Given: Average of 15 innings = 94 | Runs in 16^th inning = 111.

Formula Used: Total runs = Average × Number of innings.

⇒ Total runs after 15 innings = 15 × 94 = 1410.

⇒ Total runs after 16 innings = 1410 + 111 = 1521.

⇒ New average for 16 innings = 1521 ÷ 16 = 95.0625.

⇒ Increase in average = New average − Old average

⇒ Increase in average = 95.0625 − 94 = 1.0625.

⇒ Rounded to nearest whole number = 1.

∴ The correct answer is 1.

Additional Information

Net Deviation Method

Increase in average = (New value − Old average) ÷ Total number of items including the new one.

Weighted Average

The combined average of two groups with n₁ and n₂ items and averages a₁ and a₂ is (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Batting Average Formula

Batting Average = (Total runs scored) ÷ (Number of times the batsman got out/Total innings played).

Shortcut Trick

Total votes = 14,000

Valid votes = 90% of 14,000 = 12,600

Candidate A got 75% of valid votes → Candidate B got 25% of valid votes

Votes for Candidate B = 12,600 × 1/4 = 3,150

∴ The correct answer is 3150.

Alternate Method

Given:

Total votes = 14,000

Invalid percentage = 10%

Candidate A valid vote share = 75%

Calculations:

⇒ Total Valid Votes = 14,000 − (10% of 14,000)

⇒ Total Valid Votes = 14,000 − 1,400 = 12,600

⇒ Candidate B share % = 100% − 75% = 25%

⇒ Candidate B votes = 25% of 12,600

⇒ Candidate B votes = 12,600 ÷ 4 = 3,150

∴ The correct answer is 3150.

Additional Information

Valid vs Invalid Votes

In election problems, winners and losers are always calculated based on Valid Votes unless stated otherwise. Valid = Total − Invalid.

Successive Percentage Method

Votes for B = Total × (Valid% / 100) × (B% / 100). Here, 14,000 × 0.90 × 0.25 = 3,150.

Voter Turnout

If 'voters who did not cast vote' is mentioned, subtract them first from the Total Registered Voters to find total votes polled.

Shortcut Trick

Express given values as powers of 5: 125 = 5³ and 3125 = 5⁵.

By equating the exponents, we get: x − y = 3 and x + y = 5.

Add the two equations directly: (x − y) + (x + y) = 3 + 5.

⇒ 2x = 8 ⇒ x = 4.

∴ The correct answer is 4.

Alternate Method

Given:

5^{(x − y)} = 125

5^{(x + y)} = 3125

Concept Used:

If a^m = aⁿ, then m = n.

Calculations:

⇒ 125 = 5 × 5 × 5 = 5³

⇒ 3125 = 5 × 5 × 5 × 5 × 5 = 5⁵

⇒ 5^{(x − y)} = 5³

⇒ x − y = 3       ---- (1)

⇒ 5^{(x + y)} = 5⁵

⇒ x + y = 5       ---- (2)

⇒ Adding equation (1) and (2):

⇒ (x − y) + (x + y) = 3 + 5

⇒ 2x = 8

⇒ x = 8 ÷ 2

⇒ x = 4

∴ The correct answer is 4.

Additional Information

Product Rule of Exponents

When multiplying terms with the same base, you add their exponents: a^m × aⁿ = a^m+n

Quotient Rule of Exponents

When dividing terms with the same base, you subtract their exponents: a^m ÷ aⁿ = a^m−n

Power of a Power Rule

When raising a power to another power, you multiply the exponents: (a^m)ⁿ = a^m×n

Zero Exponent Rule

Any non-zero base raised to the power of zero is equal to one: a⁰ = 1

Shortcut Trick

For an angle of elevation of 45°, the horizontal distance (Base) is always equal to the perpendicular height above eye level.

Height above eye level = Distance from base = 28.7 m.

Total Height of Chimney = Height above eye level + Eye level height = 28.7 + 1.3 = 30 m.

∴ The correct answer is 30 m.

Alternate Method

Given:

Distance from base (D) = 28.7 m

Angle of elevation (θ) = 45°

Height of observer (h) = 1.3 m

Formula Used:

tan(θ) = Perpendicular / Base

Total Height = Perpendicular + height of observer

Calculations:

⇒ tan(45°) = (Height of chimney − 1.3) / 28.7

⇒ 1 = (Height − 1.3) / 28.7

⇒ Height − 1.3 = 28.7

⇒ Height = 28.7 + 1.3

⇒ Height = 30 m

∴ The correct answer is 30 m.

Additional Information

Angle of Elevation

The angle formed by the line of sight with the horizontal when looking up at an object.

Trigonometric Ratios for Standard Angles

tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3 are frequently used in height and distance problems.

