Calculation:

Total number of students is 1200.

⇒ 100% = 1200

⇒ 1% = 12

The ratio between the number of students studying in BCA and B.sc,

⇒ BCA : B.sc = 12% : 18%

⇒ BCA : B.sc = 12 : 18 = 2 : 3

∴ The required ratio is 2 : 3

Given:

Let the smaller number be x then the larger number be x + 1.

60 = x - 4

x = 64

Smaller number = 64

Larger number = x + 1 = 64 + 1 = 65

Hence, the larger number is 65.

Given:

P = 22000, n = 3 year, R = 6 %

Formula Used:

Amount = P(1 + R/100)ⁿ

C.I = A - P

Calculation:

By using the above formula

A = 22000 (1 + 6/100)³

A = 22000 × (106/100)³

A = 22000 × (106 × 106 × 106)/(100 × 100 × 100)  

A = 22000 × (1.06 × 1.06 × 1.06)

A = 26202.35

Therefore, 

C.I = A - P

C.I = 26202.35 - 22000

∴ C.I = 4202.35 

Given Data:

Pays back annually Rs. 882 in 2 equal instalments.

Compound Interest is reckoned at 5% per annum.

Concept:

Compound Interest formula and the concept of annuity.

Calculation:

The man paid rupees 882 as the amount at the end of the first year and another rupees 882, as the amount at the end of the second year.

Principal for the first year = 882/(1 + (5/100)) = 840

Principal for the second year = 882/(1 + (5/100))2 = 800

Total principal = 840 + 800 = 1640

Therefore, sum did he borrow is Rs. 1640.

Given:

Length of the field = 30 m

Width of the field = 20 m

Length of the rope = 7 m

Formula:

Area of a circle = πr².

The total area of the field = Length x Width

Solution:

Total area of the field = 30 m x 20 m = 600 m².

The area that each cow can graze makes a quadrant

⇒ πr²/4 = π × (7 m)² = 154/4 m².

The total area that 4 cows can graze

⇒ 4 ×  Area that each cow can graze

⇒ 4 ×  154/4 m² = 154 m².

So, the area of the field that cows CANNOT graze

⇒ Total area of the field - Total area that 4 cows can graze

⇒ 600 m² - 154 m² = 446 m²

Therefore, the area of the field that cows CANNOT graze is 446 m2. 

Given:-

The volume of the cube is 4096 cm³, 

Formula used:-

The volume of a cube (V )= side length³   

Calculation:-

⇒ (side length)³ = 4096   

⇒ side length = ∛4096 

⇒ side length = 16

∴ The length of the side of the cube is 16 cm.

Given:

The internal radius (r) of a hollow cylindrical pipe = 14 m

External radius (R) = 21 m

Height (h) = 14 m

Formula Used:

Total Surface area of the hollow cylinder = 2πRh + 2πrh + 2π(R² - r²)

Calculation:

Total Surface Area = 2πRh + 2πrh + 2π(R² - r²)

⇒ 2π ×  [h(R + r) + (R² - r²)]

⇒ (44/7)[2 × 14(21 + 14) + (441 - 196)]

⇒ (44/7)[(14 × 35) + 245]

⇒ (44/7)[490 + 245]

⇒ 44 × 735/7

⇒ 44× 105

⇒ 4620

Hence, the correct answer is 4620 m².

Given:

Original volume of mixture = 90L

In 90L of mixture 20% alcohol

Calculations:

volume of the mixture is 90 litres. In which the quantity of alcohol is 20%

⇒ 90 × 20/100 = 18 liters

We need 40% alcohol in the mixture.

Here suppose you mix X litre alcohol in 90 litre mixture.

Then the quantity of alcohol = 18 + X litres

and the quantity of mixture = 90 + X litres.

We need 40% of alcohol. So,

⇒ [(18 + X)/(90 + X)] × 100 = 40%

⇒ (18 + X)/(90 + X) = 40/100

⇒ (18 + X)/(90 + X) = 2/5

⇒ 90 + 5X = 180 + 2X

⇒ 5X – 2X = 180 – 90

⇒ 3X = 90

⇒ X = 90/3

⇒ X = 30

∴ we should add 30 litres of alcohol.

Alternate method

Initially alcohol = 20% of 90 = 18 litre and other  = 72 litre

Final alcohol = 40% and other = 60%

So, there is no change in other liquid

60% = 72

40% = 72 × 40/60 = 48 litre

∴ Extra quantity of alcohol = 48 - 18 = 30 litre

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

So there are total 9 positive factors of 36

Given:

Wife gets = 60% of property

Daughter gets = 75% of remaining property

Trust gets = Rest of the property

Calculation:

Let, Property value = 100 units

Wife gets = 60% of 100 = 60 units

Daughter gets = 75% of (100 - 60) = 3/4 × 40 = 30 units

Trust gets= (100 - (60 + 30)) 10 units

According to the question,

⇒ 10 units = Rs. 6,00,000

⇒ 1 unit = 6,00,000/10 = Rs. 60,000 

So, daughter gets = 60,000 × 30 = Rs. 18,00,000

∴ He gives his daughter Rs. 18,00,000 share of the property.