Quantitative Aptitude PYQs

Shortcut Trick

Initial total volume ≈ 150 liters, Soda = 50 liters → Juice = 100 liters (Ratio of Juice to Soda = 2 : 1).

Removing 30 liters of mixture keeps the ratio 2 : 1, so remaining is 120 liters → Juice = 80 liters, Soda = 40 liters.

Adding 10 liters of pure juice makes Juice = 90 liters and Soda = 40 liters.

Resultant ratio of Juice to Soda = 90 : 40 = 9 : 4.

Wait, let us check option values: 150 liters, 50 soda → 100 juice. Take out 30 liters → remaining mixture = 120 liters. Since ratio is 2:1, remaining Juice = 80, Soda = 40. Add 10 liters juice → Juice = 90, Soda = 40. Ratio = 9:4 (which is Option 5). Let's check the corrected value.

∴ The correct answer is 9:4.

Alternate Method

Given:

Total volume of mixture ≈ 150 liters

Volume of soda ≈ 50 liters

Volume of juice = 150 − 50 = 100 liters

Mixture taken out ≈ 30 liters

Pure juice added ≈ 10 liters

Calculations:

⇒ Initial Ratio of Juice : Soda = 100 : 50 = 2 : 1

⇒ In 30 liters of mixture taken out:

⇒ Juice removed = (2 ÷ 3) × 30 = 20 liters

⇒ Soda removed = (1 ÷ 3) × 30 = 10 liters

⇒ Remaining Juice = 100 − 20 = 80 liters

⇒ Remaining Soda = 50 − 10 = 40 liters

⇒ After adding 10 liters of pure juice:

⇒ New Juice volume = 80 + 10 = 90 liters

⇒ New Soda volume = 40 liters

⇒ Resultant Ratio = 90 : 40 = 9 : 4

∴ The correct answer is 9:4.

Additional Information

Mixture Withdrawal Rule

When a portion of a mixture is removed, the remaining ingredients stay in the same ratio as the original mixture.

Replacement Formula

If y liters are removed from x liters of mixture and replaced with pure component, the remaining quantity of the other component is given by Initial Quantity × (1 − y/x).

Shortcut Trick

Average of 2^nd lowest and 10^th number is 32 ⇒ Sum = 64.

Let 1^st number be x. Then (x + 1) + (x + 9) = 64 ⇒ 2x + 10 = 64 ⇒ x = 27.

Set A: 27, 28, 29, 30, 31, 32, 33, 34, 35, 36. Second highest = 35.

Set B starts at 35 (5 consecutive odd numbers). Average is the middle (3^rd) term.

Set B: 35, 37, 39, 41, 43. Middle term = 39.

∴ The correct answer is 39.

Alternate Method

Given: Set A has 10 consecutive numbers. Average of 2^nd and 10^th is 32.

Formula: Average = Sum of observations ÷ Number of observations.

⇒ Let numbers in Set A be n, n+1, ..., n+9.

⇒ [(n + 1) + (n + 9)] ÷ 2 = 32

⇒ 2n + 10 = 64 ⇒ 2n = 54 ⇒ n = 27.

⇒ Second highest number of Set A = n + 8 = 27 + 8 = 35.

⇒ Lowest number of Set B = 35.

⇒ Set B (5 consecutive odd): 35, 37, 39, 41, 43.

⇒ Average of Set B = (35 + 43) ÷ 2 = 39.

∴ The correct answer is 39.

Additional Information

Average of Arithmetic Progression

For any series in AP, the average is simply (First term + Last term) ÷ 2 or the middle term if the number of terms is odd.

Consecutive Odd/Even Numbers

Consecutive odd or even numbers always have a common difference of 2. The average of n terms is the (n+1)/2 term.

Common solution:

Let the total vehicles (Petrol, EV and Diesel) manufactured by D be 100a

Petrol vehicles manufactured = 100a × {25/100} = 25a

Diesel vehicles manufactured = 25a × {60/100} = 15a

Given,

100a – 25a – 15a = 240

60a = 240

so, a = 4

The total vehicles (Petrol, EV and Diesel) manufactured = 100a = 400

Petrol vehicles manufactured =100

Diesel vehicles manufactured = 60

Similarly,

 

Calculation:

Total number of vehicles manufactured by A = 90 + 90 + 36 = 216

Total number of diesel vehicles manufactured by C, D and B together = 150 + 60 + 50 = 260

Required difference = 260 - 216 = 44

Common solution:

Let the total vehicles (Petrol, EV and Diesel) manufactured by D be 100a

Petrol vehicles manufactured = 100a × {25/100} = 25a

Diesel vehicles manufactured = 25a × {60/100} = 15a

Given,

100a – 25a – 15a = 240

60a = 240

so, a = 4

The total vehicles (Petrol, EV and Diesel) manufactured = 100a = 400

Petrol vehicles manufactured =100

Diesel vehicles manufactured = 60

Similarly,

 

Calculation:

From the calculated table:

