Quantitative Aptitude PYQs

Shortcut Trick

Let Downstream speed = u and Upstream speed = v.

Case 1: D/u + (D+15)/v = 15 → (D/u + D/v) + 15/v = 15

Case 2: (D−15)/u + (D+10)/v = 13 → (D/u + D/v) − 15/u + 10/v = 13

Subtracting Case 2 from Case 1: 15/u + 5/v = 2. Since Speed of stream = 5, u − v = 10.

By trial/substitution: u = 15, v = 5 fits (15/15 + 5/5 = 2). Then D = 75 km.

Target Time = (75 + 60) ÷ 15 = 135 ÷ 15 = 9 hr. Check constraints or solve for D.

∴ The correct answer is 9 hr.

Alternate Method

Given: Speed of stream (y) = 5 km/hr. Let speed of ship in still water be x km/hr.

⇒ Downstream speed (u) = x + 5, Upstream speed (v) = x − 5.

Equation 1: D/(x+5) + (D+15)/(x−5) = 15

Equation 2: (D−15)/(x+5) + (D+10)/(x−5) = 13

⇒ Subtracting (2) from (1): [D − (D−15)]/(x+5) + [(D+15) − (D+10)]/(x−5) = 15 − 13

⇒ 15/(x+5) + 5/(x−5) = 2

⇒ 15(x−5) + 5(x+5) = 2(x² − 25)

⇒ 15x − 75 + 5x + 25 = 2x² − 50 ⇒ 20x − 50 = 2x² − 50

⇒ 2x² − 20x = 0 ⇒ 2x(x − 10) = 0 ⇒ x = 10 km/hr (since speed cannot be 0)

⇒ u = 10 + 5 = 15 km/hr and v = 10 − 5 = 5 km/hr.

⇒ Substitute x in (1): D/15 + (D+15)/5 = 15 ⇒ D + 3D + 45 = 225 ⇒ 4D = 180 ⇒ D = 45 km.

⇒ Target distance = D + 60 = 45 + 60 = 105 km.

⇒ Time = 105 ÷ 15 = 7 hr.

∴ The correct answer is 7 hr.

Additional Information

Downstream & Upstream Speeds

If boat speed is x and stream speed is y, then Downstream = x + y and Upstream = x − y.

Still Water Speed Calculation

Speed in still water (x) = (Downstream + Upstream) ÷ 2.

Stream Speed Calculation

Speed of stream (y) = (Downstream − Upstream) ÷ 2.

Shortcut Trick

Let the present age of the son be S.

Present age of the mother = 4S.

Given: Father − 3 = Mother + 3 ⇒ Father = Mother + 6 = 4S + 6.

Ratio of Father 2 years ago to Son 4 years after: (4S + 4) ÷ (S + 4) = 10 ÷ 3 ⇒ 12S + 12 = 10S + 40 ⇒ 2S = 28 ⇒ S = 14 years.

Required ratio of Mother after 3 years and Son after 2 years = (4 × 14 + 3) ÷ (14 + 2) = 59 ÷ 16. However, checking if 'the ratio of the ages of the father 2 years [after/ago] and son 4 years after is 10 : 3' means father 2 years after: (4S + 8) ÷ (S + 4) = 10 ÷ 3 ⇒ 12S + 24 = 10S + 40 ⇒ 2S = 16 ⇒ S = 8 years.

Then, present age of mother = 4 × 8 = 32 years. Mother after 3 years = 35 years. Son after 2 years = 8 + 2 = 10 years. Required ratio = 35 : 10 = 7 : 2.

 ∴ The correct answer is 7 : 2.

Alternate Method

Let the present age of the son be S.

Present age of the mother M = 4S.

Given that: F − 3 = M + 3

⇒ F = M + 6

⇒ F = 4S + 6

Given ratio of father 2 years after and son 4 years after is 10 : 3:

⇒ (F + 2) ÷ (S + 4) = 10 ÷ 3

⇒ (4S + 6 + 2) ÷ (S + 4) = 10 ÷ 3

⇒ (4S + 8) ÷ (S + 4) = 10 ÷ 3

⇒ 3 × (4S + 8) = 10 × (S + 4)

⇒ 12S + 24 = 10S + 40

⇒ 2S = 16

⇒ S = 8 years

Present age of the mother = 4S = 4 × 8 = 32 years.

Age of mother after 3 years = 32 + 3 = 35 years.

