Quantitative Aptitude PYQs

Shortcut Trick

Days for (A+B) = 32/5, (B+C) = 64/9, (A+C) = 16/3.

L.C.M of numerators (32, 64, 16) = 64 units (Total Work).

Efficiencies: (A+B) = 10, (B+C) = 9, (A+C) = 12. Sum = 31.

Efficiency of (A+B+C) = 31 ÷ 2 = 15.5 units/day.

Time = 64 ÷ 15.5 = 128 ÷ 31 = 4(4/31) days.

∴ The correct answer is 4(4/31) days.

Alternate Method

Given: Time for (A+B) = 32/5 days, (B+C) = 64/9 days, (A+C) = 16/3 days.

⇒ Total efficiency of 2(A + B + C) = 10 + 9 + 12 = 31

⇒ Efficiency of (A + B + C) = 31/2

⇒ Time taken by A, B and C together = Total Work ÷ Efficiency

⇒ Time = 64 ÷ (31/2) = 128/31

⇒ Time = 4(4/31) days

∴ The correct answer is 4(4/31) days.

Additional Information

Total Work using LCM

When time is given in fractions, Total Work is the LCM of the numerators of the time values.

Efficiency Formula

Efficiency = Total Work ÷ Time taken. It represents the work done in one unit of time.

Combined Efficiency

If pairs work together, summing their individual pair efficiencies gives twice the total efficiency of all individuals: 2(A+B+C).

Shortcut Trick

Let the Marked Price (MP) be 100%.

Successive discounts are 36% and 10%.

Effective Selling Price (SP) factor = (100 − 36)% × (100 − 10)% = 0.64 × 0.90 = 0.576.

Given SP = ₹7,200 ⇒ 0.576 × MP = 7,200.

MP = 7,200 ÷ 0.576 = 12,500.

∴ The correct answer is ₹12,500.

Alternate Method

Given: Selling Price (SP) = ₹7,200, Discount₁ (d₁) = 36%, Discount₂ (d₂) = 10%.

Formula: SP = MP × (100 − d₁)/100 × (100 − d₂)/100

⇒ 7,200 = MP × (64/100) × (90/100)

⇒ 7,200 = MP × (16/25) × (9/10)

⇒ 7,200 = MP × (144/250)

⇒ MP = (7,200 × 250) ÷ 144

⇒ MP = 50 × 250 = 12,500.

∴ The correct answer is ₹12,500.

Additional Information

Successive Discount Formula

For two successive discounts of a% and b%, the single equivalent discount is (a + b − ab/100)%.

Marked Price Definition

The Marked Price (MP) is the price printed on the label of an item, and discounts are always calculated on this value.

Shortcut Trick

Calculate total days: February (28 − 9 = 19) + March (31) + April (23) = 73 days.

Time in years = 73 ÷ 365 = 1/5 years.

Interest = (Principal × Rate × Time) ÷ 100

Interest = (2000 × 7 × 1/5) ÷ 100 = 20 × 7 ÷ 5 = 4 × 7 = ₹28.

∴ The correct answer is ₹28.

Alternate Method

Given:

Principal (P) = ₹2,000

Rate (R) = 7% per annum

Time Period: 9 February 2023 to 23 April 2023

Formula Used:

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

Calculations:

⇒ Total days = (28 − 9) in Feb + 31 in Mar + 23 in Apr

⇒ Total days = 19 + 31 + 23 = 73 days

⇒ Time (T) in years = 73 ÷ 365 = 1/5 years

⇒ SI = (2000 × 7 × 1/5) ÷ 100

⇒ SI = (400 × 7) ÷ 100

⇒ SI = 2800 ÷ 100

⇒ SI = ₹28

∴ The correct answer is ₹28.

Additional Information

Counting Days

While calculating the period for interest, the day on which money is borrowed is typically excluded, while the day on which money is returned is included.

Leap Year Check

For a non-leap year (like 2023), February has 28 days. For a leap year, February has 29 days. Always check if the year is divisible by 4.

Time Conversion

To convert days into years, divide by 365 (standard year). Common periods include 73 days (1/5 year), 146 days (2/5 year), and 219 days (3/5 year).

Shortcut Trick

For two objects moving towards each other, Relative Speed = Sum of individual speeds.

Total Distance = Sum of lengths of both trains = 496 + 490 = 986 m.

