Quantitative Aptitude PYQs

Common Calculation

Students who did not pass:

A: 180 − 90 = 90

B: 450 − 180 = 270

C: 270 − 162 = 108

Calculation:

Total appeared in B = 450

Girls appeared = 40% of 450 = 180

→ Boys appeared = 450 − 180 = 270

Total passed = 180

→ Not passed = 450 − 180 = 270

Girls not passed = 60

→ Boys not passed = 270 − 60 = 210

Girls passed = 180 − 60 = 120

Difference = |210 − 120| = 90

Answer: 90

Common Calculation

Students who did not pass:

A: 180 − 90 = 90

B: 450 − 180 = 270

C: 270 − 162 = 108

Calculation:

Average passed (A,B,D)=150

→ Total passed = 150 × 3 = 450

Passed A+B = 90 + 180 = 270

→ Passed D = 450 − 270 = 180

70% did not pass in D

→ Total appeared in D = 180/0.3 = 600

Students not passed D = 70% of 600 = 420

Boys not passed = Girls not passed = 420/2 = 210

Girls passed = 40% of passed B = 0.4 × 180 = 72

Total girls in D = 72 + 210 = 282

→ Total boys in D = 600 − 282 = 318

Answer: 318 boys

Shortcut Trick

Given: a × c = 18 where a is a prime number and c is a multiple of 2.

Prime factors of 18 are 2 and 3. Possible values for a are 2 or 3.

If a = 3, then c = 18 ÷ 3 = 6 (which is a multiple of 2).

Given: c × b = 24 ⇒ 6 × b = 24 ⇒ b = 4.

∴ The correct answer is 4.

Alternate Method

Given:

1. a is a prime number.
2. c is a multiple of 2.
3. a × c = 18
4. c × b = 24

Calculations:

⇒ Possible factors of 18: (1, 18), (2, 9), (3, 6).

⇒ Since a must be prime, a can be 2 or 3.

⇒ Case 1: If a = 2, then c = 18 ÷ 2 = 9. But c must be a multiple of 2. So, a ≠ 2.

⇒ Case 2: If a = 3, then c = 18 ÷ 3 = 6. Here c is a multiple of 2. This is valid.

⇒ Substitute c = 6 in the second equation: 6 × b = 24.

⇒ b = 24 ÷ 6 = 4.

∴ The correct answer is 4.

Additional Information

Prime Numbers

A number that has exactly two factors: 1 and itself. Example: 2, 3, 5, 7, 11, etc.

Mixed Fraction Structure

A mixed fraction is written as a(b/c) where a is the whole number, b is the numerator, and c is the denominator.

Multiples

A multiple of 2 is any even number that can be expressed as 2 × n where n is an integer.

Shortcut Trick

Work P + Q = (3/2) work in 9 days → 1 work in 6 days.

Work 2R + P = 1 work in 5 days.

We have 2 equations:

(1) P + Q = 1/6 and (2) 2R + P = 1/5.

Question asks for 1.2 work by P + Q + 2Q = P + 3Q.

Since we cannot isolate P and Q individually from the given data, P + 3Q cannot be determined.

∴ The correct answer is CND.

Alternate Method

⇒ Efficiency of (P + Q) = 5 units/day

⇒ Efficiency of (P + 2R) = 6 units/day

⇒ From 1^st eq: P = 5 − Q

⇒ From 2^nd eq: 2R + (5 − Q) = 6 → 2R − Q = 1

⇒ Required combined efficiency = P + Q + 2Q (since R efficiency is twice Q efficiency)

⇒ Required efficiency = P + 3Q

⇒ Since we only know P + Q = 5, we cannot find the specific value of P + 3Q without knowing the individual value of Q or a relationship between P and Q.

∴ The correct answer is CND.

Additional Information

Efficiency and Time Relationship

Time is inversely proportional to efficiency. Total Work = Efficiency × Time.

System of Equations

To find the values of n variables, we generally require n independent linear equations. Here, 3 variables (P, Q, R) and only 2 equations make it Indeterminate.

Work Scaling

If work increases by 20%, the new work becomes 1.2 × Original Work. Time taken = (1.2 × Total Work) ÷ Combined Efficiency.