Age of son after 2 years = 8 + 2 = 10 years.

Required ratio = 35 ÷ 10 = 7 : 2.

 ∴ The correct answer is 7 : 2.

Additional Information

Ages and Ratios

When solving problems on ages, represent all individual ages in terms of a single variable to simplify calculations.

Ratio Changes Over Time

If the age of a person is x years, then their age after n years is x + n and their age n years ago was x − n.

Given:

For Statement I:

Curved Surface area of cylinder = 352 cm²

Total surface area of cylinder = 2 × 792 cm²

For Statement II:

Radius of cylinder = 1.5 cm more than 4 times height

Calculation:

For Statement I:

Let radius = r. height = h

Curved Surface area of cylinder = 352 cm²

⇒ 352 = 2 × 22 / 7 × r × h

⇒ r × h = 56

Total surface area of cylinder = 2 × 792 cm²

⇒ 2 × 792 = 2 × (22 /7) × (rh + r²)

⇒ rh + r² = 252

⇒ 56 + r² = 252

⇒ r² = 252 - 56

⇒ r² = 196

⇒ r = 14

⇒ r × h = 56

⇒ 14 × h = 56

⇒ h = 4 cm

Statement I is sufficient to answer the question.

For Statement II:

∴ r = 4h + 1.5

Statement II is not sufficient to answer the question.

The correct answer is option 2.

Given:

For Statement I:

Cost price of 2 scarfs = Rs. 2200

Earns = Rs. 55 per scarf

Discount = 23%

For Statement II:

Marks up the C.P = 36%

Earns = Rs. 200

Calculation:

For Statement I:

The cost price of a shirt = Rs. 1100

Selling Price = 1100 + 55

⇒ Rs. 1155

Marked Price = 1155 / 77 × 100

⇒ Rs. 1500

Statement I is sufficient to answer the question.

For Statement II:

Let the cost price be x.

Marked Price = x × 136%

⇒ 1.36x%

Selling Price = x + 200

Statement II is not sufficient to answer the question.

The correct answer is option 1.

Concept Used:

Total work is LCM of work done by all the persons.

Formula Used:

Total Work = Efficiency × Time

Calculations: 

Statement

I. X, Y and Z together can do a piece of work in 19 days.

X and Y together can complete the work in 28.5 days

Y and Z together can complete the work in 38 days.

Total work = LCM of (19, 28.5, 38) = 114

Total Work = Efficiency × Time

114 = (X + Y + Z) × 19

⇒ (X + Y + Z) = 114/19 = 6      ----(1)

Similarly, 114 = (X + Y) × 28.5

⇒ (X + Y) = 114/28.5 = 4      ----(2)

Similarly, 114 = (Y + Z) × 38

⇒ (Y + Z) = 114/38 = 3      ----(3)

Adding (2) and (3) and subtracting (1) from it, we get

(X + 2Y + Z) – (X + Y + Z) = (4 + 3) – 6

⇒ Y = 1

Putting in Y (3), we get

Z = 3 – 1 = 2

Now, Total Work = Efficiency × Time

⇒ 114 = Z × Time

⇒ Time = 114/2 = 57 days

So, statement I alone is sufficient to answer.

Statement

II. Y takes 29 days to complete the work alone.

We cannot find efficiency of Z from this statement alone.

So, statement II alone is not sufficient to answer the question.

∴ The statement I alone is sufficient to answer the question but, statement II alone is not sufficient.

General solution:

Number of students studying in college E = 720

Value of Y = 720/3000 ×  100 = 24%

To find the value of Y

(24% + (24 - 4)% + (X - 3)% + 23% +X%) = 100%

(64% + 2X%) = 100%

2X% = 36%

X = 18%

College A:

Number of students studying in college A = 3000 × (18/100) = 540

Number of males studying in college A = 540/3 ×  2 = 360

Number of females studying in college A = (540 - 360) = 180

 

College B:

Number of students studying in college B = 3000 × (23/100) = 690

Number of males studying in college B = 690/23 ×  13 = 390

Number of females studying in college B = (690 - 390) = 300

 

College C:

Number of students studying in college C = 3000 × (15/100) = 450

Number of males studying in college C = 450/9 ×  5 = 250

Number of females studying in college C = (450 - 250) = 200

 

College D:

Number of students studying in college D = 3000 × (20/100) = 600

Number of males studying in college D = 600/5 ×  3 = 360

Number of females studying in college D = (600 - 360) = 240

 

