Quantitative Aptitude PYQs

Shortcut Trick

Ratio of Perimeter (P) to Length (L) = 3 : 1

Let P = 3 units, then L = 1 unit.

Since P = 2(L + B) ⇒ 3 = 2(1 + B) ⇒ 1.5 = 1 + B ⇒ Breadth (B) = 0.5 units.

Required Ratio (B : P) = 0.5 : 3 = 1 : 6.

∴ The correct answer is 1 : 6.

Alternate Method

Given: Ratio P : L = 3 : 1 and Perimeter (P) = 108 cm.

Formula: Perimeter of rectangle = 2 × (Length + Breadth)

⇒ 3 units = 108 cm

⇒ 1 unit (Length) = 108 ÷ 3 = 36 cm

⇒ Perimeter = 2 × (Length + Breadth)

⇒ 108 = 2 × (36 + Breadth)

⇒ 54 = 36 + Breadth

⇒ Breadth = 18 cm

⇒ Ratio of Breadth to Perimeter = 18 : 108

⇒ Ratio = 1 : 6

∴ The correct answer is 1 : 6.

Additional Information

Area of Rectangle

The total space occupied by the rectangle is given by the product of its dimensions: Area = Length × Breadth.

Diagonal of Rectangle

The length of the diagonal connecting opposite vertices is calculated using Pythagoras theorem: Diagonal = √(L² + B²).

Ratio and Proportion

If a : b = c : d, then product of extremes equals product of means (ad = bc).

Shortcut Trick

Ratio of Profit Share = (Investment₁ × Time₁) : (Investment₂ × Time₂)

Priya : Soni = (57,000 × 12) : (95,000 × 6)

Divide by 1000 × 6: (57 × 2) : 95 = 114 : 95 = 6 : 5

Total units = 6 + 5 = 11 units. Given total profit = Rs. 22,000.

1 unit = 22,000 ÷ 11 = 2,000. Soni profit share = 5 × 2,000 = Rs. 10,000.

∴ The correct answer is Rs. 10,000.

Alternate Method

Given → Priya Investment = Rs. 57,000 for 12 months | Soni Investment = Rs. 95,000 for 6 months.
Formulas: Profit Share = Investment × Time Period

⇒ Priya total value = 57,000 × 12 = 6,84,000
⇒ Soni total value = 95,000 × 6 = 5,70,000
⇒ Ratio Priya : Soni = 684,000 : 570,000 = 684 : 570
⇒ Simplify by 114: Ratio = 6 : 5
⇒ Soni share = [5 ÷ (6 + 5)] × 22,000
⇒ Soni share = (5 ÷ 11) × 22,000 = 5 × 2,000 = 10,000

∴ The correct answer is Rs. 10,000.

Additional Information

Partnership Basics

When time periods are different, it is a Compound Partnership. Profit is distributed based on the product of capital and time.

Ratio Simplification

Always simplify the investment ratio first by removing common zeros to make calculations faster.

Shortcut Trick

Downstream speed (v) = 6 + 2 = 8 km/hr

Upstream speed (u) = 6 − 2 = 4 km/hr

Distance (D) = [u × v × (Time Difference)] ÷ (v − u)

Distance (D) = [4 × 8 × (40/60)] ÷ (8 − 4) = [32 × (2/3)] ÷ 4 = 16/3 km

∴ The correct answer is 16/3 km.

Alternate Method

Given:

Speed of man in still water (x) = 6 km/hr

Speed of stream (y) = 2 km/hr

Time difference = 40 minutes = 40/60 hours = 2/3 hours

Calculations:

⇒ Downstream speed = x + y = 6 + 2 = 8 km/hr

⇒ Upstream speed = x − y = 6 − 2 = 4 km/hr

⇒ Time = Distance ÷ Speed

⇒ (D/4) − (D/8) = 2/3

⇒ (2D − D)/8 = 2/3

⇒ D/8 = 2/3

⇒ D = 16/3 km

∴ The correct answer is 16/3 km.

Additional Information

Downstream and Upstream Speed

Downstream Speed = Speed in Still Water + Stream Speed. Upstream Speed = Speed in Still Water − Stream Speed.

Calculating Water/Stream Speed

Speed in Still Water = (Downstream + Upstream) ÷ 2. Stream Speed = (Downstream − Upstream) ÷ 2.

Distance Formula for Constant Distance

If a person goes and comes back in total time T, Distance = [ (x² − y²) × T ] ÷ 2x.

Shortcut Trick

Weight of staff member who left = Old Average − (Decrease × New Strength) = 50 − (−1 × 9) = 59 kg.

Weight of staff member who joined = Old Average + (Increase × New Strength) = 49 + (3 × 10) = 79 kg.

Difference = 79 − 59 = 20 kg.

∴ The correct answer is 20 kg.

Alternate Method

Given: Initial 10 staff avg = 50 kg; After 1 left (9 staff) avg = 49 kg; After 1 joined (10 staff) avg = 52 kg.

Formula: Total Weight = Average × Number of members

⇒ Total weight of 10 initial staff members = 10 × 50 = 500 kg.

⇒ Total weight after 1 staff member left (9 members) = 9 × 49 = 441 kg.

⇒ Weight of staff member who left = 500 − 441 = 59 kg.

⇒ Total weight after new staff member joins (10 members) = 10 × 52 = 520 kg.

⇒ Weight of staff member who joined = 520 − 441 = 79 kg.

⇒ Difference = 79 − 59 = 20 kg.

∴ The correct answer is 20 kg.

Additional Information

Average weight change

If the average increases, the weight of the new person is New Weight = Old Average + (Increase × New Strength).