Relative Speed = 12 + 22 = 34 m/s.

Time taken = Total Distance ÷ Relative Speed = 986 ÷ 34 = 29 sec.

∴ The correct answer is 29 sec.

Alternate Method

Given:

Length of Train A (L₁) = 496 m

Length of Train B (L₂) = 490 m

Speed of Train A (S₁) = 12 m/s

Speed of Train B (S₂) = 22 m/s

Formula Used:

Time = (L₁ + L₂) ÷ (S₁ + S₂) [When moving in opposite directions]

Calculations:

⇒ Total distance to be covered = 496 + 490 = 986 m

⇒ Relative speed = Speed of A + Speed of B

⇒ Relative speed = 12 + 22 = 34 m/s

⇒ Time required = 986 ÷ 34

⇒ Time required = 29 sec

∴ The correct answer is 29 sec.

Additional Information

Relative Speed Concept

When two objects move in the opposite direction, their relative speed is S₁ + S₂. When they move in the same direction, it is S₁ − S₂.

Unit Conversion

To convert kmph to m/s, multiply by 5/18. To convert m/s to kmph, multiply by 18/5.

Crossing a Stationary Object

When a train crosses a pole or a man, the distance covered equals the length of the train itself.

Shortcut Trick

Convert ratio to integers by multiplying with LCM of denominators (9, 2, 5) = 90.

New ratio: (7/9 × 90) : (3/2 × 90) : (2/5 × 90) = 70 : 135 : 36.

Total units = 70 + 135 + 36 = 241 units.

Given 241 units = 241 bananas → 1 unit = 1 banana.

Third monkey share = 36 units = 36 bananas.

∴ The correct answer is 36 bananas.

Alternate Method

Given: Total bananas = 241, Ratio = 7/9 : 3/2 : 2/5

⇒ Simplify the ratio: 7/9 : 3/2 : 2/5

⇒ Multiply each term by LCM(9, 2, 5) = 90

⇒ Ratio = (70/90) : (135/90) : (36/90)

⇒ Ratio in simplest form = 70 : 135 : 36

⇒ Sum of ratio terms = 70 + 135 + 36 = 241

⇒ Third monkey's share = (36 ÷ 241) × 241

⇒ Third monkey's share = 36

∴ The correct answer is 36 bananas.

Additional Information

Ratio Simplification

To convert a fractional ratio a/b : c/d into an integer ratio, multiply both terms by the Lowest Common Multiple (LCM) of the denominators b and d.

Proportional Division

If a total quantity X is divided in the ratio a : b : c, then the share of the third part is calculated as [c / (a + b + c)] × X.

Compound Ratio

The compound ratio of (a : b) and (c : d) is (a × c) : (b × d), used when combining different proportional relationships.

Shortcut Trick

Combined efficiency of P + Q = 1/15 and P = 1/24.

Efficiency of Q = 1/15 − 1/24 = (8 − 5)/120 = 3/120 = 1/40.

Time for Q to fill one-fourth = (1/4) × 40 = 10 hours.

∴ The correct answer is 10 hours.

Alternate Method

Given: P + Q = 15 hours, P = 24 hours.

Formula Used: Total Work = LCM of time; Efficiency = Total Work ÷ Time.

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

⇒ Efficiency of Q = 8 − 5 = 3 units/hour

⇒ One-fourth of cistern = 120 ÷ 4 = 30 units

⇒ Time taken by Q alone = 30 ÷ 3 = 10 hours

∴ The correct answer is 10 hours.

Additional Information

Pipes & Cisterns Efficiency

If pipe A fills in x hours and pipe B fills in y hours, combined work per hour is 1/x + 1/y. If B is an outlet pipe, it is 1/x − 1/y.

Work & Wages

Wages are always distributed in the ratio of the efficiencies of the workers (or work done), not the time taken.

Alternate Day Work

For problems where workers work on alternate days, calculate the combined work in one cycle (e.g., 2 days) and divide total work by cycle work.

Shortcut Trick

Ratio 8 years ago = 4 : 3 | Ratio 8 years later = 5 : 4

Difference in ratio units = 5 − 4 = 1 unit and 4 − 3 = 1 unit

Time difference = 8 + 8 = 16 years

⇒ 1 unit = 16 years

Aman’s age 8 years ago = 4 units = 4 × 16 = 64 years

Aman’s present age = 64 + 8 = 72 years

∴ The correct answer is 72 years.