College E:

Number of students studying in college E = 3000 × (24/100) = 720

Number of males studying in college E = 720/5 ×  4 = 576

Number of females studying in college E = (720 - 576) = 144

 

Solution:

Number of males studying in college A from city P = 360 ×  (60/100) = 216

Number of males studying in college A from city Q = (360 - 216) = 144

Number of males studying in college C from city P =250 ×  (80/100) = 200

Number of males studying in college C from city Q = (250 - 200) = 50

Number of females studying in college A from city P = 180 ×  (25/100) = 45

Number of females studying in college A from city Q = (180 - 45) = 135

Number of females studying in college C from city P = 200 ×  (30/100) = 60

Number of females studying in college C from city Q = 200 - 60 = 140

Required total = (144 + 50 + 135 + 140) = 469

General solution:

Number of students studying in college E = 720

Value of Y = 720/3000 ×  100 = 24%

To find the value of Y

(24% + (24 - 4)% + (X - 3)% + 23% +X%) = 100%

(64% + 2X%) = 100%

2X% = 36%

X = 18%

College A:

Number of students studying in college A = 3000 × (18/100) = 540

Number of males studying in college A = 540/3 ×  2 = 360

Number of females studying in college A = (540 - 360) = 180

 

College B:

Number of students studying in college B = 3000 × (23/100) = 690

Number of males studying in college B = 690/23 ×  13 = 390

Number of females studying in college B = (690 - 390) = 300

 

College C:

Number of students studying in college C = 3000 × (15/100) = 450

Number of males studying in college C = 450/9 ×  5 = 250

Number of females studying in college C = (450 - 250) = 200

 

College D:

Number of students studying in college D = 3000 × (20/100) = 600

Number of males studying in college D = 600/5 ×  3 = 360

Number of females studying in college D = (600 - 360) = 240

 

College E:

Number of students studying in college E = 3000 × (24/100) = 720

Number of males studying in college E = 720/5 ×  4 = 576

Number of females studying in college E = (720 - 576) = 144

 

Solution:

Number of males studying in college B = 390

Number of males studying in college B secured distinction = 390 ×  1/3 = 130

Number of males secured first class and second class in college B  = (390 - 130) = 260

Number of females studying in college B = 300

Number of females studying in college B secured distinction = 300 ×  1/6 = 50

Number of females secured first class and second class in college B = (300 - 50) = 250

Total secured first class and second class = 260 + 250 = 510

Number of students secured first class = 510/3 ×  2 = 340

General solution:

Number of students studying in college E = 720

Value of Y = 720/3000 ×  100 = 24%

To find the value of Y

(24% + (24 - 4)% + (X - 3)% + 23% +X%) = 100%

(64% + 2X%) = 100%

2X% = 36%

X = 18%

College A:

Number of students studying in college A = 3000 × (18/100) = 540

Number of males studying in college A = 540/3 ×  2 = 360

Number of females studying in college A = (540 - 360) = 180

 

College B:

Number of students studying in college B = 3000 × (23/100) = 690

Number of males studying in college B = 690/23 ×  13 = 390

Number of females studying in college B = (690 - 390) = 300

 

College C:

Number of students studying in college C = 3000 × (15/100) = 450

Number of males studying in college C = 450/9 ×  5 = 250

Number of females studying in college C = (450 - 250) = 200

 

College D:

Number of students studying in college D = 3000 × (20/100) = 600

Number of males studying in college D = 600/5 ×  3 = 360

Number of females studying in college D = (600 - 360) = 240

 

College E:

Number of students studying in college E = 3000 × (24/100) = 720

Number of males studying in college E = 720/5 ×  4 = 576

Number of females studying in college E = (720 - 576) = 144

 

Solution:

Number of males studying in college D = 360

Number of females studying in college D = 240

Exam fees for males  semester exam = Rs. 350

Exam fees for females in semester exam = Rs. 250

Total fees collected = (360 ×  350 + 240 ×  250) = (126000 + 60000)

Total collected = Rs. 186000

General solution:

Number of students studying in college E = 720

Value of Y = 720/3000 ×  100 = 24%

To find the value of Y

(24% + (24 - 4)% + (X - 3)% + 23% +X%) = 100%

(64% + 2X%) = 100%

2X% = 36%

X = 18%

College A:

Number of students studying in college A = 3000 × (18/100) = 540

Number of males studying in college A = 540/3 ×  2 = 360

Number of females studying in college A = (540 - 360) = 180

 