Shortcut Trick

Milk and Water in 60% of Vessel P (33.6 L): Milk = 25.2 L, Water = 8.4 L.

Let 25% of Vessel Q be 'x' L. Water in it = 0.4x, Milk in it = 0.6x.

In Vessel R: (8.4 + 0.4x) / (25.2 + 0.6x) = 52 / 141.

Solving for 0.6x (Milk from Q): 1184.4 + 56.4x = 1310.4 + 31.2x ⇒ 25.2x = 126 ⇒ x = 5.

Milk taken out from Q = 0.6 × 5 = 3 L.

∴ The correct answer is 3 liters.

Alternate Method

Given: Vessel P = 56 L (M:W = 3:1). Vessel Q = Water 40%, Milk 60%.

Calculations:

⇒ Volume of P taken = 60% of 56 = 33.6 L.

⇒ Milk in P taken = 33.6 × (3/4) = 25.2 L; Water in P taken = 33.6 × (1/4) = 8.4 L.

⇒ Let total volume taken from Q = 'V' L. Milk from Q = 0.6V, Water from Q = 0.4V.

⇒ Total Water in R / Total Milk in R = (8.4 + 0.4V) / (25.2 + 0.6V) = 52 / 141.

⇒ 141 × (8.4 + 0.4V) = 52 × (25.2 + 0.6V)

⇒ 1184.4 + 56.4V = 1310.4 + 31.2V

⇒ 25.2V = 126 ⇒ V = 5 L.

⇒ Milk taken from vessel Q = 0.6 × 5 = 3 L.

∴ The correct answer is 3 liters.

Additional Information

Mixture Concentration

When two mixtures are combined, the total quantity of a specific component is the sum of that component from each individual mixture.

Ratio and Proportion

If a mixture has components in ratio a:b, then for any quantity Q, component 1 = Q × a/(a+b) and component 2 = Q × b/(a+b).

Percentage to Ratio

A 40% water content implies a ratio of Water:Milk = 40:60, which simplifies to 2:3.

Common Calculation

Monday:

Given: Total visitors = 115; Males (Tue) = Males (Mon) + 25; Females (Mon) = Males (Tue) + 20

⇒ Females (Mon) = (Males (Mon) + 25) + 20 = Males (Mon) + 45

⇒ Males (Mon) + Females (Mon) = 115

⇒ Males (Mon) + (Males (Mon) + 45) = 115

⇒ 2 × Males (Mon) = 115 − 45

⇒ 2 × Males (Mon) = 70

⇒ Males (Mon) = 35

⇒ Females (Mon) = 35 + 45 = 80

∴ Monday: Males = 35, Females = 80

Tuesday:

Given: Males (Tue) = Males (Mon) + 25; Females (Tue) = 10% less than Males (Tue)

⇒ Males (Tue) = 35 + 25 = 60

⇒ Females (Tue) = 60 − (10 / 100) × 60

⇒ Females (Tue) = 60 − 6 = 54

∴ Tuesday: Males = 60, Females = 54

Given:

Number of males on Monday = 35

Number of females on Monday = 80

Formula Used:

Ratio = Number of males / Number of females

Calculation:

⇒ Required ratio = 35 / 80

⇒ Required ratio = 7 / 16

∴ The correct answer is 7 : 16.

Common Calculation

Monday:

Given: Total visitors = 115; Males (Tue) = Males (Mon) + 25; Females (Mon) = Males (Tue) + 20

⇒ Females (Mon) = (Males (Mon) + 25) + 20 = Males (Mon) + 45

⇒ Males (Mon) + Females (Mon) = 115

⇒ Males (Mon) + (Males (Mon) + 45) = 115

⇒ 2 × Males (Mon) = 115 − 45

⇒ 2 × Males (Mon) = 70

⇒ Males (Mon) = 35

⇒ Females (Mon) = 35 + 45 = 80

∴ Monday: Males = 35, Females = 80

Tuesday:

Given: Males (Tue) = Males (Mon) + 25; Females (Tue) = 10% less than Males (Tue)

⇒ Males (Tue) = 35 + 25 = 60

⇒ Females (Tue) = 60 − (10 / 100) × 60

⇒ Females (Tue) = 60 − 6 = 54

∴ Tuesday: Males = 60, Females = 54

 

Given:

Number of males who visited the park on Monday = 35

Number of males on Tuesday was 25 more than Monday.