Alternate Method

Let Aman’s age and Riya’s age 8 years ago be 4x and 3x respectively.

Present ages: Aman = 4x + 8, Riya = 3x + 8

Ages 8 years from now: Aman = 4x + 16, Riya = 3x + 16

According to the question:

⇒ (4x + 16) / (3x + 16) = 5 / 4

⇒ 4(4x + 16) = 5(3x + 16)

⇒ 16x + 64 = 15x + 80

⇒ x = 80 − 64 = 16

⇒ Aman’s present age = 4x + 8 = 4 × 16 + 8

⇒ 64 + 8 = 72 years

∴ The correct answer is 72 years.

Additional Information

Ratio Difference Method

If the difference between ratio parts is same (5−4 = 1 and 4−3 = 1), then the difference corresponds directly to the years passed.

Age Difference Constancy

The numerical difference between the ages of two persons remains constant throughout their lives, regardless of how many years pass.

Cross-Multiplication Method

Used for solving ratio changes: (Initial Ratio) → (Add Years) → (Final Ratio) to find the value of one unit quickly.

Shortcut Trick

The surface area of a sphere is given by 4πr².

Equating the given value: 4πr² = 144π

Dividing both sides by 4π: r² = 36

Taking the square root: r = 6 units.

∴ The correct answer is 6 units.

Alternate Method

Given:

Surface area of the sphere = 144π sq units

Formula Used:

Surface Area of a Sphere = 4πr², where r is the radius.

Calculations:

⇒ 4 × π × r² = 144 × π

⇒ 4r² = 144

⇒ r² = 144 ÷ 4

⇒ r² = 36

⇒ r = √36

⇒ r = 6 units

∴ The correct answer is 6 units.

Additional Information

Volume of a Sphere

The amount of space occupied by a sphere is given by the formula V = (4/3)πr³.

Hemisphere Properties

For a hemisphere, the Curved Surface Area (CSA) is 2πr² and the Total Surface Area (TSA) is 3πr².

Diameter of a Sphere

The diameter is the longest distance through the sphere, calculated as D = 2 × r.

Shortcut Trick

Direct formula: LCM × HCF = Product of two numbers.

LCM × 12 = 2160

LCM = 2160 ÷ 12 = 180

∴ The correct answer is 180.

Alternate Method

Given:

HCF = 12

Product of two numbers = 2160

Formula Used:

HCF × LCM = n₁ × n₂

Calculations:

⇒ 12 × LCM = 2160

⇒ LCM = 2160 ÷ 12

⇒ LCM = 180

∴ The correct answer is 180.

Additional Information

HCF and LCM Relation

For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b.

HCF of Fractions

HCF of fractions = HCF of Numerators ÷ LCM of Denominators.

LCM of Fractions

LCM of fractions = LCM of Numerators ÷ HCF of Denominators.

Shortcut Trick

Convert Mass to grams: 3.168 kg = 3168 g.

Find Volume: 3168 ÷ 3.5 = 6336/7 cm³.

Solve for Radius (r): (4/3) × (22/7) × r³ = 6336/7 ⇒ r³ = 216 ⇒ r = 6 cm.

Find Surface Area: 4 × (22/7) × 6² = 3168/7 cm².

Calculate Total Cost: (3168/7) × 5.6 = 3168 × 0.8 = ₹2534.40.

∴ The correct answer is ₹2,534.40.

Alternate Method

Given:

Density of the spherical ball = 3.5 g/cm³

Total Mass = 3.168 kg = 3168 g

Rate of painting = ₹5.6 per cm²

Formula Used:

Volume (V) = Mass ÷ Density

Volume of sphere = (4/3) × π × r³

Surface Area of sphere = 4 × π × r²

Calculations:

⇒ Volume of the ball = 3168 ÷ 3.5 = 6336/7 cm³

⇒ (4/3) × (22/7) × r³ = 6336/7

⇒ (88/21) × r³ = 6336/7

⇒ r³ = (6336/7) × (21/88)

⇒ r³ = (6336 ÷ 88) × (21 ÷ 7)

⇒ r³ = 72 × 3 = 216

⇒ r = √216 = 6 cm

⇒ Surface Area of the ball = 4 × (22/7) × 6²

⇒ Surface Area = (4 × 22 × 36) ÷ 7 = 3168/7 cm²

⇒ Total Cost of Painting = Surface Area × Rate

⇒ Cost = (3168/7) × 5.6

⇒ Cost = 3168 × 0.8 = ₹2534.40

∴ The correct answer is ₹2,534.40.