College B:

Number of students studying in college B = 3000 × (23/100) = 690

Number of males studying in college B = 690/23 ×  13 = 390

Number of females studying in college B = (690 - 390) = 300

 

College C:

Number of students studying in college C = 3000 × (15/100) = 450

Number of males studying in college C = 450/9 ×  5 = 250

Number of females studying in college C = (450 - 250) = 200

 

College D:

Number of students studying in college D = 3000 × (20/100) = 600

Number of males studying in college D = 600/5 ×  3 = 360

Number of females studying in college D = (600 - 360) = 240

 

College E:

Number of students studying in college E = 3000 × (24/100) = 720

Number of males studying in college E = 720/5 ×  4 = 576

Number of females studying in college E = (720 - 576) = 144

 

Solution:

1/3^rd of number of males studying in college D = 360 ×  1/3 = 120

1/4 th of the number of males studying in college E = 576 × 1/6 = 96

1/6 th of the number of females studying in college D = 240 ×  1/6 = 40

1/8 th of the number of females studying in college E = 144 × 1/8 =  18

Required difference = (120 + 96) - (40 + 18) = (216 - 58) = 158

General solution:

Number of students studying in college E = 720

Value of Y = 720/3000 ×  100 = 24%

To find the value of Y

(24% + (24 - 4)% + (X - 3)% + 23% +X%) = 100%

(64% + 2X%) = 100%

2X% = 36%

X = 18%

College A:

Number of students studying in college A = 3000 × (18/100) = 540

Number of males studying in college A = 540/3 ×  2 = 360

Number of females studying in college A = (540 - 360) = 180

 

College B:

Number of students studying in college B = 3000 × (23/100) = 690

Number of males studying in college B = 690/23 ×  13 = 390

Number of females studying in college B = (690 - 390) = 300

 

College C:

Number of students studying in college C = 3000 × (15/100) = 450

Number of males studying in college C = 450/9 ×  5 = 250

Number of females studying in college C = (450 - 250) = 200

 

College D:

Number of students studying in college D = 3000 × (20/100) = 600

Number of males studying in college D = 600/5 ×  3 = 360

Number of females studying in college D = (600 - 360) = 240

 

College E:

Number of students studying in college E = 3000 × (24/100) = 720

Number of males studying in college E = 720/5 ×  4 = 576

Number of females studying in college E = (720 - 576) = 144

 

Solution:

Number of males studying in college C = 250

Number of males studying in college D = 360

Number of females studying in college A = 180

Number of females studying in college B = 300

Required ratio = (250 + 360): (180 + 300) = (610: 480) = 61 : 48

Shortcut Trick

Let total members be 100%.

Remaining after Amazon Prime (20%) = 80%.

Remaining after Netflix (50% of 80%) = 40%.

Remaining after Hotstar (30% of 40%) = 40% − 12% = 28%.

28% = 6300 ⇒ 1% = 225 ⇒ 100% = 22500.

∴ The correct answer is 22500 members.

Alternate Method

Let total members be x.

⇒ Amazon Prime users = 20% of x = 0.20x

⇒ Remaining after Amazon = x − 0.20x = 0.80x

⇒ Netflix users = 50% of 0.80x = 0.40x

⇒ Remaining after Netflix = 0.80x − 0.40x = 0.40x

⇒ Hotstar users = 30% of 0.40x = 0.12x

⇒ Remaining (Youtube) = 0.40x − 0.12x = 0.28x

⇒ 0.28x = 6300

⇒ x = 6300 ÷ 0.28 = 22500

∴ The correct answer is 22500 members.

Additional Information

Successive Percentage Decrease

When values are deducted from the 'remaining' part, it follows a successive pattern: Final Value = Initial Value × (1 − r₁/100) × (1 − r₂/100) × ...

Base Change in Percentages

Always identify the base of the percentage. If it says 'of the remaining', the previous balance becomes the new 100% for that specific step.

Shortcut Trick

Emma age = 45 − 25 = 20 years.

Sophia present age = 20 + 8 = 28 years.

Sophia age 7 years ago = 28 − 7 = 21 years (which is 7 units).

Ava age 7 years ago = 9 units = 27 years → Present age = 34 years.

50% of Ava present age = 34 ÷ 2 = 17 years.

∴ The correct answer is 17 years.