Formula Used:

Males (Tuesday) = Males (Monday) + 25

Calculation:

⇒ Males (Tuesday) = 35 + 25

⇒ Males (Tuesday) = 60

∴ The correct answer is 60.

Common Calculation

Monday:

Given: Total visitors = 115; Males (Tue) = Males (Mon) + 25; Females (Mon) = Males (Tue) + 20

⇒ Females (Mon) = (Males (Mon) + 25) + 20 = Males (Mon) + 45

⇒ Males (Mon) + Females (Mon) = 115

⇒ Males (Mon) + (Males (Mon) + 45) = 115

⇒ 2 × Males (Mon) = 115 − 45

⇒ 2 × Males (Mon) = 70

⇒ Males (Mon) = 35

⇒ Females (Mon) = 35 + 45 = 80

∴ Monday: Males = 35, Females = 80

Tuesday:

Given: Males (Tue) = Males (Mon) + 25; Females (Tue) = 10% less than Males (Tue)

⇒ Males (Tue) = 35 + 25 = 60

⇒ Females (Tue) = 60 − (10 / 100) × 60

⇒ Females (Tue) = 60 − 6 = 54

∴ Tuesday: Males = 60, Females = 54

 

Given:

Males (Tuesday) = 60

Females (Tuesday) = 54

Formula Used:

Total visitors = Males + Females

Calculation:

⇒ Total visitors (Tuesday) = 60 + 54

⇒ Total visitors (Tuesday) = 114

∴ The correct answer is 114.

Common Calculation

Monday:

Given: Total visitors = 115; Males (Tue) = Males (Mon) + 25; Females (Mon) = Males (Tue) + 20

⇒ Females (Mon) = (Males (Mon) + 25) + 20 = Males (Mon) + 45

⇒ Males (Mon) + (Males (Mon) + 45) = 115

⇒ 2 × Males (Mon) = 115 − 45

⇒ 2 × Males (Mon) = 70

⇒ Males (Mon) = 35

⇒ Females (Mon) = 35 + 45 = 80

∴ Monday: Males = 35, Females = 80, Total = 115

Tuesday:

Given: Males (Tue) = Males (Mon) + 25; Females (Tue) = 10% less than Males (Tue)

⇒ Males (Tue) = 35 + 25 = 60

⇒ Females (Tue) = 60 − (10 / 100) × 60

⇒ Females (Tue) = 60 − 6 = 54

⇒ Total (Tue) = 60 + 54 = 114

∴ Tuesday: Males = 60, Females = 54, Total = 114

 

Given:

Females on Monday = 80

Total visitors on Monday = 115

Formula Used:

Percentage = (Part / Total) × 100

Calculation:

⇒ Required Percentage = (80 / 115) × 100

⇒ Required Percentage = (16 / 23) × 100

⇒ Required Percentage = 1600 / 23

⇒ Required Percentage = 69.5652...%

⇒ Required Percentage ≈ 69.57%

∴ The correct answer is 69.57%.

Common Calculation

Monday:

Given: Total visitors = 115; Males (Tue) = Males (Mon) + 25; Females (Mon) = Males (Tue) + 20

⇒ Females (Mon) = (Males (Mon) + 25) + 20 = Males (Mon) + 45

⇒ Males (Mon) + (Males (Mon) + 45) = 115

⇒ 2 × Males (Mon) = 115 − 45

⇒ 2 × Males (Mon) = 70

⇒ Males (Mon) = 35

⇒ Females (Mon) = 35 + 45 = 80

∴ Monday: Males = 35, Females = 80, Total = 115

Tuesday:

Given: Males (Tue) = Males (Mon) + 25; Females (Tue) = 10% less than Males (Tue)

⇒ Males (Tue) = 35 + 25 = 60

⇒ Females (Tue) = 60 − (10 / 100) × 60

⇒ Females (Tue) = 60 − 6 = 54

⇒ Total (Tue) = 60 + 54 = 114

∴ Tuesday: Males = 60, Females = 54, Total = 114

 

Given:

Number of females on Monday = 80

Visitors on Wednesday = 20% more than females on Monday

Formula Used:

Total visitors (Wednesday) = Females (Monday) × (1 + Percentage Increase / 100)

Calculation:

⇒ Total visitors (Wednesday) = 80 × (1 + 20 / 100)

⇒ Total visitors (Wednesday) = 80 × 1.20

⇒ Total visitors (Wednesday) = 96

∴ The correct answer is 96.