Observer Height Rule

If the observer has a significant height, it must be added to the calculated vertical distance from the eye level to find the total height from the ground.

Shortcut Trick

Average speed for equal distances = 2uv ÷ (u + v)

Original Avg Speed = (2 × 8 × 6) ÷ (8 + 6) = 96 ÷ 14 = 48/7 km/hr

New Speed = (48/7) × 70% = (48/7) × 0.7 = 4.8 km/hr

Time = Distance ÷ New Speed = 120 ÷ 4.8 = 25 hr

∴ The correct answer is 25 hr.

Alternate Method

Given: Total Distance = 120 km, Speed₁ = 8 km/hr, Speed₂ = 6 km/hr, Speed Reduction = 30%

Formula: Average Speed = Total Distance ÷ Total Time

⇒ Time for 1^st half = 60 ÷ 8 = 7.5 hr

⇒ Time for 2^nd half = 60 ÷ 6 = 10 hr

⇒ Original Average Speed = 120 ÷ (7.5 + 10) = 120 ÷ 17.5 = 1200 ÷ 175 = 48/7 km/hr

⇒ Reduced overall speed = (48/7) × (100 − 30)/100 = (48/7) × 0.7 = 4.8 km/hr

⇒ Required Time = 120 ÷ 4.8 = 25 hr

∴ The correct answer is 25 hr.

Additional Information

Average Speed (Equal Distances)

When a journey is divided into two equal distances with speeds u and v, the average speed is given by (2uv) / (u + v).

Percentage Speed Change

If speed decreases by x%, the new speed is (100 − x)% of the original speed. Time taken is inversely proportional to speed for a fixed distance.

General Average Speed Formula

Average Speed = (Total Distance) ÷ (Total Time taken), regardless of the number of segments or distances involved.

Shortcut Trick

Using the Alligation or Weighted Average method for Income (I), Expenditure (E), and Savings (S).

Ratio of E : S = 250 : 100 = 5 : 2.

Net change in Income = [(Expenditure % change × E ratio) + (Savings % change × S ratio)] ÷ Total ratio

Net change = [(−3 × 5) + (21.5 × 2)] ÷ 7 = [−15 + 43] ÷ 7 = 28 ÷ 7 = 4%.

∴ The correct answer is 4%.

Alternate Method

Given:

Let Savings = 100

Expenditure = 100 + 150% of 100 = 250

Income = Expenditure + Savings = 250 + 100 = 350

Calculations:

⇒ New Expenditure = 250 − (3% of 250) = 250 − 7.5 = 242.5

⇒ New Savings = 100 + (21.5% of 100) = 100 + 21.5 = 121.5

⇒ New Income = 242.5 + 121.5 = 364

⇒ Increase in Income = 364 − 350 = 14

⇒ % Increase = (14 ÷ 350) × 100

⇒ % Increase = (1 ÷ 25) × 100 = 4%

∴ The correct answer is 4%.

Additional Information

Income Equation

The fundamental relation in financial arithmetic is Income = Expenditure + Savings.

Percentage Change in Sum

If Z = X + Y, the % change in Z is given by (ΔX + ΔY)/Z_initial × 100, which is the weighted average of individual changes.

Base Change Property

When a value is increased by x%, it becomes (100+x)/100 times its original value.

Shortcut Trick

2 Chairs + 1 Table = ₹350

Multiplying by 2: 4 Chairs + 2 Tables = ₹700

Given: 3 Chairs + 2 Tables = ₹600

Difference (1 Chair) = ₹700 − ₹600 = ₹100

Cost of 4 Chairs = 4 × 100 = ₹400

∴ The correct answer is ₹400.

Alternate Method

Given:

Cost of 3 chairs and 2 tables = ₹600

Cost of 2 chairs and 1 table = ₹350

Formula Used:

Linear equations in two variables: ax + by = c

Calculations:

Let the cost of one chair be C and one table be T.

⇒ 3C + 2T = 600 --- (i)

⇒ 2C + T = 350 --- (ii)

⇒ From (ii), T = 350 − 2C

⇒ Substitute T in (i): 3C + 2(350 − 2C) = 600

⇒ 3C + 700 − 4C = 600

⇒ −C = 600 − 700

⇒ C = 100

⇒ Cost of 4 chairs = 4 × 100 = 400

∴ The correct answer is ₹400.

Additional Information

Elimination Method

A process of solving simultaneous equations by multiplying equations by suitable constants so that adding or subtracting them eliminates one variable.

Substitution Method

Solving for one variable in terms of the other from one equation and substituting it into the second equation.

Unitary Method

Finding the value of a single unit first (1 Chair) and then multiplying by the required number of units (4 Chairs).