Total vehicles manufactured by D = 400

Total vehicles manufactured by F =400 x {125}/100} = 500

Petrol vehicles manufactured by F = {300/2} = 150

Given,

Diesel vehicles manufactured by B: F = 10:19

Diesel vehicles manufactured by B = 50

Diesel vehicles manufactured by F = 50 x {19/10} = 95

Total EVs manufactured by F =500 – 150 – 95 = 255

Common solution:

Let the total vehicles (Petrol, EV and Diesel) manufactured by D be 100a

Petrol vehicles manufactured = 100a × {25/100} = 25a

Diesel vehicles manufactured = 25a × {60/100} = 15a

Given,

100a – 25a – 15a = 240

60a = 240

so, a = 4

The total vehicles (Petrol, EV and Diesel) manufactured = 100a = 400

Petrol vehicles manufactured =100

Diesel vehicles manufactured = 60

Similarly,

 

Calculation:

Total vehicles manufactured by C = 180 + 300 + 150 = 630

Total EVs manufactured by B = 120

Required ratio = 630:120 = 21:4

Common solution:

Let the total vehicles (Petrol, EV and Diesel) manufactured by D be 100a

Petrol vehicles manufactured = 100a × {25/100} = 25a

Diesel vehicles manufactured = 25a × {60/100} = 15a

Given,

100a – 25a – 15a = 240

60a = 240

so, a = 4

The total vehicles (Petrol, EV and Diesel) manufactured = 100a = 400

Petrol vehicles manufactured =100

Diesel vehicles manufactured = 60

Similarly,

 

Calculation:

Required percentage = (108 – 60)/60 x 100 = 80%

Common solution:

Let the total vehicles (Petrol, EV and Diesel) manufactured by D be 100a

Petrol vehicles manufactured = 100a × {25/100} = 25a

Diesel vehicles manufactured = 25a × {60/100} = 15a

Given,

100a – 25a – 15a = 240

60a = 240

so, a = 4

The total vehicles (Petrol, EV and Diesel) manufactured = 100a = 400

Petrol vehicles manufactured =100

Diesel vehicles manufactured = 60

Similarly,

 

Calculation:

Required difference = (120 + 200 + 50) – 60 = 370 – 60 = 310

Shortcut Trick

Let the Cost Price (CP) of both items be 100%.

Difference in Profit Percentage = 35% − 25% = 10%.

According to the question, 10% of CP = Rs 750.

Therefore, 100% of CP = 750 × (100 ÷ 10) = Rs 7500.

∴ The correct answer is Rs 7500.

Alternate Method

Given: CP_X = CP_Y, Profit_X = 25%, Profit_Y = 35%, Difference in Profit = Rs 750.

Formulas: Profit = CP × (Profit% ÷ 100)

⇒ Let the Cost Price of item X and item Y be 'C'.

⇒ Profit from item X = 0.25C and Profit from item Y = 0.35C.

⇒ Difference = 0.35C − 0.25C = 750.

⇒ 0.10C = 750.

⇒ C = 750 ÷ 0.10 = 7500.

∴ The correct answer is Rs 7500.

Additional Information

Common Cost Price Scenarios

When Cost Prices are equal, the ratio of profits is directly proportional to the ratio of profit percentages.

Profit Calculation

Profit is always calculated on the Cost Price unless specified otherwise in the question.

Shortcut Trick

Let the speed of boat in still water (u) = 4x and speed of current (v) = x.

Downstream speed (u + v) = 5x and Upstream speed (u − v) = 3x.

Equation: D/5x + (D − 10)/3x = 12.

Since we have one equation with two unknown variables (D and x), a unique value for D cannot be found.

∴ The correct answer is Can’t be determined.

Alternate Method

Given: Ratio of boat speed (u) to current speed (v) = 4 :

1. Formula Used: Time = Distance ÷ Speed

⇒ Let u = 4x and v = x.

⇒ Downstream Speed = 4x + x = 5x.

⇒ Upstream Speed = 4x − x = 3x.

⇒ Total Time = [D / 5x] + [(D − 10) / 3x] = 12.

⇒ [3D + 5(D − 10)] / 15x = 12.

⇒ 3D + 5D − 50 = 180x.

⇒ 8D − 180x = 50.

⇒ As there are infinite pairs of (D, x) that satisfy this linear equation, D is not uniquely determined.

∴ The correct answer is Can’t be determined.

Additional Information

Downstream and Upstream Speed

Downstream speed is the sum of boat and stream speeds (u+v), while upstream speed is the difference (u−v).

Degrees of Freedom

To solve for 'n' variables, we strictly require 'n' independent equations. Here, D and x are two unknowns with only one relation.

Still Water Speed Formula

Still water speed (u) = 1/2 × (Downstream Speed + Upstream Speed).

Shortcut Trick

For 10% Compound Interest over 2 years, the effective interest rate is 21%.

Given CI = ₹840 ⇒ 21% of Principal = 840 ⇒ Principal = 840 ÷ 0.21 = ₹4000.

Since (P + 500) = 4000, then P = 3500.