Shortcut Trick

Present ratio A : B = 3 : 5 (difference between parts = 2).

Future ratio (after 8 years) = 2 : 3 (difference between parts = 1).

To equate differences, multiply future ratio by 2: 2 : 3 → 4 : 6.

Increase in units for B = 6 − 5 = 1 unit.

As per question, 1 unit = 8 years.

B's present age = 5 units = 5 × 8 = 40 years.

∴ The correct answer is 40 years.

Alternate Method

Given:

Present ratio of A and B = 3 : 5

Ratio after 8 years = 2 : 3

A (3x) B (5x) Present + 8 Years New Ratio = 2 : 3

Formula used: Ratio Proportion (ax + k) / (bx + k) = m / n

⇒ Let the present age of A be 3x and B be 5x.

⇒ After 8 years, A's age = 3x + 8

⇒ After 8 years, B's age = 5x + 8

⇒ (3x + 8) / (5x + 8) = 2 / 3

⇒ 3 × (3x + 8) = 2 × (5x + 8)

⇒ 9x + 24 = 10x + 16

⇒ 10x − 9x = 24 − 16

⇒ x = 8

⇒ B's present age = 5x = 5 × 8 = 40 years.

∴ The correct answer is 40 years.

Additional Information

Constant Age Difference

The difference between the ages of two people remains constant throughout their lives. If A is 2 years older than B today, A will always be 2 years older than B.

Ratio Balancing

If the difference between ratio parts (3:5 diff is 2, 2:3 diff is 1) is not same, multiply the ratios by the other's difference to make the unit change uniform.

Cross Product Rule

For a ratio a:b becoming c:d after adding k to both, the common factor x is calculated as:

x = [k × (d − c)] ÷ (ad − bc).

Shortcut Trick

If the first divisor (15) is a multiple of the second divisor (5), the new remainder is simply the remainder of (Old Remainder ÷ New Divisor).

New Remainder = 7 ÷ 5

7 = (5 × 1) + 2

The remainder is 2.

∴ The correct answer is 2.

Alternate Method

Given:

Number N ÷ 15 → Remainder = 7

New Divisor = 5

Formula Used:

Dividend = (Divisor × Quotient) + Remainder

Multiple of 15 (15k) Remainder 7  5 2 Number N = 15k + 7 Since 15k is divisible by 5, remainder depends on 7 only.

⇒ Let the number be N. Then N = 15k + 7, where k is an integer.

⇒ We can rewrite 15k as (5 × 3k).

⇒ N = (5 × 3k) + 7

⇒ N = (5 × 3k) + (5 × 1 + 2)

⇒ N = 5(3k + 1) + 2

⇒ This is in the form N = 5q + r, where the remainder r = 2.

∴ The correct answer is 2.

Additional Information

Euclid Division Lemma

It states that for any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b.

Property of Divisibility

If a divisor D₁ is a multiple of another divisor D₂, then the remainder when a number is divided by D₂ is the same as the remainder when the first remainder R₁ is divided by D₂.

Remainder Range

The remainder of any division must always be non-negative and strictly less than the divisor.

Shortcut Trick

Initial Ratio (Milk : Water) = 3 : 1 (Total = 4 units)

New Ratio (Milk : Water) = 3 : 2 (Milk stays same)

Increase in water parts = 2 − 1 = 1 unit

Initial total = 4 units = 40 litres → 1 unit = 10 litres

Water to be added = 1 unit = 10 litres

∴ The correct answer is 10 litres.

