Quantitative Aptitude PYQs

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

39 × 24 – 19 × 14 + (82 × 50%) = ? + 2

⇒ (936) – (266) + (64 × 50%) = ? + 2

⇒ (670) + (32) = ? + 2

⇒ 702 – 2 = ?

⇒ ?  = 700

∴ ? = 700

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

?2 = 27.27% × 7 × (272 – 162) – 3

⇒ ?2 = (3/11) × 7 × (729 – 256) – 3

⇒ ?2 = (3/11) × 7 × (473) – 3

⇒ ?2 = (3) × 7 × (43) – 3

⇒ ?2  = 903 – 3

∴ ? = 30

Given:

Speed of train = 72 km/hr

Time to cross pole = 25 sec

Increase in speed = 18 km/hr

Formula used:

Speed = Distance ÷ Time

Time = Distance ÷ Speed

Calculations:

Convert speed into m/sec

72 km/hr = 72 × 5 ÷ 18 = 20 m/sec

Length of train = Speed × Time

⇒ Length = 20 × 25 = 500 m

New speed = 72 + 18 = 90 km/hr

90 km/hr = 90 × 5 ÷ 18 = 25 m/sec

New time to cross pole = Distance ÷ Speed

⇒ Time = 500 ÷ 25 = 20 sec

Less time taken = 25 − 20 = 5 sec

∴ The train will take 5 seconds less to cross the pole.

Given:

Investment of Rina = Rs. 5600

Investment of Tina = Rs. 4000

Time = 1 year (same for both)

Profit of Rina = Rs. 8400

Formula used:

Profit ratio = Investment ratio (when time is same)

Calculations:

Ratio of investments = 5600 : 4000

⇒ Divide by 800

⇒ Investment ratio = 7 : 5

So, profit ratio of Rina : Tina = 7 : 5

Profit of Rina (7 parts) = 8400

⇒ Value of 1 part = 8400 ÷ 7 = 1200

⇒ Profit of Tina = 5 × 1200 = 6000

∴ The profit amount of Tina is Rs. 6000.

Calculation

Total students of College B = (x + 22)

Total students in College B = 126 + 131 + 145 = 402

x + 22 = 402

x = 380

Calculation

Difference = 145 − 118 = 27

Percentage = (27 / 118) × 100 = 22.88%

Answer: 22.88% more

Calculation

Total Science students = 102 + 131 + 105 = 338

Average = 338 / 3 = 112.67 students

Answer: 112.67 students

Calculation

Total students in College A = 148 + 102 + 127 = 377

Total students in College C = 118 + 105 + 134 = 357

Required difference = 377 - 357 = 20

Calculation

Average Economics = (148 + 126 + 118) / 3 = 130.67

Average Sociology = (127 + 145 + 134) / 3 = 135.33

Difference = 135.33 − 130.67 = 4.66

Given:

Cost Price (CP) = 100

Increase in CP = 40%

Discount given = 20%

Formula used:

Increased Price = CP × (1 + Increase%)

Selling Price = Marked Price × (1 − Discount%)

Profit % = (Profit ÷ CP) × 100

Calculations:

Let CP = 100

Increased price = 100 × (1 + 40/100)

⇒ Increased price = 100 × 1.4 = 140

Discount = 20% on 140

Selling Price (SP) = 140 × (1 − 20/100)

⇒ SP = 140 × 0.8 = 112

Profit = SP − CP

⇒ Profit = 112 − 100 = 12

⇒ Profit % = (12 ÷ 100) × 100 = 12%

∴ The profit percentage is 12%.

Given:

Weight of item A = 200 kg

Weight of item C is 20% more than item A

Weight of item B is 25% more than item C

Formula used:

Increased weight = Original weight × (1 + Increase%)

Calculations:

Weight of item C = 200 × (1 + 20/100)

⇒ Weight of item C = 200 × 1.2 = 240 kg

Weight of item B = 240 × (1 + 25/100)

⇒ Weight of item B = 240 × 1.25 = 300 kg

Total weight = Weight of A + Weight of B + Weight of C

⇒ Total weight = 200 + 300 + 240

⇒ Total weight = 740 kg

∴ The total weight of all three items together is 740 kg.

