Quantitative Aptitude PYQs

Calculation

Breadth = 4x

Length = 4x + 6

Height = 25% more than breadth = 4x + [25/100] × 4x = 4x + x=5x

Volume=Length × Breadth × Height =

Or, (4x + 6)(4x)(5x) =3240

(4x + 6)(4x)(5x) = 3240

⇒ (4x + 6) x2 = 162

Or, 4x3 + 6x2 = 162

Try x =1,2,3…. [All value is integer]

108 + 54 = 162 [x = 3]

Breadth = 4x = 12 m

Length = 4x + 6 = 18 m

Height = 5x = 15 m

TSA = 2(lb + bh + hl)

= 2[(18 × 12) + (12 × 15) + (15 × 18)]

= 2(216 + 180 + 270) = 2 × 666 = 1332 m²

Given:

Marked Price = 80% above Cost Price

First discount = 20%

Second discount = x%

Profit = 8%

Calculation:

⇒ Let the Cost Price = ₹100

⇒ Marked Price = 100 + 80 = ₹180

⇒ Price after first discount = 180 × (80/100) = ₹144

⇒ Selling Price = 100 + 8 = ₹108

⇒ According to the question,

144 × (100 − x)/100 = 108

⇒ (100 − x)/100 = 108/144

⇒ (100 − x)/100 = 3/4

⇒ 100 − x = 75

⇒ x = 25%

Final Answer = 25%

Solution:

Total quantity of milk and water = 5: 4

Total quantity of milk and water in the final mixture = 81 litres

Quantity of milk in the mixture = 81/9 ×  5 = 45

Quantity of water in the mixture = (81 - 45) = 36

Quantity of milk taken out = 36/9 ×  5 = 20

Quantity of water taken out = (36 - 20) = 16

(45 - 20 +x)/( 36 - 16 + (x - 5)) = 7/5

(25 + x) (15 + x) = 7/5

(125 + 5x) = (105 + 7x)

2x = 20

x = 10 

Final quantity of mixture = (25 + 10 + 20 + 5) = 60 litres

Solution:

The average of five consecutive even numbers = 5 × 42 = 210

Let the even numbers be a, (a + 2), (a + 4), (a + 6) and (a + 8) 

(a + a + 2 + a + 4 + a + 6 + a + 8) = 210

(5a + 20) = 210

a = 190/5 = 38

Smallest even number is 2 more than x

If smallest even number = 38

Value of x = (38 - 2) = 36

Largest even number = 46

Value of y = 46 + 1 = 47

25% of x = 36/4 = 9

200% of y = 47 × (200/100) = 94

Required sum = (9 + 94) = 103

Unsold pants of A = 800-560=240

Pants transferred from A = 25% x 240 = 60

Unsold pants of C = 1200 – 900 = 300

Pants transferred from C = 40% x 300 = 120

Total pants received by B = 60 + 120 = 180

Pants sold from the received stock = 75% x 180 = 135

Revised sales of B = 760 + 135= 895

Pants sold at the regular price = 60% x 1000=600

Revenue from these pants = 600 x 750=₹4,50,000

Discounted selling price = 80% x ₹750=₹600

Remaining pants sold = 1000 – 600 = 400

Revenue from discounted pants = 400 x 600 = ₹2,40,000

Total revenue = ₹4,50,000+₹2,40,000=₹6,90,000

Manufacturing cost = 1400 x 450=₹6,30,000

Packaging expense = 1000 x 30=₹30,000

Total cost = ₹6,30,000+₹30,000=₹6,60,000

Profit = ₹6,90,000 - ₹6,60,000 = ₹30,000

Given:

205 , 236 , 279 , 304 , 341

Calculation:

Here the logic follows as,

Hence, 279 is the wrong term

\(\therefore\) The correct answer is 279.

Quantity A:

Distance covered by the train in the same time = 1260 × 6/7 = 1080 km

Quantity B:

A 320 m long train crosses a tunnel thrice its length in 32 sec

⇒ Speed of the train = (320 + 320 × 3) /32 = 40 m/s

⇒ Distance covered by the train in 8 hours = 40 × 8 × 18/5 = 1152 km

∴ Quantity A < Quantity B

Quantity I:

Age of grandson = 19 – 9 = 10 years

Age of Rohit = 10 × 6 + 11 = 71 years

Quantity II:

Required average \(= \frac{{12; \times ;30 - 2; \times ;25}}{{10}}\)

= \(\frac{{360 - 50}}{{10}}\)

= 31 years

∴ Quantity I > Quantity II

General Solution:

Orchard Area Division

Total land = 6 acres

Rajat : Suman = 4 : 2 ⇒  2 : 1

Apple Production in 2021:

Let Rajat's production = R₁ kg

He gave 60 kg to Suman, which was 10% of his production

⇒ 10% of R₁ = 60 ⇒ R₁ = 600 kg

Suman got 60 kg which increased his total by 30%

⇒ 60 = 30% of S₁ ⇒ S₁ = 200 kg

2021: Rajat = 600 kg, Suman = 200 kg

2022 Production:

Suman's 2022 production = 50% more than 2021 = 200 + 50% of 200 = 300 kg

He gives 20% of 300 = 60 kg to Rajat

Let Rajat's 2022 own production = R₂

Total apples with Rajat = R₂ + 60 = 15% more than R₂

⇒ R₂ + 60 = R₂ + 15% of R₂ = R₂ × 1.15

⇒ R₂ + 60 = 1.15R₂ ⇒ 60 = 0.15R₂ ⇒ R₂ = 400 kg

2022: Rajat = 400 kg, Suman = 300 kg

2023 Production:

Both produced equal quantities

Rajat's 2023 production is 20% more than previous year = 400 + 20% of 400 = 480 kg