Additional Information

Volume and Surface Area of Sphere

For a sphere of radius r, the volume is (4/3)πr³ and the total surface area is 4πr².

Density Formula

Density is mass per unit volume (ρ = Mass ÷ Volume). Ensure mass and density units are compatible (e.g., grams and g/cm³).

Hemisphere Properties

For a solid hemisphere, Curved Surface Area = 2πr², Total Surface Area = 3πr², and Volume = (2/3)πr³.

Shortcut Trick

Assume a base value (Assumed Mean) of 50.

Calculate deviations from 50: −3, +21, +32, +9, −28, −7, −4, +46, +6.

Sum of deviations = (−3 + 21 + 32 + 9 + 46 + 6) − (28 + 7 + 4) = 111 − 39 = 72.

Average deviation = 72 ÷ 9 = +8.

Actual Mean = Assumed Mean + Average deviation = 50 + 8 = 58.

∴ The correct answer is 58.

Alternate Method

Given: Observations are 47, 71, 82, 59, 22, 43, 46, 96, and 56.

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

⇒ Total sum of observations = 47 + 71 + 82 + 59 + 22 + 43 + 46 + 96 + 56

⇒ Total sum = 522

⇒ Total number of observations (n) = 9

⇒ Arithmetic Mean = 522 ÷ 9

⇒ Arithmetic Mean = 58

∴ The correct answer is 58.

Additional Information

Arithmetic Mean of First n Natural Numbers

The mean of the first n natural numbers is given by the formula: (n + 1) ÷ 2.

Empirical Relationship

The relationship between mean, median, and mode is: Mode = 3 × Median − 2 × Mean.

Effect of Change in Origin and Scale

If a constant k is added to or multiplied by each observation, the new mean becomes Mean + k or Mean × k respectively.

Shortcut Trick

If Savings = 60%, then Expenditure = 100% − 60% = 40%.

Given, 40% of Income = ₹560.

100% of Income = (560 ÷ 40) × 100 = 14 × 100 = ₹1400.

∴ The correct answer is ₹1400.

Alternate Method

Given:

Savings percentage = 60%

Total Expenditure = ₹560

Formula Used:

Income = Expenditure + Savings

Expenditure % = 100% − Savings %

Calculations:

⇒ Expenditure % = 100% − 60% = 40%

⇒ Let Total Income be 'I'.

⇒ 40% of I = 560

⇒ (40 ÷ 100) × I = 560

⇒ I = (560 × 100) ÷ 40

⇒ I = 14 × 100

⇒ I = 1400

∴ The correct answer is ₹1400.

Additional Information

Percentage Change in Income

If income increases by x% and expenditure increases by y%, the change in savings is calculated using the base equation: Income = Expenditure + Savings.

Base Change Property

When a value is expressed as a percentage of a total, the total can always be found by: (Value ÷ Percentage) × 100.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 70 + 80 + 50 = 200 km

Total Time = (70/60) + (80/80) + (50/40) = 7/6 + 1 + 5/4 = (14 + 12 + 15)/12 = 41/12 hours

Average Speed = 200 × (12/41) = 2400/41 ≈ 58.54 km/hr

∴ The correct answer is 58.54 km/hr.

Alternate Method

Given:

Distance₁ = 70 km, Speed₁ = 60 km/hr

Distance₂ = 80 km, Speed₂ = 80 km/hr

Distance₃ = 50 km, Speed₃ = 40 km/hr

Formula Used:

Time = Distance ÷ Speed

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = 70 + 80 + 50 = 200 km

⇒ Time₁ = 70/60 = 7/6 hours

⇒ Time₂ = 80/80 = 1 hour

⇒ Time₃ = 50/40 = 5/4 hours

⇒ Total Time = 7/6 + 1 + 5/4

⇒ Total Time = (14 + 12 + 15) / 12 = 41/12 hours

⇒ Average Speed = 200 ÷ (41/12) = (200 × 12) / 41

⇒ Average Speed = 2400 / 41 ≈ 58.5365...

∴ The correct answer is 58.54 km/hr.

