Quantitative Aptitude PYQs

Shortcut Trick

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

Net discount = 25 + 12 − (25 × 12) ÷ 100 = 37 − 3 = 34%

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

SP = 6400 × (100 − 34) ÷ 100 = 6400 × 0.66 = 4224

∴ The correct answer is ₹4,224.

Alternate Method

Given: Marked Price (MP) = ₹6,400, First Discount (d₁) = 25%, Second Discount (d₂) = 12%.
Formulas: SP = MP × (100 − d₁)% × (100 − d₂)%

⇒ Price after first discount = 6400 × (1 − 25/100) = 6400 × 3/4 = ₹4,800
⇒ Price after second discount (Final SP) = 4800 × (1 − 12/100)
⇒ Final SP = 4800 × 88/100 = 48 × 88
⇒ Final SP = ₹4,224

∴ The correct answer is ₹4,224.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the base for each subsequent discount is the value after the previous discount.

Marked Price & Selling Price

Selling Price = Marked Price − Discount. Discount is always calculated on the Marked Price unless stated otherwise.

Shortcut Trick

Assume an arbitrary mean (let A = 50) and calculate deviations from it.

Deviations: (+35, +23, +39, −21, −30, +2, −28, −25, +5).

Sum of deviations = (35 + 23 + 39 + 2 + 5) − (21 + 30 + 28 + 25) = 104 − 104 = 0.

Correct Mean = Assumed Mean + (Sum of Deviations ÷ Total Count) = 50 + (0 ÷ 9) = 50.

∴ The correct answer is 50.

Alternate Method

Given: Observations = 85, 73, 89, 29, 20, 52, 22, 25, 55

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

⇒ Sum = 85 + 73 + 89 + 29 + 20 + 52 + 22 + 25 + 55

⇒ Sum = 450

⇒ Number of observations (n) = 9

⇒ Arithmetic Mean = 450 ÷ 9

⇒ Arithmetic Mean = 50

∴ The correct answer is 50.

Additional Information

Properties of Arithmetic Mean

The sum of the deviations of all observations from their arithmetic mean is always zero: Σ(x_i − mean) = 0.

Effect of Change of Origin

If a constant value k is added to or subtracted from every observation, the new mean will be (original mean + k) or (original mean − k).

Empirical Relationship

For a moderately skewed distribution, the relationship between measures of central tendency is: Mode = 3 × Median − 2 × Mean.

Shortcut Trick

Let A = 0°.

Substitute A = 0° in the expression: (1 / (1 − sin 0°) + 1 / (1 + sin 0°)) × cos² 0°

⇒ (1 / (1 − 0) + 1 / (1 + 0)) × 1² = (1 + 1) × 1 = 2

Check options with A = 0°: Option (3) is 2.

∴ The correct answer is 2.

Alternate Method

Given:

Expression: (1 / (1 − sin A) + 1 / (1 + sin A)) × cos² A

Formula Used:

⇒ (a − b)(a + b) = a² − b²

⇒ 1 − sin² A = cos² A

Calculations:

Simplify the term inside the bracket by taking the LCM:

⇒ (1 + sin A + 1 − sin A) / ((1 − sin A)(1 + sin A)) × cos² A

⇒ 2 / (1 − sin² A) × cos² A

⇒ 2 / cos² A × cos² A

⇒ 2

∴ The correct answer is 2.

Additional Information

Trigonometric Identities

The three basic Pythagorean identities are: sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Reciprocal Identities

sec θ = 1 / cos θ, cosec θ = 1 / sin θ, and cot θ = 1 / tan θ.

Shortcut Trick

Age difference remains constant at 16 years.

Present sum = 56 + (6 × 2) = 68 years.

Vijay's age = (Sum − Difference) ÷ 2

Vijay's age = (68 − 16) ÷ 2 = 52 ÷ 2 = 26 years.

∴ The correct answer is 26 years.

Alternate Method

Given:

Difference between Ajay and Vijay = 16 years.

Sum of ages 6 years ago = 56 years.

Let Vijay's present age be x years.

∴ Ajay's present age = x + 16 years.

⇒ (x − 6) + (x + 16 − 6) = 56

⇒ 2x + 4 = 56

⇒ 2x = 52

⇒ x = 26

∴ The correct answer is 26 years.

