Quantitative Aptitude PYQs

Solution:

67.89 + 11.01² - 77.18 + 40.05% of 399.95 – 65.769 = x

68 + 11² - 77 + 40/100 ×  400 – 66 = x

68 + 121 – 77 + 160 – 66 = x

x = 206

Solution:

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.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

30% of 299.97 – 1/17 of 84.98 + 1/8 of  39.88 – 133.33/0.33 = x

30 % of 300 – 1/17 ×  85 + 1/8 ×  40 – 133.33/1/3 = x

90 – 5 + 5 – 400 = x

x = -310

Let speed of boat in still water be B km/hr, and speed of stream be S km/hr.

ATQ,

(B + S) - (B - S) = 20

Or, 2S = 20

Or, S = 10 km/hr

Also, B = 200% of S

B = 2S = 20 km/hr

Downstream speed = 20 + 10 = 30 km/hr

Upstream speed = 20 – 10 = 10 km/hr

ATQ,

((D – 50) ÷ 30) = ((D – 100) ÷ 10) - 5

(D – 50) = 3 x (D - 100) – 150

Or, D – 50 = 3D – 300 – 150

Or, D – 50 = 3D – 450

Or, 2D = 400

Or, D = 200

Total clothes sold = 1200

Shirts sold by B = 8% of 1200 = 96

Jeans sold by C = 20% of 1200 = 240

Let the number of shirts sold by A, B and C be 11x, 4x and 15x, respectively.

Since, 4x = 96

x = 24

Therefore, Shirts sold by A = 11 × 24 = 264

Shirts sold by B = 96

Shirts sold by C = 15 × 24 = 360

Total shirts sold = 264 + 96 + 360 = 720

Total jeans sold = 1200 – 720 = 480

Given,

Jeans sold by A = 180

Jeans sold by B = 324

Required ratio = 360: 180 = 2: 1

Total clothes sold = 1200

Shirts sold by B = 8% of 1200 = 96

Jeans sold by C = 20% of 1200 = 240

Let the number of shirts sold by A, B and C be 11x, 4x and 15x, respectively.

Since, 4x = 96

x = 24

Therefore, Shirts sold by A = 11 × 24 = 264

Shirts sold by B = 96

Shirts sold by C = 15 × 24 = 360

Total shirts sold = 264 + 96 + 360 = 720

Total jeans sold = 1200 – 720 = 480 

Now, Shirts sold by E are 50% less than Jeans sold by A = 180 x 50% = 90

Shirts sold by F are 30% less than Jeans sold by C = 240 x 70% = 168

Therefore, Shirts sold by E and F together = 90 + 168 = 258

Total clothes sold = 1200

Shirts sold by B = 8% of 1200 = 96

Jeans sold by C = 20% of 1200 = 240

Let the number of shirts sold by A, B and C be 11x, 4x and 15x, respectively.

Since, 4x = 96

x = 24

Therefore, Shirts sold by A = 11 × 24 = 264

Shirts sold by B = 96

Shirts sold by C = 15 × 24 = 360

Total shirts sold = 264 + 96 + 360 = 720

Total jeans sold = 1200 – 720 = 480 

Required percentage = (324 – 264)/324 x 100 = 18.52% = 19% less approx.

Ratio = 7:9:8

Total ratio parts = 7 + 9 + 8 = 24

Actual amount spent = (3x + 200) + (2x + 500) + (3x − 300) = 8x + 400

Bharat's fair share to maintain the ratio = (9/24) X (8x + 400)

Bharat's actual spends = 2x + 500

Since Bharat needs to pay Rs. 650 to Aman, his fair share was Rs. 650 more than what he spent.

So, (9/24) × (8x + 400) = (2x + 500) + 650

9 × (8x + 400) = 24 × (2x + 1150)

72x + 3600 = 48x + 27600

24x = 24000

Or, x = 1000

Bharat's total fair expense share = (2 × 1000) + 500 + 650 = Rs. 3150

Time taken by A for 100% work = (9/0.6) = 15 days

Time taken by A and C for 100% work = (27/5) ÷ 0.9 = 6 days

Let the total work be 60 units (LCM of 15 and 6)

Efficiency of A = (60/15) = 4 units/day

Efficiency of (A + C) = (60/6) = 10 units/day

Efficiency of C = 10 - 4 = 6 units/day

Efficiency of B is 50% less than A = 4 × 0.5 = 2 units/day

Efficiency of B and C together = 2 + 6 = 8 units/day

Required days = (0.80 × 60) ÷ 8 = 48 ÷ 8 = 6 days

Let the length of each train be L.

Let Speed of train B = V.

Speed of train A = 1.2V

Speed of train C = 1.2V + 6

When A crosses B in opposite direction:

So, 2L/(1.2V + V) = 12

Or, 2L/2.2V = 12

Or, 2L = 26.4V

When A crosses C in opposite direction:

So, 2L/(2.4V + 6) = 10

Substitute 2L = 26.4V

26.4V/(2.4V + 6) = 10

Or, 26.4V = 24V + 60

Or, 2.4V = 60

Or, V = 25

Speed of train A = 1.2V = 1.2 x 25 = 30 m/sec

Let A's present age = 11y and B's present age = 8y.

So, 11y - 8y = 12

Or, 3y = 12

Or, y = 4

A's present age = 44 years

B's present age = 32 years.