Additional Information

Average Speed for Equal Distances

If a car covers two equal distances at speeds u and v, the average speed is given by (2 × u × v) ÷ (u + v).

Unit Conversion

To convert speed from km/hr to m/s, multiply by 5/18. To convert from m/s to km/hr, multiply by 18/5.

Relative Speed

When two objects move in the same direction, relative speed is the difference of their speeds. In opposite directions, it is the sum of their speeds.

Shortcut Trick

Ratio of Cost Price (CP) to Marked Price (MP) is CP : MP = (100 − Discount%) : (100 + Profit%).

CP : MP = (100 − 10) : (100 + 10) = 90 : 110 = 9 : 11.

Given 11 units = &8377;880 ⇒ 1 unit = &8377;80.

Therefore, 9 units = 9 × 80 = &8377;720.

∴ The correct answer is &8377;720.

Alternate Method

Given → Marked Price (MP) = &8377;880, Discount = 10%, Gain = 10%.
Formulas: SP = MP × (100 − D%) ÷ 100 | CP = SP × 100 ÷ (100 + G%).

⇒ Selling Price (SP) = 880 × (100 − 10) ÷ 100 = 880 × 0.9 = &8377;792.

⇒ Cost Price (CP) = 792 × 100 ÷ (100 + 10) = 792 × 100 ÷ 110.

⇒ CP = 72 × 10 = &8377;720.

∴ The correct answer is &8377;720.

Additional Information

Marked Price and Discount

The Marked Price (MP) is the price printed on the article. Discount is always calculated on the MP to arrive at the Selling Price (SP).

CP-MP Relation Formula

The direct relation between CP and MP is given by CP / MP = (100 − D%) / (100 + P%), where D is discount and P is profit percentage.

Shortcut Trick

Prime numbers (60 to 70): 61, 67 → Average = 128 ÷ 2 = 64

Multiples of 4 (50 to 58): 52, 56 → Average = 108 ÷ 2 = 54

Difference = 64 − 54 = 10

∴ The correct answer is 10.

Alternate Method

Given:

Range 1: Prime numbers between 60 and 70.

Range 2: Multiples of 4 between 50 and 58.

Calculations:

⇒ Prime numbers between 60 and 70 = {61, 67}

⇒ Average of primes = (61 + 67) ÷ 2 = 128 ÷ 2 = 64

⇒ Multiples of 4 between 50 and 58 = {52, 56}

⇒ Average of multiples = (52 + 56) ÷ 2 = 108 ÷ 2 = 54

⇒ Required Difference = 64 − 54 = 10

∴ The correct answer is 10.

Additional Information

Prime Numbers between 1 and 100

There are 25 prime numbers between 1 and 100. These are numbers having exactly two factors: 1 and the number itself.

Average of an Arithmetic Progression

The average of any series in arithmetic progression (like multiples of a number) is simply (First Term + Last Term) ÷ 2.

Composite Numbers

Numbers with more than two factors are composite numbers. Note that 1 is neither prime nor composite.

Shortcut Trick

Split inside root: √(a × b) = √a × √b

= √144×√49 + √64×√25 − √100×√36

= 12×7 + 8×5 − 10×6

= 84 + 40 − 60 = 64

∴ Answer = 64

Alternate Method

Given:

√(144 × 49) + √(64 × 25) − √(100 × 36)

Concept Used:

√(a × b) = √a × √b

Calculation:

⇒ √(144 × 49) = √144 × √49 = 12 × 7 = 84

⇒ √(64 × 25) = √64 × √25 = 8 × 5 = 40

⇒ √(100 × 36) = √100 × √36 = 10 × 6 = 60

⇒ Expression = 84 + 40 − 60

⇒ = 124 − 60

⇒ = 64

∴ The correct answer is 64.

Additional Information

Square Root Property

√(a × b) = √a × √b

Perfect Squares

144 = 12², 49 = 7², 64 = 8², 25 = 5²

Simplification Tip

Break numbers into perfect squares for quick solving

Common Pattern

Use factorization inside root to simplify faster

Shortcut Trick

To get the maximum selling price, the total discount percentage must be the minimum.

For two successive discounts a% and b%, effective discount = a + b − (a × b ÷ 100).

Scheme I: 14 + 14 − 1.96 = 26.04% | Scheme II: 22 + 29 − 6.38 = 44.62%.

