Given:

Total marks obtained by Manish in Math, Science, Hindi and English = 261

The ratio of marks of Math and Science = 7: 6

The ratio of marks of Science and Hindi = 6 : 5

The ratio of marks of Hindi and English = 4 : 3 

Calculation:

Let marks of hindi be x

According to the question,

Hindi and English = 4 : 3

⇒ Hindi/English = 4/3

⇒ x/English = 4/3

⇒ English = 3x/4

Again, 

Science and Hindi = 6 : 5

⇒ Science/Hindi = 6/5

⇒ Science/x = 6/5

⇒ Science = 6x/5

Again,

Math and Science = 7: 6

⇒ Math/Science = 7/6

⇒ Math = 7/6 × 6x/5 = 7x/5

Now,

Math + Science + Hindi + English = 261

⇒ 7x/5 + 6x/5 + x + 3x/4 = 261

⇒ (28x + 24x + 20x + 15x)/20 = 261

⇒ 87x/20 = 261

⇒ x = 60

∴  Marks of hindi is 60.

Given:

Ratio of three numbers = 3/4 : 5/8 : 7/12

Calculation:

Let three numbers be 3a/4, 5a/8 and 7a/12 respectively.

⇒ 3a/4 - 7a/12 = 48

⇒ 2a/12 = 48

⇒ a = 288

∴ Greatest number = 3a/4 = 3 × 288/4 = 216

Given:

The ratio of seats of Mathematics, Physics and Biology = 4 : 5 : 8 

Increase in the seats of Mathematics = 50% 

Increase in the seats of Physics = 20%

Increase in the seats of Biology = 25%

Calculation:

Let the number of seats of Mathematics, Physics and Biology be 40a, 50a and 80a respectively. 

Increased seats of Mathematics = 40a + 40a × 50/100 

⇒ 60a 

Increased seats of Physics= 50a + 50a × 20/100 

⇒ 60a 

Increased seats of Biology = 80a + 80a × 25/100 

⇒100a 

∴ The ratio of increased seats of Mathematics, Physics and Biology is 60a : 60a : 100a respectively.

⇒ 3 : 3 : 5

Shortcut Trick The ratio of seats of Mathematics, Physics and Biology = 4 : 5 : 8

∴ The required ratio of increased seats = 4 × 150/100 : 5 × 120/100 : 8 × 125/100 

⇒ 6 : 6 : 10 

⇒ 3 : 3 : 5  

Given:

A + B + C = 342

Calculation:

A : B = 3 : 2 = 9 : 6

B : C = 3 : 2 = 6 : 4

A : B : C = 9 : 6 : 4

∴ Runs made by A = 9/19 × 342 = 162

Given:

Ratio of A : B = 4 : 5 and A : C = 8 : 9,

Difference between the ages of A and C is 3 years.

Calculation:

ATQ,

A : B : C = 8 : 10 : 9

let the present ages of A, B and C be 8X,

10X and 9X respectively.

The difference b/w C - A = 3 years

9X - 8X = 3

X = 3

Then the sum of the ages of A, B and C

after 7 years:

(A + 7) + (B + 7) + (C + 7)

(A + B + C) + 21

⇒ (8X + 10X + 9X) + 21 

⇒ 27X + 21

⇒ 27 × 3 + 21

⇒ 102 years

Given:

A + B + C = 650

Concept:

If N is divided into a ∶ b, then

First part = N × a/(a +  b)

Second part = N × b/(a + b)

Calculation:

Ratio of share of A, B and C after deduction of Rs. 30 each = 2x ∶ 3x ∶ 4x

According to the question,

(A – 30) + (B – 30) + (C – 30) = 2x + 3x + 4x

⇒ A + B + C – 90 = 9x

⇒ 650 – 90 = 9x

⇒ 9x = 560

⇒ x = 560/9

Share of B = 560/9 × 3 + 30 = 560/3 + 30 = (560 + 90)/3 = 650/3 = 216.66

∴ The amount received by B is Rs. 216.66.

Given:

The distance covered by a stone is inversely proportional to square of its weight. A 3 kg stone covers a distance of 9 meter when it is thrown.

Calculation:

According to the question, 

Let the distance be D and Weight be W

Distance is covered by a proportional to square of its weight

⇒ D = K(1/W²)

⇒ 9 = K(1/9)

⇒ K = 81

Distance is covered by a 4 kg stone

⇒ D = 81(1/4²)

⇒ D = 81/16

⇒ D = 5.0625

∴ The distance covered by a 4 kg stone when it is thrown will be 5.0625 m.

Formula used in this type of question, 

D = (weight₁)² × given distance/(weight₂)²

⇒ 3² × 9/4²

⇒ 81/16

⇒ 5.0625 m

∴ The distance covered by a 4 kg stone when it is thrown will be 5.0625 m.

Given:

Three numbers are 25% and 125% and 250%

Formula used

Ratio = first numbers: second numbers: third numbers

Calculation

Let the fourth number be X

And first three number a, b, and c

Then according to question,

a = 1.25X, b = 2.25X and c = 3.50X

a ∶ b ∶ c = 1.25X ∶ 2.25X ∶ 3.50X

a ∶ b ∶ c = 5 ∶ 9 ∶ 14

∴ a ∶ b ∶ c is 5 ∶ 9 ∶ 14

Given:

The ratio of present ages = 6 ∶ 7

12 year ago, the ratio of ages = 3 ∶ 4

Calculation:

Let the present ages of P and Q are 6x and 7x respectively

According to the question

(6x - 12) ∶ (7x - 12) = 3 ∶ 4

⇒ (6x - 12) × 4 = (7x - 12) × 3

⇒ 24x - 48 = 21x - 36

⇒ 24x - 21x = 48 - 36

⇒ 3x = 12

⇒ x = 4

Sum of present ages = (6x + 7x) = (6 × 4 + 7 × 4)

⇒ 52 years

∴ The sum of total of their present ages is 52 years. 

Given: 

Ram : Mohit = 4 : 9

Ram + Mohit + Ganesh = 76

Concept used:

If a and b are two numbers then their mean proportion is √(ab).

Calculation:

Let the age of Ram be 4R and the age of Mohit be 9R.

The age of Ganesh = √(4R × 9R)

⇒ 6R

Ram + Mohit + Ganesh = 76

⇒ 4R + 9R + 6R = 76

⇒ 19R = 76

⇒ R = 4

The age of Ganesh = 6R

⇒ 6 × 4 

⇒ 24

∴ The age of the Ganesh is 24.