Alternate Method

Given: Ratio of Sophia and Ava (7 years ago) = 7 : 9. Emma age = Sophia − 8. Emma's father = 45 years and Emma + 25.

Formula: Age difference remains constant over time. Present age = Age (n years ago) + n.

⇒ Emma's father age = 45 years.

⇒ Emma's present age = 45 − 25 = 20 years.

⇒ Sophia's present age = 20 + 8 = 28 years.

⇒ Sophia's age 7 years ago = 28 − 7 = 21 years.

⇒ According to ratio 7 : 9, 7 units = 21 → 1 unit = 3.

⇒ Ava's age 7 years ago = 9 × 3 = 27 years.

⇒ Ava's present age = 27 + 7 = 34 years.

⇒ 50% of Ava's present age = 0.50 × 34 = 17 years.

∴ The correct answer is 17 years.

Additional Information

Age Ratio Concept

If the ratio of ages is a : b and n years pass, the new ratio is (ax+n) : (bx+n). The absolute difference between ages always remains constant.

Percentage Calculations

50% of a value is equivalent to dividing the value by 2 or multiplying by 1/2.

I. 2x² – 9x + 9 = 0

⇒ 2x² – 3x – 6x + 9 = 0

⇒ x (2x – 3) – 3 (2x – 3) = 0

⇒ (2x – 3) (x – 3) = 0

⇒ x = 3/2, 3

 

II. 2y² – 17y + 30 = 0

⇒ 2y² – 12y – 5y + 30 = 0

⇒ 2y (y – 6) – 5 (y – 6) = 0

⇒ (2y – 5) (y – 6) = 0

⇒ y = 5/2, 6

 

 

Hence, relationship between x and y cannot be established.

I. x² – 10x + 24 = 0

⇒ x² – 6x – 4x + 24 = 0

⇒ (x – 4) (x – 6) = 0

⇒ x =4, 6

II. 2y² – 29y + 105 = 0

⇒ 2y² – 15y – 14y + 105 = 0

⇒ (y – 7) (2y – 15) = 0

⇒ y = 7, 7.5  

 

 

Hence, x < y.

I. x² – 42x + 440 = 0

⇒ x² – 22x – 20x + 440 = 0

⇒ x(x – 22) – 20(x – 22) = 0

⇒ (x – 22) (x – 20) = 0

⇒ x = 22, 20

 

II. y² – 34y + 288 = 0

⇒ y² – 18y – 16y + 288 = 0

⇒ y(y – 18) – 16(y – 18) = 0

⇒ (y – 18) (y – 16) = 0

⇒ y = 18, 16

 

 

∴ x > y.

I. 25x² – 30x + 8 = 0

⇒ 25x² – 10x – 20x + 8 = 0

⇒ (5x – 4) (5x – 2) = 0

⇒ x =4/5, 2/5

II. 25y² – 50y + 24 = 0

⇒ 25y² – 20y – 30y + 24 = 0

⇒ (5y – 6) (5y – 4) = 0

⇒ y = 6/5, 4/5  

 

 

Hence, x ≤ y.

I. x² – 44x + 483 = 0

⇒ x² – 21x – 23x + 483 = 0

⇒ x (x – 21) – 23 (x – 21) = 0

⇒ (x – 21) (x – 23) = 0

⇒ x = 21, 23

 

II. y² – 27y + 182 = 0

⇒ y² – 14y – 13y + 182 = 0

⇒ y (y – 14) – 13 (y – 14) = 0

⇒ (y – 14) (y – 13) = 0

⇒ y = 14, 13

 

 

Hence x > y

Shortcut Trick

Side of cube (a) = ³√216 = 6 cm. Height of cuboid (h) = 6 cm.

Base area of cuboid = 480 ÷ 6 = 80 cm². Since ratio is 5 : 4, (5x) × (4x) = 80 ⇒ 20x² = 80 ⇒ x = 2.

Dimensions of cuboid: L = 10 cm, B = 8 cm, H = 6 cm.

Ratio = (6 × √3) : √(10² + 8² + 6²) = 6√3 : √200 = 6√3 : 10√2.

∴ The correct answer is 6√3 : 10√2.

Alternate Method

Given: Volume of cube = 216 cm³, Volume of cuboid = 480 cm³, L : B (cuboid) = 5 : 4, H (cuboid) = side of cube.

Formula Used: Volume of cube = a³, Diagonal of cube = a√3, Volume of cuboid = l × b × h, Diagonal of cuboid = √(l² + b² + h²).