Additional Information

Age Difference Property

The difference between the ages of two people always remains the same regardless of the number of years passed or preceding.

Sum of Ages Calculation

To find the sum of ages ‘n’ years ago for ‘k’ people, subtract (n × k) from the present sum.

Linear Equations in Ages

Problems involving two variables are best solved by substituting one variable to form a single-variable linear equation.

Shortcut Trick

Difference in Rate of Interest = 7% − 3.5% = 3.5% p.a.

Total difference in Percentage for 3 years = 3.5% × 3 = 10.5%

Positive difference in Simple Interest = 10.5% of ₹5,00,000

⇒ (10.5/100) × 5,00,000 = 10.5 × 5,000 = ₹52,500

∴ The correct answer is ₹52,500.

Alternate Method

Given:

Principal (P) = ₹5,00,000 for both banks.

Rate for Bank A (R₁) = 3.5% | Rate for Bank B (R₂) = 7%

Time (T) = 3 years

Formula Used: Simple Interest (SI) = (P × R × T) / 100

Calculations:

⇒ SI paid to Bank A = (5,00,000 × 3.5 × 3) / 100

⇒ SI paid to Bank A = 5,000 × 10.5 = ₹52,500

⇒ SI paid to Bank B = (5,00,000 × 7 × 3) / 100

⇒ SI paid to Bank B = 5,000 × 21 = ₹1,05,000

⇒ Positive Difference = ₹1,05,000 − ₹52,500

⇒ Positive Difference = ₹52,500

∴ The correct answer is ₹52,500.

Additional Information

Simple Interest (SI) Properties

The Simple Interest remains constant every year if the principal and rate are unchanged. It is calculated only on the original Principal amount.

Interest Difference Formula

When the Principal (P) and Time (T) are the same, the difference in interest is given by: Difference = P × T × (R_high − R_low) / 100.

Total Amount

The total amount (A) to be repaid at the end of the term is the sum of the Principal and the Simple Interest: A = P + SI.

Shortcut Trick

Factorize 30 into two consecutive integers: 30 = 5 × 6.

For the positive series x, the value is the larger factor: x = 6.

For the negative series y, the value is the smaller factor: y = 5.

Product xy = 6 × 5 = 30. When 30 is divided by 7, the remainder is 2 (since 7 × 4 = 28).

∴ The correct answer is 2.

Alternate Method

Given: \(x = \sqrt{30 + \sqrt{30 + \sqrt{30 + \dots \infty}}} \text{ and } y = \sqrt{30 - \sqrt{30 - \sqrt{30 - \dots \infty}}}\)

Formula Used: For \(\sqrt{n \pm \sqrt{n \pm \dots}}\), the value is \(\frac{\sqrt{4n+1} \pm 1}{2}\).

⇒ x = \(\frac{\sqrt{4 \times 30 + 1} + 1}{2} = \frac{\sqrt{121} + 1}{2} = \frac{11+1}{2} = 6\)

⇒ y = \(\frac{\sqrt{4 \times 30 + 1} - 1}{2} = \frac{\sqrt{121} - 1}{2} = \frac{11-1}{2} = 5\)

⇒ Product xy = 6 × 5 = 30

⇒ Remainder of (30 ÷ 7) ⇒ 30 = (7 × 4) + 2

⇒ Remainder = 2

∴ The correct answer is 2.

Additional Information

Infinite Nested Radicals

If n = k(k+1), then √(n+√(n+...)) = k+1 and √(n−√(n−...)) = k.

Relation between Roots

For any number n, the difference between the positive and negative infinite series is always x − y = 1 and their product is x × y = n.

Remainder Theorem

The remainder of a product (A × B) ÷ n is equal to (Rem(A/n) × Rem(B/n)) ÷ n.

Shortcut Trick

Number = 3.6(27)

Decimal part = 0.6 + 0.0272727…

= 6/10 + 27/990

= 3/5 + 3/110 = 66/110 + 3/110 = 69/110

Total = 3 + 69/110 = (330 + 69)/110 = 399/110

∴ Answer = 399/110

Alternate Method

Given:

x = 3.6272727… (27 repeating)

Formula used:

Multiply and subtract method

Calculation:

⇒ x = 3.6272727…

⇒ 10x = 36.272727…

⇒ 1000x = 3627.272727…

⇒ Subtract: 1000x − 10x

⇒ 990x = 3591

⇒ x = 3591/990

⇒ Divide by 9 ⇒ x = 399/110

∴ The correct answer is 399/110.