Given:

Ratio of milk and water = 9 : 5

Water added = 10 L

New ratio of milk and water = 9 : 7

Formula used:

If ratio is a : b, then quantities = ax and bx

Calculations:

Let initial quantity of milk = 9x

Let initial quantity of water = 5x

After adding water:

Milk = 9x

Water = 5x + 10

⇒ (9x) : (5x + 10) = 9 : 7

⇒ 7 × 9x = 9 × (5x + 10)

⇒ 63x = 45x + 90

⇒ 63x − 45x = 90

⇒ 18x = 90

⇒ x = 5

Initial quantity of milk = 9x = 9 × 5 = 45 L

∴ The initial quantity of milk is 45 L.

Considering the given series

5, 4, 7, 20, 79, 386, 2363

The logic of the given series can be explained as

5 × 1 – 1 = 4

4 × 2 – 1 =7

7 × 3 – 1 = 20

20 × 4 – 1 = 79

79 × 5 – 1 = 394

394 × 6 – 1 = 2363

∴ wrong term of the series is 386

The pattern followed by the series is

123 - 4 = 119 

119 - 8 = 111

111 - 12 = 99

99 - 16 = 83 

83 - 20 = 63

The series follows the following pattern:

12 × 2 = 24

24 ÷ 3 = 8

8 × 4 = 32

32 ÷ 5 = 6.4

6.4 × 6 = 38.4

∴ The wrong term in the series is 6.2.

The series follows the following pattern:

11² - 2 = 119

12² - 3 = 141

13² - 5 = 164

14² - 7 = 189

15² - 11 = 214

16² - 13 = 243

∴ The wrong term in the series is 213.

The series follows the following pattern:

1440 ÷ 6 = 240

240 ÷ 5 = 48

48 ÷ 4 = 12

12 ÷ 3 = 4 

4 ÷ 2 = 2

∴ The wrong term in the series is 16.

Given:

Ratio of present age of Dimpi and Kajal = 3 : 4

Ratio of age of Dimpi before 3 years and Kajal after 6 years = 4 : 7

Formula used:

If present ages are in ratio a : b, then ages = ax and bx

Calculations:

Let present age of Dimpi = 3x

Let present age of Kajal = 4x

Dimpi’s age before 3 years = 3x − 3

Kajal’s age after 6 years = 4x + 6

⇒ (3x − 3) : (4x + 6) = 4 : 7

⇒ 7 × (3x − 3) = 4 × (4x + 6)

⇒ 21x − 21 = 16x + 24

⇒ 21x − 16x = 24 + 21

⇒ 5x = 45

⇒ x = 9

Present age of Dimpi = 3x = 3 × 9 = 27 years

∴ The present age of Dimpi is 27 years.

Given:

Increase of number = 40%

Decrease of number = 80%

Difference between both results = 192

Formula used:

Increased value = Number × (1 + increase%)

Decreased value = Number × (1 − decrease%)

Calculations:

Let the number = x

Increased number = x × (1 + 40/100) = 1.4x

Decreased number = x × (1 − 80/100) = 0.2x

⇒ Difference = 1.4x − 0.2x

⇒ 1.2x = 192

⇒ x = 192 ÷ 1.2 = 160

25% of the number = 25/100 × 160

⇒ 25% = 40

∴ 25% of the number is 40.

Detailed Solution:

Cricketer makes total runs in 26 innings = 28 × 26 = 728

Average after he makes a total 272 runs in his next five innings = (728 + 272)/31 = 1000/31 = 32.258

Increase in his average = 32.258 – 28 = 4.258

Short Trick:

For maintain the average at 28 after he makes a total 272 runs in his next five innings, he needs 140 runs.

∴ Remaining runs = 272 – 140 = 132

∴ These 132 runs will spend in increasing the average of cricketer after 31 innings.

⇒ Increase in his average = 132/31 = 4.258