**Mixtures and Alligations and problems based on Numbers**

**1). In a mixture of 60 L the ratio of acid and water is 2: 1. If the ratio of acid and water is to be 1:2, then what is the amount of water (in litres) to be added to the mixture?**

a) 55

b) 60

c) 50

d) 45

e) None of these

**2). In what proportion must grocer mix wheat at Rs.2.04 per kg and Rs. 2.88 per kg so as to make a mixture of worth Rs. 2.52 per kg?**

a) 2:3

b) 3:2

c) 5:3

d) 3:4

e) None of these

**3). A container has 40 litres of wine. From this container, 4 litres of wine is taken out and replaced with water. This process is repeated two more times. What will be the final quantity of water (in litres) in the container?**

a) 12

b) 10.84

c) 29.16

d) 28

e) None of these

**4). Vikram has some cows and some ducks. If the total number of heads is 90 and the total number of feet is 248, what is the total number of cows?**

a) 56

b) 42

c) 34

d) 48

e) None of these

**5). An alloy of zinc and tin contains 35% of zinc by weight. What quantity of zinc must be added to 400 lb of this alloy such that there is 60% of zinc by weight in the final mixture?**

a) 400 lb

b) 350 lb

c) 250 lb

d) 450 lb

e) None of these

**6). When the digits of a two-digit number are interchanged, the number obtained is less than the original number by 36. What is the original number if the difference of the two digits is 4?**

a) 84

b) 51

c) 73

d) Cannot be determined

e) None of these

**7). The product of two successive numbers is 3422. Which is the smaller of the two numbers?**

a) 68

b) 46

c) 58

d) 59

e) None of these

**8). The sum of five consecutive even numbers is 380. What is the sum of largest and smallest number?**

a) 152

b) 132

c) 150

d) 164

e) None of these

**9). Out of three given numbers, the first number is twice the second and thrice the third. If the average of these three numbers is 154, then what is the difference between the first and the third numbers?**

a) 126

b) 42

c) 168

d) 52

e) None of these

**10). If five times of a positive integer is equal to three less than twice the square of that number than find the number?**

a) 33

b) 23

c) 13

d) 3

e) None of these

**Answers:**

**1)b 2)d 3)b 4)c 5)c 6)d 7)c 8)a 9)c 10)d**

__Explanation:__**1). B)**

Quantity of acid in the mixture = (2/3) × 60 = 40L

∴ the quantity of water in the mixture = 60 – 40 = 20 L

The required quantity of water added to the mixture is,

40/ (20 + x) = 1/2

x = 60 L

**2). D)**

∴ Required ratio = 0.36 : 0.48 = 3: 4

**3). B)**

Final Qty of wine = starting Qty of container [1- Qty of wine withdrawn/ starting Qty of container] ^ no.of times

= 40[1- 4/40]

^{3}= 29.16 L

^{}∴ final Qty of water = 40 – 29.16 = 10.84 L.

**4). C)**

The total no.of headsè C + D = 90

The total no.of feet è 4C + 2D = 248

Hence, the total no.of cows, C = 34

**5). C)**

Q1 : Q2 = 8: 5

èQ1/Q2 = 8/5è 400 / Q2 = 8/5 = 250 lb

**6). D)**

Let the original numbers be XY

Hence, interchanged number is YX

According to the question,

èi) YX = XY – 36

èii) X ~ Y = 4

option a) 84è i) 84 -36 = 48 ii) 8-4 = 4

option b) 51èi) 51 -36 = 15 ii) 5-1 = 4

option c) 73èi) 73 -36 = 37 ii) 7-3 = 4

All are satisfying the above condition. So cannot be determined.

**7). C)**

X × (X + 1) = 3422

X

^{2}+ X – 3422 = 0X = 58, 59

∴ the smallest number is 58.

**8). A)**

X +(X + 2) + (X + 4) + (X + 6)+ (X+8)= 5X+ 20 = 380

è X= 72

∴ the sum of largest and smallest number is, 72 + 80 = 152

**9). C)**

Let the third number be, X

Then, the first number is, 3X

And second number is, 3X/2

è(x + 3x + (3x/2)) / 3 = 154è x = 84

∴ the difference between the first and the third numbers are, 3X – X = 2X

è 2 × 84 = 168

**10). D)**

Let the number be X,

5X= 2X

^{2}– 32X

^{2}– 5X- 3 =0∴ X= 3, – 1/2

Hence, required positive integer is 3.

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