Additional Information

Recurring Decimal Rule

Use powers of 10 to align repeating digits and subtract.

Shortcut Method

For mixed recurring decimals: (Full number − non-repeating part) ÷ (99…0 form)

Denominator Rule

Use 9s for repeating digits and 0s for non-repeating digits.

Shortcut Trick

Direct formula: 2 × Mean = 3 × Median − Mode

Substitute the given values: 2 × Mean = 3(23) − 27.5

2 × Mean = 69 − 27.5 = 41.5

Mean = 41.5 ÷ 2 = 20.75

∴ The correct answer is 20.75.

Alternate Method

Given:

Mode of the data = 27.5

Median of the data = 23

Formula Used:

The Empirical relationship between Mean, Median, and Mode is:

Mode = 3 × Median − 2 × Mean

Calculations:

⇒ 27.5 = 3 × (23) − 2 × Mean

⇒ 27.5 = 69 − 2 × Mean

⇒ 2 × Mean = 69 − 27.5

⇒ 2 × Mean = 41.5

⇒ Mean = 41.5 ÷ 2

⇒ Mean = 20.75

∴ The correct answer is 20.75.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship is: Mode = 3 × Median − 2 × Mean or Mean − Mode = 3(Mean − Median).

Symmetrical Distribution

In a perfectly symmetrical distribution, the values of Mean, Median, and Mode are all equal (Mean = Median = Mode).

Positively Skewed Distribution

In a positively skewed distribution, the tail on the right side is longer, and generally: Mean > Median > Mode.

Negatively Skewed Distribution

In a negatively skewed distribution, the tail on the left side is longer, and generally: Mean < Median < Mode.

Shortcut Trick

Combined efficiency of A, B and C = 4 + 3 + 1 = 8 units/day (taking Total Work as 12 units).

Twice the work = 12 × 2 = 24 units.

Time taken to complete twice the work together = 24 ÷ 8 = 3 days.

∴ The correct answer is 3 days.

Alternate Method

Given:

Time taken by A = 3 days

Time taken by B = 4 days

Time taken by C = 12 days

Formula Used:

Efficiency = Total Work ÷ Time Taken

Calculations:

⇒ Total efficiency of A, B and C = 4 + 3 + 1 = 8 units/day

⇒ New work to be completed = 2 × Total Work = 2 × 12 = 24 units

⇒ Time taken together = New work ÷ Total efficiency

⇒ Time taken together = 24 ÷ 8 = 3 days

∴ The correct answer is 3 days.

Additional Information

LCM Method for Time and Work

Taking the LCM of individual days as the total work simplifies calculations by avoiding fractions, making the determination of individual efficiencies straightforward.

Work and Efficiency Relation

Efficiency is inversely proportional to the time taken to complete a task. If the amount of work changes, the time taken changes proportionally for a constant efficiency.

Shortcut Trick

Using the Multiplying Factor method for successive changes.

Net Factor = (1 − 0.55) × (1 − 0.40) × (1 − 0.15) × (1 + 0.60)

Net Factor = 0.45 × 0.60 × 0.85 × 1.60 = 0.3672

Percentage Change = (0.3672 − 1) × 100 = −63.28%

∴ The correct answer is Decreases by 63.28%.

Alternate Method

Given: Initial price decreases by 55%, 40%, 15% and then increases by 60%.

⇒ Let the Original Price be 100.

⇒ Price after 1^st month = 100 − 55% of 100 = 45

⇒ Price after 2^nd month = 45 − 40% of 45 = 45 − 18 = 27

⇒ Price after 3^rd month = 27 − 15% of 27 = 27 − 4.05 = 22.95

⇒ Price after 4^th month = 22.95 + 60% of 22.95 = 22.95 + 13.77 = 36.72

⇒ Total Decrease = 100 − 36.72 = 63.28

⇒ Percentage Decrease = (63.28 ÷ 100) × 100 = 63.28%

∴ The correct answer is Decreases by 63.28%.

Additional Information

Successive Percentage Change Formula

For two changes a% and b%, the effective change is [a + b + (a×b)/100]%.

Successive Discount/Decrease

If values are decreasing, use negative signs in the formula or multiplying factors less than 1.

