**(01) If x : y = 3 : 2, then the ratio ( 2x² + 3y² ) : ( 3x² – 2y² ) is:**

Given –

x : y = 3 : 2, then x = 3y / 2

( 2x² + 3y² ) : ( 3x² – 2y² ) = ( 2 × 9y²/4 + 3y² ) : ( 3 × 9y² / 4 – 2y² )

= 15y² / 2 : 19y² / 4 = 30 : 19

**Hence 30 : 19 is the required ratio**

**(02)** **If a : b = b : c, then a ^{4 }: b^{4 }is:**

Sol:

a : b = b : c, thus, b² = ac

Thus, a^{4 }: b^{4 }= a^{4 }/ ac × ac = **a² : c²**

**(03) If a : b = c : d = e : f = 1 : 2, then ( 3a + 5c + 7e ) : ( 3b + 5d + 7f ) is:**

Sol:

a = x, c = x and e = x

Then, b = 2x, d = 2x and f = 2x

Thus, ( 3a + 5c + 7e ) : ( 3b + 5d + 7f ) = 15x / 30x = ½ = 1 : 2

**Hence the required ratio is 1 : 2**

**(04) If x : y = 2 : 3, then the value of 3x + 2y / 9x + 5y is:**

Sol: x = 2y / 3

Thus, 3 (2y/3) + 2y / 9 (2y/3) + 5y) = 4y / 11y = 4 / 11

**Hence 4/11 is the required value**

**(05) The ratio of the first and second class fares between two railway stations is 4 : 1 and that of the number of passengers travelling by first and second classes is 1 : 40. If on a day Rs. 1100 are collected as total fare, the amount collected from the first class passengers is**

First class fare = 4x and Second class fare = x

Passenger in first class 1 and second class = 40

Thus, 4x + 40x = 1100

x = 25

First class fare = 4 × 25 = Rs. 100

**(06) What number should be added to each of 6, 14, 18 and 38, so that the resulting numbers make a proportion?**

Let the required number be x

6 + x / 14 + x = 18 + x / 38 + x

x = 2

Hence 2 should be added to make these numbers a proportion

**(07) The ratio of two numbers is 3 : 4 and their LCM is 48. The sum of the two numbers is:**

First number = 3x and Second number = 4x

LCM = 48

( 3 × 4 ) x = 48

x = 4

Numbers = 3 (4) and 4 (4) = 12 and 16

Required sum = 12 + 16 = 28

**(08) The ratio of weekly income of A and B is 9 : 7 and the ratio of their expenditures is 4 : 3. If each saves Rs. 200 per week, then the sum of their weekly income is:**

Income of A = 9x, Income of B = 7x

Expenditure of A = 4y, Expenditure of B = 3y

9x – 4y = 200 and 7x – 3y = 200

On solving both equations, x = 200, y = 400

Income of A = 9 (200) = Rs. 1800 and Income of B = 7 (200) = Rs. 1400

Required Sum = 1800 + 1400 = Rs. 3200

**(09) 94 is divided into two parts in such a way that the fifth part of the first and the eighth part of the second are in the ratio 3 : 4. The first part is:**

First part = x , Second part = 94 – x

(x/5) : (94 – x) /8 = 3 / 4

x/5 × 8/94 –x = 3 /4

8x / 470 – 5x = 3 / 4

32x = 1410 – 15x

x = 1410 / 47 = 30

**Hence 30 is the first part**

**(10) A, B and C are Batsmen. The ratio of the runs scored by them in a certain match are A : B = 5 : 3 and B : C = 4 : 5. In all they scored 564 runs. The number of runs scored by B is**

A : B = 5 : 3 and B : C = 4 : 5,

thus, A : B : C = 20 : 12 : 15

Runs scored by B =( 12 / 47) × 564 = 144