Given:

The average age of Ram, Raman, and Rohan = 23 years

Average age of Raman and Rohan = 27 years

Formula used:

Average = Sum of values/Number of values

Solution:

Let's assume the current age of Ram is R, Raman is Rm, and Rohan is Rh.

Using the formula for average, we can write the following equations:

(R + Rm + Rh)/3 = 23 ---(Equation 1)

(Rm + Rh)/2 = 27 ---(Equation 2)

To find Ram's age 5 years ago, we need to determine Ram's current age.

Solving Equation 2 for Rm + Rh:

Rm + Rh = 2 × 27

Rm + Rh = 54 ---(Equation 3)

Substituting Equation 3 into Equation 1:

(R + 54)/3 = 23

R + 54 = 3 × 23

R + 54 = 69

R = 69 - 54

R = 15

Ram's current age is 15 years.

Ram's age 5 years ago:

Ram's age 5 years ago = 15 - 5

Ram's age 5 years ago = 10 years old.

Therefore, Ram's age 5 years ago was 10 years.

Given:

A motor boat can travel at a speed of 10 km per hour in still water, it goes 36 km downstream in the river and returns the same. It took him a total of 20 hours. 

Calculation:

Let the flow of water be x km/h

Speed downstream = (10 + x) km/h

Speed upstream = (10 - x) km/h

⇒ ( 10 + x ) (10 - x ) = 36

⇒ 100 - x² = 36

⇒ x²  = 64

x = 8km/h

Concept used:

BODMAS

Calculations:

⇒ 29 + 25 - 10

⇒ 54 - 10

⇒ 44

∴ Required simplified value is 44.

Calculation:

The total number of cakes sold by Bakery C on Saturday and Sunday,

⇒ 195 + 235 = 430

The total number of cakes sold by Bakery E on Tuesday,

⇒ 325

According to the question, 

⇒ 430/325 × 100 

⇒ 430/13 × 4

⇒ 132.30

∴ It is approximately 132%

For this to be divisible by 11, sum of numbers at even places - sum of numbers at odd places must be zero or divisible by 11

⇒ (4 + 1) - (3 + 0) = 5 - 3 = 2

instead of 2 there must be 0, so that it will be divisible by 11

∴ 2 must be subtracted from the number to make it divisible by 11

Alternate Method

3401 = 3399 × 11 + 2

Therefore, in order to make the number entirely divisible by 11, 2 must be subtracted.

Let the radius of the base of the cone be r cm and the height of the cone be h cm.

The area of the base of the cone is 144π cm²,

⇒ πr² = 144π

⇒ r = 12

The cone is remoulded to obtain a solid sphere,

⇒ √(12² + h²) = 13

⇒ 144 + h² = 169

⇒ h² = 25

⇒ h = 5

⇒ Volume of the cone = 1/3 × π × 12² × 5 = 240π cm³

Let the radius of the sphere be R cm.

⇒ 4/3 × π × R³ = 240π

⇒ R³ = 180

⇒ R = ∛180

∴ Radius of the sphere = ∛180 cm

Given:

Pipe A can fill an empty tank in 6 h and pipe B in 8 h.

Both the pipes are opened at the same time and pipe A is closed after 2 hours.

Calculation:

Total work = LCM of (6, 8) = 24 unit

Efficiency of pipe A = 24/6 = 4 unit and efficiency of pipe B = 24/8 = 3 unit

In the 1st two hours both pipes are opened, the work done = (4 + 3) × 2 = 14 unit

Remaining = (24 - 14) = 10 unit

Given:

Principle = 550

Rate = 20%

Formula Used:

The formula for Instalments in the case of compound Interest

Principal = Instalment/(1+r/100) + Instalment/(1+r/100)²

Calculation:

Let, the Instalment = A

By using the above formula

⇒ 550 = A/(1+20/100) + A/(1+20/100)²

⇒ 550 = A/(6/5) + A/(6/5)²

⇒ 550 = A × 5/6 + A × ( 5/6)²

⇒ 550 = A × (55/36)

⇒ A = 360

∴ The value of each instalment will be 360.

Given:

LCM = 225, HCF = 5, and One of the number is 25.

Formula used:

First Number × Second Number = LCM × HCF

Calculation:

Let the second number be x.

First Number × Second Number = LCM × HCF

⇒ 25 × x = 5 × 225

⇒ x = (5 × 225)/25

⇒ x = 5 × 9 = 45

∴ The second number is 45.

Given:

Length (l) of the cuboid = 7 cm

Breadth (b) of the cuboid = 11 cm

Height (h) of the cuboid = 13 cm

Concept used:

The total surface area of a cuboid = 2(lb + bh + hl)

Calculation:

Using the concept

⇒ 2[(7 × 11) + (11 × 13) + (13 × 7)]

⇒ [77 + 143 + 91]

⇒ 2 × 311 = 622 cm²

∴ The total surface area of the cuboid is 622 cm².