Net Multiplying Factor

The final value is found by multiplying the initial value by (1 ± r₁/100)(1 ± r₂/100)...

Shortcut Trick

Initial profit = 14%, so initial SP = 114% of CP = ₹ 1,425.

Required profit = 8%, so required SP = 108% of CP.

Using unitary method: SP = (1,425 ÷ 114) × 108.

SP = 12.5 × 108 = ₹ 1,350.

∴ The correct answer is ₹ 1,350.

Alternate Method

Given: Selling Price₁ = ₹ 1,425, Profit₁ = 14%, Profit₂ = 8%.
Formulas: CP = SP × 100 ÷ (100 + Profit%), SP = CP × (100 + Profit%) ÷ 100.

⇒ First, find the Cost Price (CP): CP = 1,425 × 100 ÷ 114 = ₹ 1,250.
⇒ Now, calculate the new Selling Price (SP) for 8% profit: SP = 1,250 × (100 + 8) ÷ 100.
⇒ SP = 1,250 × 108 ÷ 100 = 12.5 × 108 = ₹ 1,350.

∴ The correct answer is ₹ 1,350.

Additional Information

Relationship between CP and SP

If there is a profit, SP is always greater than CP. SP = CP + Profit. If there is a loss, CP is greater than SP. SP = CP − Loss.

Constant CP Method

Since the article is the same, CP remains constant. We can directly compare the percentage values: (SP₁ ÷ (100 + P₁%)) = (SP₂ ÷ (100 + P₂%)).

Shortcut Trick

Total distance to cover = Sum of lengths of both trains = 402 + 286 = 688 m.

Relative speed (opposite direction) = Sum of speeds = 6 + 37 = 43 m/s.

Time taken = Total distance ÷ Relative speed = 688 ÷ 43 = 16 sec.

∴ The correct answer is 16 sec.

Alternate Method

Given:

Length of Train A (L₁) = 402 m

Length of Train B (L₂) = 286 m

Speed of Train A (S₁) = 6 m/s

Speed of Train B (S₂) = 37 m/s

Formula Used:

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

Calculations:

⇒ Total Distance = 402 + 286 = 688 m

⇒ Relative Speed = 6 + 37 = 43 m/s

⇒ Time = 688 ÷ 43

⇒ Time = 16 sec

∴ The correct answer is 16 sec.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, the relative speed is the difference of their speeds: |S₁ − S₂|.

Speed Conversion

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

Crossing a Point Object

When a train crosses a pole or a standing man, the distance covered is equal to the length of the train itself.

Shortcut Trick

Total heads = 180. If all animals were Parrots (2 legs), total legs = 180 × 2 = 360.

Actual legs = 520. Extra legs = 520 − 360 = 160.

Difference in legs between a Rabbit and a Parrot = 4 − 2 = 2.

Number of Rabbits = Extra legs ÷ Difference = 160 ÷ 2 = 80.

∴ The correct answer is 80 rabbits.

Alternate Method

Given: Total animal heads = 180, Total animal legs = 520.

Formula: Let number of Rabbits be R and Parrots be P.

Let the number of Rabbits be R and Parrots be P.

⇒ R + P = 180 — (Eq. 1)

⇒ 4R + 2P = 520 — (Eq. 2)

⇒ Divide (Eq. 2) by 2: 2R + P = 260 — (Eq. 3)

⇒ Subtract (Eq. 1) from (Eq. 3): (2R + P) − (R + P) = 260 − 180

⇒ R = 80

⇒ Number of Rabbits = 80

∴ The correct answer is 80 rabbits.

Additional Information

Direct Formula for 4-legged animals

Number of 4-legged animals = (Total Legs − 2 × Total Heads) ÷ 2. This accounts for the 2 extra legs each animal has over the base of 2 legs.

Direct Formula for 2-legged animals

Number of 2-legged animals = (4 × Total Heads − Total Legs) ÷ 2. This assumes all are 4-legged and subtracts the deficiency.

Alligation Application

Ratio of 2-legged to 4-legged animals = (Legs of 4-legged − Avg Legs) : (Avg Legs − Legs of 2-legged).

Shortcut Trick

To gain the maximum advantage, Rohit must choose the option with the highest total discount percentage.