⇒ So, Suman’s 2023 production = 480 kg

2023: Rajat = 480 kg, Suman = 480 kg

Thus:

 

Calculations:

Apple prices per year:

2021: ₹50 per kg

2022: ₹50 + 10% = ₹55 per kg

2023: ₹55 + 10% = ₹60.5 per kg

Suman's final apple quantity each year

2021: He had 200 kg + 60 kg from Rajat = 260 kg

2022: Produced 300 kg – gave 60 kg to Rajat = 240 kg

2023: Produced = 480 kg

Calculate Revenue for each year:

2021: 260 kg × ₹50 = ₹13,000

2022: 240 kg × ₹55 = ₹13,200

2023: 480 kg × ₹60.5 = ₹29,040

Total Revenue = 13,000 + 13,200 + 29,040 = ₹55,240

Thus, the correct answer is ₹55,240.

General Solution:

Orchard Area Division

Total land = 6 acres

Rajat : Suman = 4 : 2 ⇒  2 : 1

Apple Production in 2021:

Let Rajat's production = R₁ kg

He gave 60 kg to Suman, which was 10% of his production

⇒ 10% of R₁ = 60 ⇒ R₁ = 600 kg

Suman got 60 kg which increased his total by 30%

⇒ 60 = 30% of S₁ ⇒ S₁ = 200 kg

2021: Rajat = 600 kg, Suman = 200 kg

2022 Production:

Suman's 2022 production = 50% more than 2021 = 200 + 50% of 200 = 300 kg

He gives 20% of 300 = 60 kg to Rajat

Let Rajat's 2022 own production = R₂

Total apples with Rajat = R₂ + 60 = 15% more than R₂

⇒ R₂ + 60 = R₂ + 15% of R₂ = R₂ × 1.15

⇒ R₂ + 60 = 1.15R₂ ⇒ 60 = 0.15R₂ ⇒ R₂ = 400 kg

2022: Rajat = 400 kg, Suman = 300 kg

2023 Production:

Both produced equal quantities

Rajat's 2023 production is 20% more than previous year = 400 + 20% of 400 = 480 kg

⇒ So, Suman’s 2023 production = 480 kg

2023: Rajat = 480 kg, Suman = 480 kg

Thus:

 

Calculations:

2022 Apple Quantities:

Rajat's own production in 2022 = 400 kg

He received 60 kg from Suman

Total apples with Rajat = 400 + 60 = 460 kg

Suman's production = 300 kg

He gave 20% of 300 = 60 kg to Rajat

Total apples left with Suman = 300 − 60 = 240 kg

Required Ratio:

⇒ Rajat : Suman = 460 : 240 ⇒ 23 : 12

Thus, the correct answer is 23 : 12.

General Solution:

Orchard Area Division

Total land = 6 acres

Rajat : Suman = 4 : 2 ⇒  2 : 1

Apple Production in 2021:

Let Rajat's production = R₁ kg

He gave 60 kg to Suman, which was 10% of his production

⇒ 10% of R₁ = 60 ⇒ R₁ = 600 kg

Suman got 60 kg which increased his total by 30%

⇒ 60 = 30% of S₁ ⇒ S₁ = 200 kg

2021: Rajat = 600 kg, Suman = 200 kg

2022 Production:

Suman's 2022 production = 50% more than 2021 = 200 + 50% of 200 = 300 kg

He gives 20% of 300 = 60 kg to Rajat

Let Rajat's 2022 own production = R₂

Total apples with Rajat = R₂ + 60 = 15% more than R₂

⇒ R₂ + 60 = R₂ + 15% of R₂ = R₂ × 1.15

⇒ R₂ + 60 = 1.15R₂ ⇒ 60 = 0.15R₂ ⇒ R₂ = 400 kg

2022: Rajat = 400 kg, Suman = 300 kg

2023 Production:

Both produced equal quantities

Rajat's 2023 production is 20% more than previous year = 400 + 20% of 400 = 480 kg

⇒ So, Suman’s 2023 production = 480 kg

2023: Rajat = 480 kg, Suman = 480 kg

Thus:

 

Calculations:

2021 total = 600 (Rajat) + 200 (Suman) = 800 kg

2023 total = 480 + 480 = 960 kg

Change over 2 years = 960 − 800 = 160 kg

Average annual % increase = [(Final − Initial)/Initial] ÷ 2 × 100

⇒ (960 − 800)/800 × 100 = 20% over 2 years ⇒ Annual average = 10%

2024 projection = 960 × (1 + 10/100) = 960 × 1.10 = 1056 kg

∴ Approximate total production in 2024 = 1056 kg

Given:

P invested = ₹60,000 for 12 months

Q invested = ₹80,000 for 9 months

R invested = ₹x for 8 months

P's share in profit = 30%

Calculation:

⇒ Profit ratio is proportional to Investment × Time

⇒ P's investment unit

= 60,000 × 12 = 7,20,000

⇒ Q's investment unit

= 80,000 × 9 = 7,20,000

⇒ R's investment unit = 8x

⇒ According to the question,

7,20,000/(7,20,000 + 7,20,000 + 8x) = 30/100

⇒ 7,20,000/(14,40,000 + 8x) = 3/10

⇒ 72,00,000 = 43,20,000 + 24x

⇒ 28,80,000 = 24x

⇒ x = ₹1,20,000