Alternate Method

Given:

Initial total mixture = 40 litres

Initial ratio (Milk : Water) = 3 : 1

Required ratio (Milk : Water) = 3 : 2

Formula Used:

Quantity of component = (Component ratio ÷ Total ratio) × Total mixture

Milk: 30L Water: 10L Initial (40L)  + Water (x)   Milk: 30L Water: 20L Final (50L)

Calculations:

⇒ Sum of initial ratio parts = 3 + 1 = 4

⇒ Initial quantity of Milk = (3 ÷ 4) × 40 = 30 litres

⇒ Initial quantity of Water = (1 ÷ 4) × 40 = 10 litres

⇒ Let x litres of water be added to the mixture.

⇒ New ratio of Milk to Water = 30 ÷ (10 + x) = 3 ÷ 2

⇒ 30 × 2 = 3 × (10 + x)

⇒ 60 = 30 + 3x

⇒ 3x = 30

⇒ x = 10 litres

∴ The correct answer is 10 litres.

Additional Information

Constant Quantity Rule

When one component of a mixture is added or removed, the quantity of the other component remains unchanged. Use this constant to equate the initial and final states.

Ratio Balancing

Ratios can be multiplied by a common factor to make specific terms equal across different scenarios, facilitating direct comparison of the remaining parts.

Mixture Replacement Formula

If a certain quantity is replaced by water multiple times: Final Milk = Initial Milk × (1 − Replacement/Total)ⁿ.

Given:

14.5 of 18 + 15.5 of 28 = 10 × ?

Concept Used:

​

Calculation:

14.5 of 18 + 15.5 of 28 = 10 × ?

⇒ 261 + 434 = 10 × ?

⇒ 695/10 = ? 

⇒ ? = 69.5

∴ The value of (?) is 69.5

Concept Used:

Follow BODMAS rule to solve this question, as per the order given below, 

Calculation:

25% of 900 ÷ 0.75 + √289 = ?

⇒ 25 × 9 ÷ 0.75 + 17 = ?

⇒ 25 × 9 × (4/3) + 17 = ?

⇒ 300 + 17 = ?

⇒ 317 = ?

∴ The value of ? is 317

Concept Used:

Follow BODMAS rule to solve this question, as per the order given below, 

Calculation:

(25% of 32 × 3) ÷ 4 – 23  = ?

⇒ [(25/100) × 32 × 3] ÷ 4 – 23  = ?

⇒ (8 × 3) ÷ 4 – 23  = ? 

⇒ 6 – 23  = ?

∴ The value of ? is -17.

Concept used:

Calculation:

Our equation is 352 ÷ 4 – 108 + 17 × 4

⇒ 88 – 108 + 17 × 4

⇒ 88 – 108 + 68

⇒ 156 – 108

⇒ 48

∴ The value of the given expression is 48

GIVEN:

57.14% of 343 + 28.57% of 49 = ?

FORMULA USED:

These types of questions, the knowledge of conversion from percentage to fraction should be known.

Concept :

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

CALCULATION:

57.14% of 343 = (4/7) × 343 = 4 × 49 = 196

28.57% of 49 = (2/7) × 49 = 2 × 7 = 14

Given expression is

57.14% of 343 + 28.57% of 49 = ?

⇒ 196 + 14 = ?

⇒ 210 = ?

∴ ? = 210

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is

72.5 of 4 – 300% of √6241 = √?

⇒ 290 – 3 × 79 = √?

⇒ 290 – 237 = √?

⇒ √? = 53

⇒ ? = 53²

∴ ? = 2809

Given:

643 ÷ 16 ÷ 8 – 36 × 25 = 4 × ?

Concept:

Follow the BODMAS rule according to the table given below:

Calculation:

64³ ÷ 16 ÷ 8 – 36 × 25 = 4 × ?

⇒ (2⁶)3 × \(1\over16\) × \(1\over8\) – 36 × 25 = 4 × ?

⇒ 2¹⁸ × \(1\over2^4\) × \(1\over2^3\) – 36 × 25 = 4 × ?

⇒ 2¹¹ - 900 = 4 × ?

⇒ 2048 – 900 = 4 × ?

⇒ 4 × ? = 2048 – 900

⇒ ? = 1148/4 = 287

∴ The correct answer is 287.