Quantitative Aptitude PYQs

 

Total number of items manufactured by A and B = 240 + 290 = 530

Total number of items sold by C and D = 240 + 270 = 510

Required ratio = 530: 510 = 53: 51

 

Total number of items sold = 180 + 210 + 240 + 270 = 900

Number of items returned from company A = 20% of 180 = 36

Number of items returned from company D = 10% of 270 = 27

Total number of items effectively sold = 900 − 36 – 27 = 837

 

Number of unsold items of B : Number of unsold items of C = 80 : 50 = 8 : 5

Calculation

Initial mixture = 180 litres

Milk : Water = 5 : 4

⇒ Total parts = 5 + 4 = 9

⇒ Milk = [5/9] × 180 = 100 L

⇒ Water = [4/9] × 180 = 80 L

Remove 25% of mixture

25% of 180 = 45 litres removed

Milk removed = [100/180] × 45=25 L

Water removed = [80/180] × 45 = 20

After removal:

Milk left = 100 – 25 = 75 L

Water left = 80 – 20 = 60 L

Add 15 litres of milk

Milk = 75 + 15 = 90 L

Water = 60 L

Total = 90 + 60 = 150 L

Milk % = [90/150] × 100 =60%

⇒ x + 10 = 60

⇒ x = 50

Water % = [60/150] × 100 = 40%

⇒ y + 10 = 40 ⇒ y = 30

So, x + y = 80

Given:

1^st Discount = 25% of M.P

2^nd Discount = 20% of 1^st Discount

S.P = Rs. 600

Concept Used:

D = M.P × Rate of Discount 

Successive Discount = [a + b - (ab/100)]%

M.P = Marked Price, D = Discount, S.P = Selling Price

Calculation:

Let the marked price be x.

According to the question,

x × (75/100) × (80/100) = 600

⇒ x = (600 × 100 × 100)/(75 × 80)

⇒ x = 1000

∴ The Marked Price is Rs. 1000.

Shortcut Trick

Ratio of Stream Speed (v) : Still Water Speed (u) = 4 : 9

Upstream Speed (u−v) = 5 units | Downstream Speed (u+v) = 13 units

Ratio of Distances: 270 / 468 = 15 : 26

Using Time = Distance / Speed: (15/5) / (26/13) = 3 : 2 (Time Ratio)

Difference (3−2) = 1 unit → 6 hours ∴ Still speed = 27 kmph

∴ The correct answer is 216 km.

Alternate Method

Given: Ratio v : u = 4 : 9. Upstream dist = 270 km, Downstream dist = 468 km.

Formula: Distance = Speed × Time

⇒ Let u = 9x and v = 4x. Upstream speed = 5x, Downstream speed = 13x.

⇒ 270 / 5x = t and 468 / 13x = t − 6

⇒ 54/x = t and 36/x = t − 6

⇒ 54/x − 36/x = 6 ⇒ 18/x = 6 ⇒ x = 3

⇒ Speed of boat in still water = 9 × 3 = 27 kmph

⇒ Distance in 8 hours = 27 × 8 = 216 km

∴ The correct answer is 216 km.

Additional Information

Downstream Speed

The effective speed of the boat when traveling in the same direction as the stream. Downstream = u + v.

Upstream Speed

The effective speed of the boat when traveling against the direction of the stream. Upstream = u − v.

Still Water Calculation

Speed of boat in still water (u) = (Downstream + Upstream) ÷ 2.

Given:

Compound Interest Rate = 20% p.a.

Time = 2 years

CI = ₹1698.4

New Principal = X + 500

Simple Interest Rate = 23% p.a.

Time = 3.5 years

Formula used:

CI = P\([(1+\frac{r}{100})^t - 1 ]\)

SI = (P × R × T) ÷ 100

Calculations:

⇒ 1698.4 = X × ((1 + 20/100)² - 1)

⇒ 1698.4 = X × (1.44 - 1) = X × 0.44

⇒ X = 1698.4 ÷ 0.44 = 3860

Now, New Principal = X + 500 = 3860 + 500 = ₹4360

⇒ SI = 4360 × 23 × 3.5 ÷ 100 = 3509.8

∴ Simple Interest received = ₹3509.8

Solution:

10 years ago, let the age of mother = 5x years, age of daughter = 2x years

Present Age of mother = 5x + 10

Present Age of daughter = 2x + 10

8 years hence, mother age = 5x + 18 years

Daughter age = 2x + 18 years

(5x+18)/ (2x+18) = 7:4

x = 9

Present age of mother = (5 × 9 + 10) = 45 = 55

Present age of daughter = (2 × 9 + 10) = 28

Present age of father = (55 + 5) = 60

Therefore the age of father and daughter 10 years ago = (60 + 28 - 20) = 68

Common Calculation

Given:

Total employees = 750

Monday : Tuesday : Wednesday = 6 : 5 : 4

Male : Female on Monday = 4 : 2

Female on Tuesday = 25% more than Female on Monday

Male on Wednesday = 20 less than Male on Tuesday

Formula:

Number = (Ratio Share ÷ Total Ratio) × Total

Calculation:

⇒ Total parts = 6 + 5 + 4 = 15

⇒ Monday = (6/15) × 750 = 300

⇒ Tuesday = (5/15) × 750 = 250

⇒ Wednesday = (4/15) × 750 = 200

Monday

⇒ Male : Female = 4 : 2 = 2 : 1

⇒ Male = (2/3) × 300 = 200

⇒ Female = (1/3) × 300 = 100

Tuesday

⇒ Female = 100 × 125/100 = 125

⇒ Male = 250 – 125 = 125

Wednesday

⇒ Male = 125 – 20 = 105

⇒ Female = 200 – 105 = 95

Final Summary

Given:

Female employees on Wednesday = 95

Male employees on Monday = 200

Formula:

New Number = Original Number × (100 ± Percentage)/100

Calculation:

⇒ Female employees on Wednesday after 20% increase = 95 × 120/100 = 114

⇒ Male employees on Monday after 10% decrease = 200 × 90/100 = 180

⇒ Required ratio = 114 : 180 = 19 : 30

∴ Answer = 19 : 30

Common Calculation

Given:

Total employees = 750

Monday : Tuesday : Wednesday = 6 : 5 : 4

Male : Female on Monday = 4 : 2

Female on Tuesday = 25% more than Female on Monday

Male on Wednesday = 20 less than Male on Tuesday

Formula:

Number = (Ratio Share ÷ Total Ratio) × Total

Calculation:

⇒ Total parts = 6 + 5 + 4 = 15

⇒ Monday = (6/15) × 750 = 300

⇒ Tuesday = (5/15) × 750 = 250

⇒ Wednesday = (4/15) × 750 = 200

Monday

⇒ Male : Female = 4 : 2 = 2 : 1

⇒ Male = (2/3) × 300 = 200

⇒ Female = (1/3) × 300 = 100

Tuesday

⇒ Female = 100 × 125/100 = 125

⇒ Male = 250 – 125 = 125

Wednesday

⇒ Male = 125 – 20 = 105

⇒ Female = 200 – 105 = 95

Final Summary

Given:

Female employees on Monday and Wednesday = 100 + 95

Male employees on all three days = 430

Formula:

Percentage = (Difference ÷ Original) × 100

Calculation:

⇒ Female employees on Monday and Wednesday = 100 + 95 = 195

⇒ Male employees on all three days = 200 + 125 + 105 = 430

⇒ Difference = 430 – 195 = 235

⇒ Required percentage = (235/430) × 100 = 54.65% ≈ 55%

∴ Answer = 55%

Common Calculation

Given:

Total employees = 750

Monday : Tuesday : Wednesday = 6 : 5 : 4

Male : Female on Monday = 4 : 2

Female on Tuesday = 25% more than Female on Monday

Male on Wednesday = 20 less than Male on Tuesday

Formula:

Number = (Ratio Share ÷ Total Ratio) × Total

Calculation:

⇒ Total parts = 6 + 5 + 4 = 15

⇒ Monday = (6/15) × 750 = 300

⇒ Tuesday = (5/15) × 750 = 250

⇒ Wednesday = (4/15) × 750 = 200

Monday

⇒ Male : Female = 4 : 2 = 2 : 1

⇒ Male = (2/3) × 300 = 200

⇒ Female = (1/3) × 300 = 100

Tuesday

⇒ Female = 100 × 125/100 = 125

⇒ Male = 250 – 125 = 125

Wednesday

⇒ Male = 125 – 20 = 105

⇒ Female = 200 – 105 = 95

Final Summary

Given:

Male Monday = 200

Male Wednesday = 105

Calculation:

⇒ Male employees on Monday after transfer = 200 – 25 = 175

⇒ Male employees on Wednesday after transfer = 105 + 25 = 130

⇒ Required ratio = 175 : 130 = 35 : 26

∴ Answer = 35 : 26

Common Calculation

Given:

Total employees = 750

Monday : Tuesday : Wednesday = 6 : 5 : 4

Male : Female on Monday = 4 : 2

Female on Tuesday = 25% more than Female on Monday

Male on Wednesday = 20 less than Male on Tuesday

Formula:

Number = (Ratio Share ÷ Total Ratio) × Total

Calculation:

⇒ Total parts = 6 + 5 + 4 = 15

⇒ Monday = (6/15) × 750 = 300

⇒ Tuesday = (5/15) × 750 = 250

⇒ Wednesday = (4/15) × 750 = 200

Monday

⇒ Male : Female = 4 : 2 = 2 : 1

⇒ Male = (2/3) × 300 = 200

⇒ Female = (1/3) × 300 = 100

Tuesday

⇒ Female = 100 × 125/100 = 125

⇒ Male = 250 – 125 = 125

Wednesday

⇒ Male = 125 – 20 = 105

⇒ Female = 200 – 105 = 95

Final Summary

Given:

Monday = 300

Tuesday = 250

Wednesday = 200

Formula:

Average = Sum of Observations ÷ Number of Observations

Calculation:

⇒ Average attendance on Monday and Wednesday = (300 + 200)/2 = 500/2 = 250

⇒ Average attendance on Tuesday = 250

⇒ Difference = 250 – 250 = 0

∴ Answer = 0