Excluded value

When a member is excluded and the average decreases, the excluded value = Old Average + (Decrease × New Strength).

Net Deviation

In any group, the sum of deviations from the average must be zero.

The total investment of Indumathi in ELSS and LIC together = (19500 + 24500) = 44000

The total investment of Chutki in NPS and ELSS together = (27500 + 18500) = 46000

Required ratio = 44000: 46000 = 22: 23

The investment of Giyan in NPS = (18500 + 2500) = 21000

The investment of Giyan in ELSS = (19500 – 3500) = 16000

Required average = (21000 + 16000)/2 = 37000/2 = 18500

The investment of Chutki in ELSS and NPSS together = (18500 + 27500) = 46000

The investment of Indumathi in NPS and LIC together = (19500 + 12500) = 32000

Required percentage = [(46000 - 32000)/32000] × 100 = 43.75%

The investment of Chayan in ELSS = (50/100) × [(29500 + 27500)/2] = 14250

Required average = (27500 + 12500 + 18500)/3 = 58500/3 = 19500

Concept used:

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 second, 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculations:

250 × 24 ÷ 12 + 6 + 2 of 3 of 18 = ?

⇒ 250 × 24 ÷ 12 + 6 + 108 = ?

⇒ 250 × 2 + 6 + 108 = ?

⇒  500 + 6 + 108 = ?

⇒ ? = 614

Hence, 614 will come in the place of (?).

Concept used:

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 second, 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculations:

36 × 9 + 4 × 3 – 70 × 4 + 144 ÷ 24 = ? ÷ 48

⇒ 36 × 9 + 4 × 3 – 70 × 4 + 6 = ? ÷ 48

⇒ 324 + 12 – 280 + 6 = ? ÷ 48

⇒  62 = ? ÷ 48

⇒ ? = 62 x 48

⇒ ? = 2976

Hence, 2976 will come in the place of (?).

Concept used:

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 second, 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculations:

20% of 2500 - 22.5% of 1200 = 15% of 1140 + (?)

⇒ 500 - 270 = 171 + ?

⇒ 500 - 270 - 171 = ?

⇒ ? = 59

Hence, 59 will come in the place of (?).

Concept used:

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 second, 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculations:

840 ÷ 14 + 6 × 9 + 11 - 3 + ? = 187

⇒ 60 + 6 × 9 + 11 - 3 + ? = 187

⇒ 60 + 54 + 11 - 3 + ? = 187

⇒ 125 + ? = 187 + 3

⇒ 125 + ? = 190

⇒ ? = 190 - 125

⇒ ? = 65

Hence, 65 will come in the place of (?).

Concept used:

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 second, 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculations:

15 × 100 - 10 × 800 + 60 ÷ 6 = ? × 50 ÷ 10

⇒ 15 × 100 - 10 × 800 + 10 = ? × 5

⇒ 1500 - 8000 + 10 = ? × 5

⇒ -6490 = ? × 5

⇒ ? = -6490/5

⇒ ? = -1298

Hence, -1298 will come in the place of (?).

45 × 3 + 7 + ? + 36 ÷ 6 × 9 = 100

⇒ 45 × 3 + 7 + ? + 6 × 9 = 100

⇒ 135 + 7 + ? + 54 = 100

⇒ 196 + ? = 100

⇒ ? = 100 - 196

⇒ ? = -96

Concept used:

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 second, 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculations:

85 - 5 × [20 × (120 - 110)] ÷ 10 + 40 = ?

⇒ 85 - 5 × [20 × 10] ÷ 10 + 40 = ?

⇒ 85 - 5 × 200 ÷ 10 + 40 = ?

⇒ 85 - 5 × 20 + 40 = ?

⇒ 85 - 100 + 40 = ?

⇒ 125 - 100 = ?

⇒ ? = 25

Hence, 25 will come in the place of (?).

Concept used:

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 second, 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculations:

30% of 50 - 55% of 250 = ? + (200 - 99 × 2) ÷ 4

⇒ 15 - 137.5 = ? + (200 - 99 × 2) ÷ 4

⇒ 15 - 137.5 = ? + 2 ÷ 4

⇒ 15 - 137.5 = ? + 0.5

⇒ 15 - 137.5 - 0.5 = ?

⇒ ? = -123

Hence, -123 will come in the place of (?).

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 the 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculation:

Given expression is 

(953 + 487 - 220) ÷ 5 = 482 - 62 + ?

⇒ 1220 ÷ 5 = 482 - 62 + ?

⇒ 244 = 482 - 62 + ?

⇒ 244 + 62 - 482 = ?

⇒ - 176

Hence, 176 will come in the place of (?).

48 × 27 + 115 × 62 + 79 × 23 = ? - √256

⇒ 1296 + 7130 + 1817 = ? - √256

⇒ 1296 + 7130 + 1817 = ? - 16

⇒ 1296 + 7130 + 1817 + 16 = ?

⇒ ? = 10259

Hence, 10259 will come in the place of (?).

Given:

√ 289 × 5 - 60 + 82 = 33 + 45 - ?

Concept used:

Follow the 'BODMAS' Rule

B ⇒ Bracket, O ⇒ of, D ⇒ Division, M ⇒ Multiplication, A ⇒ Addition, S ⇒ Subtraction

Calculation:

⇒ √ 289 × 5 - 60 + 82 = 33 + 45 - ?

⇒ 17 × 5 - 60 + 64 = 27 + 45 - ?

⇒ 85 - 60 + 64 = 72 - ?

⇒ 89 = 72 - ?

⇒ -17 

∴ The value of ? is -17.