ATQ,

(44 - (X - 2) ) ÷ (32 + (X + 1) ) = (40/39)

Or, (46 - X) /(33 + X) = (40/39)

Or, 39(46 - X) = 40(33 + X)

Or, 1794 - 39X = 1320 + 40X

Or, 474 = 79X

Or, X = 6.

Age of A (X + 3) years hence = 44 + 9 = 53 years.

Age of B (X - 6) years hence = 32 + 0 = 32 years.

Required ratio = 53:32

Common Solution:

Shop 'A',

Total number of laptops sold = 450 × 3 = 1350

Sum of the number of HP and Dell laptops sold = 1350 − 390 = 960

Number of HP laptops sold = (7/12) × 960 = 560

Number of Dell laptops sold = (5/12) × 960 = 400

Similarly,

 

Calculation:

Required average = (390 + 720 + 600) ÷ 3 = 1510 ÷ 3 = 570

Common Solution:

Shop 'A',

Total number of laptops sold = 450 × 3 = 1350

Sum of the number of HP and Dell laptops sold = 1350 − 390 = 960

Number of HP laptops sold = (7/12) × 960 = 560

Number of Dell laptops sold = (5/12) × 960 = 400

Similarly,

Calculation:

Required percent = (600 – 560)/560 x 100 = 7.14%

Common Solution:

Shop 'A',

Total number of laptops sold = 450 × 3 = 1350

Sum of the number of HP and Dell laptops sold = 1350 − 390 = 960

Number of HP laptops sold = (7/12) × 960 = 560

Number of Dell laptops sold = (5/12) × 960 = 400

Similarly,

 

Calculation:

Number of Dell laptops sold by shop E = (120/100) x 400 = 480

Number of HP laptops sold by shop E = (80/100) x 480 = 384

Required average = (480 + 384) ÷ 2 = 432

Common Solution:

Shop 'A',

Total number of laptops sold = 450 × 3 = 1350

Sum of the number of HP and Dell laptops sold = 1350 − 390 = 960

Number of HP laptops sold = (7/12) × 960 = 560

Number of Dell laptops sold = (5/12) × 960 = 400

Similarly,

Calculation:

Required ratio = (560 + 600): (720 + 600) = 1160:1320 = 29:33

Common Solution:

Shop 'A',

Total number of laptops sold = 450 × 3 = 1350

Sum of the number of HP and Dell laptops sold = 1350 − 390 = 960

Number of HP laptops sold = (7/12) × 960 = 560

Number of Dell laptops sold = (5/12) × 960 = 400

Similarly,

 

Calculation:

Number of Dell laptops sold by shop X = 400 x (100/80) = 500

Number of HP laptops sold by shop X = 560 x (100) /50) = 1120

Required total number of Dell and HP laptops in shop X = 500 + 1120 = 1620

Selling Price per kg rice = ₹240

Cost Price per kg rice = ₹8(X + 5)

ATQ,

240 = 1.2 × 8(X + 5)

Or, 240 = 9.6(X + 5)

To avoid decimal calculation, multiply both sides by 5:

1200 = 48(X + 5)

Or, 1200 = 48X + 240

Or, 48X = 960

So, X = 20

Cost Price per kg rice = 8(20 + 5) = 200

New Selling Price per kg rice = 4 × 20 = 80

Loss percentage = (200 - 80) / 200 × 100 = 60%

Let total population = 100m

Number of Males = 50m

Number of Females = 50m

Total newspaper readers = 65% of 100m = 65m

Male readers = 80% of 50m = 40m

Female readers = 65m − 40m = 25m

Female non-readers = 50m − 25m = 25m

Percentage of females not reading newspapers = (25m/50m) x 100 = 50%

Semicircle circumference = πr + 2r

Or, r(π + 2) = 6X

Or, r(22/7 + 2) = 6X

Or, r X (36/7) = 6X

So, r = 7X/6

Now,

(1/2) πr² = 1232

Or, (1/2) x (22/7) x (7X/6)² = 1232

So, X = 24

Radius of circle = (7 x 24)/6 = 28 cm

Radius of cylinder = (28/2) = 14 cm

Height = 9 x (24/8) = 27 cm

Curved surface area = 2 x (22/7) x 14 x 27 = 2376 cm²

Let initial speed of 'P' and 'Q' be 5x km/h and 4x km/h respectively

Time taken to travel by 'Q' = 5 hr

Time taken to travel by 'P' = 6 hr

Distance travelled by 'P' = 5x × 6 = 30x

Distance travelled by 'Q' (hourly) = 4x + (4x − 20) + (4x − 40) + (4x − 60) + (4x − 80)

= 20x − 200

ATQ,

30x + 20x − 200 = 1800

Or, 50x = 2000

So, x = 40

Speed of 'Q' = 4 × 40 = 160 km/h

LCM of 6, 9, 18 = 18 units

Let the total tank capacity be 18 units (LCM of 6, 9, 18)

A's 1 hour work = (18/6) = 3 units

B's 1 hour work = (18/9) = 2 units

C's 1 hour work = (18/18) = 1 unit

From 1 PM to 2 PM (A only) :

Work = 3 units

Remaining = 18 − 3 = 15 units

From 2 PM to 3 PM (A + B) :

Work = 3 + 2 = 5 units

Remaining = 15 − 5 = 10 units

From 3 PM onwards (A + B + C) :

Work per hour = 3 + 2 + 1 = 6 units

Time to finish = 10/6 hours

10/6 hours = 1 hour 40 minutes

Final Time = 3:00 PM + 1 hour 40 minutes = 4:40 PM