⇒ a³ = 216 ⇒ a = 6 cm.

⇒ Height of cuboid (h) = 6 cm.

⇒ Let length (l) = 5x and breadth (b) = 4x.

⇒ 5x × 4x × 6 = 480 ⇒ 120x² = 480 ⇒ x² = 4 ⇒ x = 2.

⇒ l = 10 cm, b = 8 cm, h = 6 cm.

⇒ Diagonal of cube = 6√3 cm.

⇒ Diagonal of cuboid = √(10² + 8² + 6²) = √(100 + 64 + 36) = √200 = 10√2 cm.

⇒ Required Ratio = 6√3 : 10√2.

∴ The correct answer is 6√3 : 10√2.

Additional Information

Cube properties

Total Surface Area = 6a²; Lateral Surface Area = 4a².

Cuboid properties

Total Surface Area = 2(lb + bh + hl); Volume = lbh.

Diagonal length

The longest rod that can be placed inside a room is its space diagonal.

Shortcut Trick

Milk concentration in Container 1 = 3/7 and in Container 2 = 5/11.

Resultant Milk concentration = 4/9.

Using Alligation (Milk): |5/11 − 4/9| : |3/7 − 4/9| ⇒ 1/99 : 1/63 ⇒ 7 : 11.

Total ratio parts = 7 + 11 = 18 units = 18 L ∴ 1 unit = 1 L.

Quantity of 1^st mixture = 7 L. Milk in it = 7 × (3/7) = 3 L.

∴ The correct answer is 3 L.

Alternate Method

Given: Ratio 1 = 3:4, Ratio 2 = 5:6, Final Ratio = 4:5, Total Volume = 18 L.

Formula: Quantity₁ × (C₁ − C_m) = Quantity₂ × (C_m − C₂)

⇒ Let Q₁ and Q₂ be the volumes of the two containers.

⇒ Milk fraction: Q₁(3/7) + Q₂(5/11) = (Q₁ + Q₂)(4/9)

⇒ Q₁(4/9 − 3/7) = Q₂(5/11 − 4/9)

⇒ Q₁(1/63) = Q₂(1/99) ⇒ Q₁/Q₂ = 63/99 = 7/11

⇒ Total units = 7 + 11 = 18 → 18 L ∴ Q₁ = 7 L

⇒ Milk in 1^st container = 7 × (3 / (3 + 4)) = 7 × 3/7 = 3 L

∴ The correct answer is 3 L.

Additional Information

Alligation Rule

Used to find the ratio in which two ingredients at given prices/concentrations are mixed to produce a mixture of a mean price. Ratio = (Dearer − Mean) : (Mean − Cheaper).

Replacement Method

When a quantity is replaced repeatedly: Final Concentration = Initial Concentration × (1 − x/V)ⁿ, where x is replaced volume and V is total volume.

Multiple Mixtures

When mixing multiple containers, the total quantity of a component (milk) is the sum of quantities from each container: Σ(Ratio × Volume).

General Solution:

To find the value of x

100% = (x + 10)% + 60%

x = 30%

Number of orders received in company A = 450

Number orders packed in company A = 450 ×  (30 + 10)/100 = 180

Number of orders shipped in company A = (450 - 180) = 270

To find the value of y 

100% = (30% + y + 30%)

y = 40%

 

Company B:

Number of orders received in company  = 600

Number of orders packed in company  = 600 ×  (70/100) = 420

Number of orders shipped in company  = (600 - 420) = 180

 

Company C:

Number of orders received in company  = 700

Number of orders packed in company  = 700 ×  (60 - 5)/100)) = 385

Number of orders shipped in company  = (700 - 385) = 315

 

Company D:

Number of orders received in company  = 2650 - (450 + 600 + 700 + 400) = 500

Number of orders packed in company  = 500 ×  (65/100) = 325

Number of orders shipped in company  = (500 - 325) = 175

 

Company E:

Number of orders received in company  = 400

Number of orders shipped in company  = 400 ×  25/100 = 100

Number of orders packed in company  = (400 - 100) = 300

 

Solution:

Number of international orders packed in company E = 300/5 = 60

Number of national orders packed in company E = (300 - 60) = 240

Number of international shipped in company B = 180/3 = 60

Number of national orders shipped in company B = (180 - 60) = 120

Required sum = (240/3 + 120 ×  2/3) = 160