Scheme III: 22 + 7 − 1.54 = 27.46% | Scheme IV: 14 + 6 − 0.84 = 19.16%.

Since 19.16% is the lowest discount, Scheme IV results in the highest selling price.

∴ The correct answer is IV.

Alternate Method

Given → Four different successive discount schemes.
Formulas: Effective Discount = a + b − (ab ÷ 100) | SP = MP × (100 − Discount%) ÷ 100.

⇒ Calculate Effective Discount (ED) for each scheme:
⇒ Scheme I: 14 + 14 − (14 × 14 ÷ 100) = 28 − 1.96 = 26.04%
⇒ Scheme II: 22 + 29 − (22 × 29 ÷ 100) = 51 − 6.38 = 44.62%
⇒ Scheme III: 22 + 7 − (22 × 7 ÷ 100) = 29 − 1.54 = 27.46%
⇒ Scheme IV: 14 + 6 − (14 × 6 ÷ 100) = 20 − 0.84 = 19.16%
⇒ Comparing all, Scheme IV has the minimum discount of 19.16%.

∴ The correct answer is IV.

Additional Information

Marked Price & Selling Price

The price printed on an article is the Marked Price (MP). Selling Price is obtained after subtracting the discount from the MP.

Successive Discount Concept

When two or more discounts are applied one after another, they are called Successive Discounts. The order of applying these discounts does not change the final selling price.

Shortcut Trick

For mean proportion between x and b to be M, the relationship is x × b = M².

Given M = 63 and b = 147.

x = 63² ÷ 147 = (63 × 63) ÷ 147.

x = (9 × 7 × 63) ÷ (21 × 7) ⇒ x = (9 × 63) ÷ 21 = 9 × 3 = 27.

∴ The correct answer is 27.

Alternate Method

Given: Mean proportion = 63, First number = x, Second number = 147.

Formula Used: Mean Proportion = √(a × b)

⇒ 63 = √(x × 147)

Squaring both sides:

⇒ 63² = x × 147

⇒ 3969 = x × 147

⇒ x = 3969 ÷ 147

⇒ x = 27

∴ The correct answer is 27.

Additional Information

Third Proportion

The third proportion of two numbers a and b is c, such that a : b :: b : c, given by c = b²/a.

Fourth Proportion

The fourth proportion of three numbers a, b, and c is d, such that a : b :: c : d, given by d = (b × c)/a.

Compounded Ratio

The compounded ratio of (a : b) and (c : d) is (a × c) : (b × d).

Shortcut Trick

In right-angled triangle BDC, ∠C = 90° − ∠DBC = 90° − 21° = 69°.

In ΔAEC, ∠AEB is the exterior angle at vertex E.

By the Exterior Angle Theorem, ∠AEB = ∠CAE + ∠ACE.

∠AEB = 27° + 69° = 96°.

∴ The correct answer is 96°.

Alternate Method

Given: BD ⊥ AC, ∠DBC = 21°, ∠CAE = 27°.

Formula Used: Angle Sum Property of a triangle (sum = 180°) and Linear Pair property.

In ΔBDC:

⇒ ∠BDC = 90° (Since BD ⊥ AC)

⇒ ∠BCD = 180° − (∠BDC + ∠DBC)

⇒ ∠BCD = 180° − (90° + 21°) = 69

Shortcut Trick

Let the number be 10 (LCM of denominators 5 and 2).

Three-fifths of 10 = 6 units.

One-half of 10 = 5 units.

Difference (6 − 5) = 1 unit → 4.

Original number (10 units) = 10 × 4 = 40.

∴ The correct answer is 40.

Alternate Method

Let the unknown number be x.

As per the problem

Statement:

⇒ (3/5) × x = (1/2) × x + 4

⇒ (3x/5) − (x/2) = 4

⇒ (6x − 5x) / 10 = 4

⇒ x / 10 = 4

⇒ x = 40

∴ The correct answer is 40.

Additional Information

Fractions to Percentage

Converting fractions to percentages often simplifies logic: 3/5 is 60% and 1/2 is 50%. The 10% difference equals 4, so 100% equals 40.

Linear Equations

A linear equation in one variable follows the form ax + b = 0. Solving involves isolating the variable x on one side.

LCM Method for Fractions

When dealing with multiple fractions, assuming the number as the LCM of the denominators eliminates fractional calculations and speeds up solving.