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**Ratio and proportion**

**1. The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of second to the third is 5 : 8 then the second number is?**

A. 20

B. 30

C. 38

D. 48

E. 52

**Correct option is : B**

**Solution:**

a:b= 2:3

b:c = 5:8

a:b:c =10 : 15 : 24

a+b+c = 98

49k = 98

k = 2

=> b = 15*2 = 30

**2. The total number of students in a school is 31700. If the ratio of boys to the girls in the school is 743:842 respectively, what is the total number of girls in the school?**

A. 14860

B. 16480

C. 15340

D. Cannot be determined

E. None of these

**Correct option is : B**

**Solution:**

Boys : Girls = 743 : 842

Total number of students = 31700

Number of girls = [842 / (743 +842)] × 31700

= (842 /1585) × 31700

= 16840

3. A sum of Rs. 221 is divided among X, Y and Z such that X gets Rs. 52 more than Y. Y gets Rs. 26 more than Z. The ratio of the shares of X , Y and Z respectively is

A. 9:5:3

B. 9:3:5

C. 5:9:3

D. 10:6:5

E. None of these

**Correct option is: A**

**Solution:**

221 is divided among X, Y and Z. Y gets Rs.(Z + 26)

X gets Rs. (Z + 26 + 52) = Rs. (Z + 78)

According to the question

Z + 78 + Z +26 + Z = 221

=> 3Z + 104 = 221

=> Z = 117/3

=> Z = 39

X = 39 + 78 = 117

Y = 39 + 26 = 65

Z = 39

117 : 65 : 39 = 9 : 5 : 3

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**4. The cost of making an article is divided between materials, labour and overheads in the ratio of 3:4:1. If the material cost Rs. 234, then the labour cost?**

A. Rs. 176

B. Rs 312

C. Rs. 78

D. Rs. 390

E. None of these

**Correct option is : B**

**Solution:**

Cost of making is divided among material :labour : overheads = 3: 4: 1

Total material cosy = Rs. 234

3x = 234

=> x = 78

=> Labor cost = 4 X 78 = Rs. 312

**< < Read More Static GK Article 2020 > >**

**5. In a school the number of boys and that of the girls are in the respective ratio of 2:3. If the number of boys is increased by 20% and that of girls is increased by 10%, what will be the new ratio of number of boys to that of the girls?**

A. 14:5

B. 5:8

C. 13:4

D. Data inadequate

E. 8:11

**Correct option is : E**

**Solution:**

Ratio of boys and girls in the school = 2:3

New, increased value = 2 * 120/100: 3 * 110/100= 240 : 330

=>24 : 33 = 8:11

**6. The ratio between two numbers is 2:3. If each numbers is increased by 4, the ratio between then become 5:7, the difference between numbers.**

A. 8

B. 6

C. 4

D. 2

E. None of these

**Correct option is : A**

**Solution:**

Ratio between two numbers = 2:3

Let x is the common factor between the ratio (2x + 4)/(3x + 4) = 5/7

=> 14x + 28 = 15x + 20

=> x = 8

=> Required difference = (3x-2x) = 8

**7. What number has to be added to each term of 4 : 7 to make the ratio 5 : 6?**

A. 13

B. 12

C. 10

D. 11

E. None of these

**Correct option is : D**

**Solution:**

Let the number to be added be x As per statement,

(4 + x) / (7 + x) = 5/6

Cross multiplying, we get 24 + 6x = 35 + 5x

6x – 5x = 35 – 24

x = 11

**8. In the 45 litres mixture of milk and water, the ratio of milk and water is 5 : 4. Find the quantity of water required to be added so that the resultant mixture will be in the ratio 4 : 5.**

A. 7.75 litres

B. 11.25 litres

C. 9.25 litres

D. 12.50 litres

E. None of these

**Correct option is : B**

**Solution:**

The ratio of milk and water is 5 : 4,

The total quantity is 45 litres.

9’s=45

=>1’s=5

So Milk=25, Water=20

25/(20+x)=4/5 (Here x is the quantity of water to be added)

=>x=11.25 litres

**9. Two natural numbers are in the ratio of 4 : 7 and their product is 112. Find both the numbers.**

A. 4 and 7

B. 8 and 14

C. 12 and 21

D. 16 and 28

E. None of these

**Correct option is : B**

**Solution:**

Let, Natural numbers are 4x and 7x, then

4x * 7x = 112

28x^{2} = 112

x^{2} = 4

=> x = 2

=> Numbers are 8 and 14

**10. The monthly income of A and B is in the ratio of 4 : 3 and their monthly expenditure is in the ratio of 3 : 2. If each of them saves Rs.6000 per month, the income of B is**

A. 12000

B. 24000

C. 18000

D. 36000

E. None of these

**Correct option is : C**

**Solution:**

Let Monthly income of A = 4x

And, Monthly income of B = 3x

Also, Monthly expenditure of A = 3y

And, Monthly expenditure of B = 2y

Since the both save Rs.6000 each per month,

Therefore, 4x – 3y = 6000

Also, 3x – 2y = 6000

By solving the equations, we get,

x = 6000 and y = 6000

=> Monthly income of B = 3x = 3 * 6000 = Rs.18000