Compare total values: Option 1 = 14%; Option 2 = 14 + 14 − (14 × 14 ÷ 100) ≈ 26.04%; Option 4 = 14 + 8 − (14 × 8 ÷ 100) ≈ 20.88%.

Option 3 = 38 + 46 − (38 × 46 ÷ 100) = 84 − 17.48 = 66.52%.

Clearly, 66.52% is the largest discount among all available choices.

∴ The correct answer is Two successive discounts of 38% and 46%.

Alternate Method

Given → Marked Price (MP) = ₹6,900.
Formulas: Successive Discount = a + b − (a × b ÷ 100).

→ Option 1: 14%.
→ Option 2: 14 + 14 − (196 ÷ 100) = 28 − 1.96 = 26.04%.
→ Option 3: 38 + 46 − (38 × 46 ÷ 100) = 84 − 17.48 = 66.52%.
→ Option 4: 14 + 8 − (14 × 8 ÷ 100) = 22 − 1.12 = 20.88%.
→ Maximum advantage is gained when the Equivalent Discount is the highest.
∴ The correct answer is Two successive discounts of 38% and 46%.

Additional Information

Successive Discounts

When two or more discounts are applied one after another, the net discount is calculated on the diminishing balance. Formula: Total = a + b − (ab/100).

Maximum Advantage

For a buyer, the best offer is the one that results in the highest effective discount rate, regardless of the initial base price.

Shortcut Trick

Pipe A works for the entire 23 minutes.

Work done by Pipe A in 23 minutes = 23 ÷ 46 = 1/2 of the tank.

Remaining 1/2 of the tank is filled by Pipe B.

Time taken by Pipe B = (1/2) × 32 = 16 minutes.

∴ The correct answer is 16 min.

Alternate Method

Given: Filling time for Pipe A = 46 min, Pipe B = 32 min. Total time to fill = 23 min.

⇒ Total capacity (LCM of 46 and 32) = 736 units.

⇒ Efficiency of Pipe A = 736 ÷ 46 = 16 units/min.

⇒ Efficiency of Pipe B = 736 ÷ 32 = 23 units/min.

⇒ Pipe A runs for the full 23 minutes: Work by A = 16 × 23 = 368 units.

⇒ Remaining work for Pipe B = 736 − 368 = 368 units.

⇒ Time for which Pipe B was open = 368 ÷ 23 = 16 minutes.

∴ The correct answer is 16 min.

Additional Information

Pipes and Cisterns Efficiency

Efficiency is inversely proportional to time. If a pipe fills a tank in 'x' hours, its 1-hour work is 1/x.

Total Work Concept

Total Work = Efficiency × Time. In problems where one pipe is closed early, the pipe that remains open throughout completes its share based on the total duration.

Shortcut Trick

Floor Area = 3888 ÷ 18 = 216 m²

Ratio of Length (L) to Width (W) = 1.5 : 1 = 3 : 2 ⇒ 3x × 2x = 216 ⇒ 6x² = 216 ⇒ x = 6

Dimensions: L = 18 m, W = 12 m

Wall Area = 4320 ÷ 9 = 480 m² ⇒ Height (H) = 480 ÷ [2 × (18 + 12)] = 8 m

Volume = Floor Area × Height = 216 × 8 = 1728 m³

∴ The correct answer is 1728 m³.

Alternate Method

Given: Cost of carpeting = ₹18/m², Total carpeting cost = ₹3,888, Cost of whitewashing walls = ₹9/m², Total whitewashing cost = ₹4,320, Length (L) = 1.5 × Width (W).

Formula Used: Area of floor = L × W | Area of 4 walls = 2H(L + W) | Volume = L × W × H

⇒ Area of the floor = 3888 ÷ 18 = 216 m²

⇒ L × W = 216 ⇒ (1.5W) × W = 216

⇒ 1.5W² = 216 ⇒ W² = 144 ⇒ Width (W) = 12 m

⇒ Length (L) = 1.5 × 12 = 18 m

⇒ Area of 4 walls = 4320 ÷ 9 = 480 m²

⇒ 2H(L + W) = 480 ⇒ 2 × H × (18 + 12) = 480

⇒ 2 × H × 30 = 480 ⇒ 60H = 480 ⇒ Height (H) = 8 m

⇒ Volume of the room = L × W × H = 18 × 12 × 8

⇒ Volume = 216 × 8 = 1728 m³

∴ The correct answer is 1728 m³.

