### Question. 1.

**In a mixture of 40 litres, the ratio of milk and water is 4:1. How much water must be added to this mixture so that the ratio of milk and water becomes 2:3.**

(a) 20 litres

(b) 32 litres

(c) 40 litres

(d) 30 litres

### Question. 2.

**If three numbers are in the ratio of 1:2:3 and half the sum is 18, then the ratio of squares of the numbers is:**

(a) 6: 12: 13

(b) 1: 2: 4

(c) 36: 144: 324

(d) None of these

### Question. 3.

**The ratio between two numbers is 3:4 and their LCM is 180. The first number is:**

(a) 60

(b) 45

(c) 15

(d) 20

### Question. 4.

**The incomes of A and B are in the ratio 3:2 and their expenditures are in the ratio 5:3. If each saves Rs. 1000, then, A's income is**

(a) Rs. 3000

(b) Rs. 4000

(c) Rs. 6000

(d) Rs. 9000

### Question. 5.

**The students in three batches at Made Easy are in the ratio 2 : 3 : 5. If 20 students are increased in each batch, the ratio change to 4:5:7. The total number of students in the three batches before the increase were.**

(a) 10

(b) 90

(c) 100

(d) 150

### Question. 6.

**The difference between two positive numbers is 10 and the ratio between them is 5:3. Find the product the two numbers**

(a) 375

(b) 175

(c) 275

(d) 125

### Question. 7.

**Four numbers in the ratio 1:3:4:7 add up to give a sum of 105. Find the value of the biggest number**

(a) 42

(b) 35

(c) 49

(d) 63

### Question. 8.

**If Rs. 58 is divided among 150 children such that each girl and each boy gets 25 p and 50 p respectively. Then how many girls are there?**

(a) 52

(b) 54

(c) 68

(d) 62

## Solutions:

#### Ans 1. (c)

SolutionsLet water is x4 x : x = milk : water

32: 8 = 4x : x (since total 40 liters)

#### Ans 2.(c)

Let numbers are

x : 2x : 3x also it is given that

6x = 36, x = 6x : 2x : 3x also it is given that

6 : 12 : 18

Ratio of squares 36 : 144 : 324: or also 1 : 4 : 9

#### Ans 3.(c)

Let number are 3x and 4x3x 4x =HCF ✕ 180

Clearly, HCF will be x

12x² = x 180, x = 15

Number will be 45:60

Note: if there are two number

Expenditures are 5y:3y

Then

3x–5y = 1000 …..(i) also

2x–3y = 1000 …..(ii)

from (i) and (ii) we get

6x-10y = 2000

+6x-9y = 3000

-y =-1000

y=1000, x= 2000

A's income is 6000

2x+20 : 3x+20 : 5x + 20 = 4 : 5 : 7

x = 10

20:30:50 = 2:3:5 and after adding 20

40:50:70

12x² = x 180, x = 15

Number will be 45:60

Note: if there are two number

#### Ans 4.(c)

Let incomes are 3x:2xExpenditures are 5y:3y

Then

3x–5y = 1000 …..(i) also

2x–3y = 1000 …..(ii)

from (i) and (ii) we get

6x-10y = 2000

+6x-9y = 3000

-y =-1000

y=1000, x= 2000

A's income is 6000

#### Ans 5.(c)

let students are 2x: 3r: 5x now According to the given condition2x+20 : 3x+20 : 5x + 20 = 4 : 5 : 7

x = 10

20:30:50 = 2:3:5 and after adding 20

40:50:70

#### Ans 6. (a)

x-y = 10 ……(i)

x:y = 5:3 ……(ii)

x:y = 5t:3t ……(iii)

according to (i) and (iii)

5t-3t = 10

2t = 10, t = 5

x = 25, y = 15

Product of two numbers = 375

re four numbers also

x + 3x + 4x + 7x = 105

15x = 105, x = 7, 7r = 49

0.25x + 0.5 = 58 ….(i)

also

x + y = 150 ….(ii)

from (i) and (ii) we get

0.5x + y = 116

x + y = 150

So, 0.5x = 34, x = 68, y = 82

x:y = 5:3 ……(ii)

x:y = 5t:3t ……(iii)

according to (i) and (iii)

5t-3t = 10

2t = 10, t = 5

x = 25, y = 15

Product of two numbers = 375

#### Ans 7.(c)

x : 3x : 4x : 7xre four numbers also

x + 3x + 4x + 7x = 105

15x = 105, x = 7, 7r = 49

#### Ans 8.(c)

Let the number of girls and boys are x and y then0.25x + 0.5 = 58 ….(i)

also

x + y = 150 ….(ii)

from (i) and (ii) we get

0.5x + y = 116

x + y = 150

So, 0.5x = 34, x = 68, y = 82

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