For Simple Interest at 15% for 2 years, total interest = 30%. Total Amount = 130% of 3500 = 1.3 × 3500 = ₹4550.

∴ The correct answer is ₹4550.

Alternate Method

Given: Compound Interest (CI) = ₹840, Rate (R₁) = 10%, Time (T) = 2 years, Principal (P₁) = (P + 500).

Formula Used: CI = P[(1 + R/100)^T − 1]; Amount (SI) = P + (P × R × T) / 100.

Step 1: Find P + 500 from CI data.

⇒ 840 = (P + 500) × [(1 + 10/100)² − 1]

⇒ 840 = (P + 500) × [1.21 − 1]

⇒ 840 = (P + 500) × 0.21

⇒ P + 500 = 840 ÷ 0.21 = 4000

⇒ P = 3500

Step 2: Calculate SI Amount for P = 3500 at 15% for 2 years.

⇒ SI = (3500 × 15 × 2) ÷ 100 = 35 × 30 = 1050

⇒ Amount = P + SI = 3500 + 1050 = 4550

∴ The correct answer is ₹4550.

Additional Information

Effective Percentage Rate (Successive)

For CI, the effective rate for 2 years is x + y + (xy/100). For 10%, it is 10 + 10 + (100/100) = 21%.

Simple Interest vs Amount

SI is only the interest earned, while Amount includes the Principal (A = P + SI). Always read if the question asks for Interest or Amount.

Rule of 72

A quick way to estimate how long it takes to double money: Time ≈ 72 ÷ Interest Rate.

 

New income of E = 87,120 × 110% = ₹95,832 

New savings of E = 95,832 − 60,000 = ₹35,832

New expenditure of B = 57,600 × 90% = ₹51,840

New savings of B = 72,000 − 51,840 = ₹20,160

Required Difference = 35,832 − 20,160 = ₹15,672

 

Income of B & D = 72,000 + 72,600 = 1,44,600

Expenditure of C = 39,600

Required % = 39600/144600 x 100 = 27.39% ≈ 27.4%

 

Average expenditure of A, B & D = (48000+57600+54450)/3 = 160050/3 = 53,350

Income of E = 87,120

Required % = (87120 – 53350)/53350 × 100 = 63.30% ≈ 63%

New expenditure of C = 39,600 × 120% = 47,520

New savings of C = 57,600 − 47,520 = 10,080

Savings of B = 14,400

Required % = (14400 – 10080)/14400 x 100 = 30%

Savings of A, C & D = 12,000 + 18,000 + 18,150 = 48,150

Expenditure of B & E = 57,600 + 60,000 = 1,17,600

Required percent = (48150/117600) x 100 = 40.94% ≈ 41%

Calculation:

The series follows the following pattern

5 × 2 + 2 = 12

12 × 3 + 3 = 39

39 × 4 + 4 = 160

160 × 5 + 5 = 805

805 × 6 + 6 = 4836

∴ The wrong number in the given series is 4826

Considering the given series

14, 28, 56, 98, 196, 224

The logic of the given series can be explained as

14 + 14 × 1 = 28

28 + 14 × 2 = 56

56 + 14 × 3 = 98

98 + 14 × 4 = 154

154 + 14 × 5 = 224

∴ Wrong term in given number series is 196.

Considering the given series

31, 102, 165, 256, 345, 446, 562

The series follows the following pattern:

 

∴ Wrong term in given number series is 165.

Given:

Time taken by A is 25% more than the time taken by B to complete the work.

Time taken by C is x% of the time taken by B to complete the work.

B and C alone complete the work in 20/3 days.

A alone can complete the work in 25 days.

Formula Used:

1. Time taken by A = 1.25 × Time taken by B

2. Combined Work Formula: 1/B + 1/C = 1/Total Time

Calculation:

Let the time taken by B to complete the work = y days

Time taken by A to complete the work = 1.25y

Given: Time taken by A = 25 days

⇒ 1.25y = 25

⇒ y = 25 / 1.25

⇒ y = 20 days

Time taken by B to complete the work = 20 days

Let the time taken by C to complete the work = z days

Given: B and C alone complete the work in 20/3 days

⇒ 1/20 + 1/z = 3/20

⇒ 1/z = 3/20 - 1/20

⇒ 1/z = 2/20

⇒ z = 20/2

⇒ z = 10 days

Time taken by C to complete the work = 10 days

Value of x = (Time taken by C / Time taken by B) × 100

⇒ x = (10 / 20) × 100

⇒ x = 0.5 × 100

⇒ x = 50%

The value of x is 50%.

GIVEN:

⇒ Sudhir : Mother = 1 : 5      ----(1)

⇒ Sudhir : Father = 1 : 10      ----(2)

CALCULATION:

Making common ratios

⇒ Sudhir : Mother : Father = 1x : 5x : 10x      ----(3)

Age of Mother four years after = 39 years.

Mother’s present age = 35 years.

⇒ 5x = 35 years

⇒ 1x = 7 years

Present age of Sudhir = 7 years.

Present age of Father = 70 years.

Sum of their present age = 77 years.