Additional Information

Area of Four Walls (Lateral Surface Area)

The lateral surface area of a cuboid (room) is the area of the 4 vertical faces, calculated as 2 × Height × (Length + Width).

Total Surface Area of a Cuboid

It includes the floor and ceiling area along with the four walls: TSA = 2(LW + WH + LH).

Longest Rod in a Room (Diagonal)

The length of the longest rod that can be placed in a room is given by √(L² + W² + H²).

Shortcut Trick

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

⇒ n = 360 ÷ 24 = 15

Number of diagonals = [n × (n − 3)] ÷ 2

⇒ Diagonals = [15 × (15 − 3)] ÷ 2

⇒ Diagonals = [15 × 12] ÷ 2 = 90

∴ The correct answer is 90.

Alternate Method

Given:

Each exterior angle of a regular polygon = 24°

Formula Used:

1. Number of sides (n) = 360° ÷ Exterior angle
2. Number of diagonals = [n × (n − 3)] ÷ 2

Shortcut Trick

Let number = x

Given: x = 66 + 20% of x

⇒ 80% of x = 66

⇒ x = 66 ÷ 0.8 = 82.5

80% of x = 66

∴ Answer = 66

Alternate Method

Given:

20% of a number + 66 = the number

Formula used:

Percentage = (part ÷ whole) × 100

Calculation:

⇒ Let the number be x

⇒ x = 66 + 20% of x

⇒ x = 66 + 0.2x

⇒ x − 0.2x = 66

⇒ 0.8x = 66

⇒ 80% of x = 66

∴ The correct answer is 66.

Additional Information

Percentage Concept

x% = x/100

Equation Formation

Translate word statement into equation.

Shortcut Idea

Bring like terms together to isolate variable.

Shortcut Trick

For fourth proportional: 12 ÷ a = 2a ÷ 54

Product of extremes = Product of means

12 × 54 = a × 2a

2a² = 648 ⇒ a² = 324

a = √324 = 18

∴ The correct answer is 18.

Alternate Method

Given: First term = 12, Second term = a, Third term = 2a, Fourth term = 54

Formula: If x, y, z, w are in proportion, then x/y = z/w

⇒ 12 / a = 2a / 54

⇒ 12 × 54 = a × 2a

⇒ 648 = 2a²

⇒ a² = 648 ÷ 2

⇒ a² = 324

⇒ a = √324

⇒ a = 18

∴ The correct answer is 18.

Additional Information

Fourth Proportional

For three numbers x, y, and z, the fourth proportional d is defined such that x/y = z/d, implying d = (y × z) / x.

Third Proportional

For two numbers x and y, the third proportional c is such that x/y = y/c, which gives c = y² / x.

Mean Proportional

The mean proportional between two numbers x and y is given by √(x × y).

Shortcut Trick

Spending = 60%, so Savings = 40%.

Ratio of Spending : Savings = 60 : 40 = 3 : 2.

Given 2 units = ₹8,242.

Then 3 units (Expenses) = (8,242 ÷ 2) × 3 = 4,121 × 3 = ₹12,363.

∴ The correct answer is ₹12,363.

Alternate Method

Given:

Spending Percentage = 60%

Monthly Savings = ₹8,242

Formula Used:

Income = Expenditure + Savings

Expenditure = Income × Spending %

Calculations:

⇒ Let Total Income be x.

⇒ Savings Percentage = 100% − 60% = 40%

⇒ 40% of x = 8,242

⇒ (40/100) × x = 8,242

⇒ x = (8,242 × 100) ÷ 40

⇒ x = 20,605

⇒ Monthly Expenses = 60% of 20,605

⇒ Monthly Expenses = (60/100) × 20,605

⇒ Monthly Expenses = 0.6 × 20,605 = 12,363

∴ The correct answer is ₹12,363.

Additional Information

Percentage Change

If income increases by a% and expenses increase by b%, the new savings can be calculated using the Income = Expenditure + Savings balance.

Base Value concept

Always ensure the Percentage is calculated on the correct base. Here, both spending and savings percentages are based on the Total Monthly Income.

Ratio Application

For quick calculations, convert percentages to fractions: 60% = 3/5 (Expenses) and 40% = 2/5 (Savings).