Dear Readers, We all knew a famous saying of the Legend Aristotle,

**“Well begun is half done”**and we also knew that this statement is 100% true. To Crack the Bank Exams you need to know where to start and how to start. Now this is the absolute correct time to kick start the preparation for upcoming IBPS Exams. To help you in this aspect and to be a part of your preparation here we, IBPS Guide Team providing Topic wise Discussion on Quantitative Aptitude, this session will be conducted regularly on daily basis. This will provide a complete overview on the topics along with exercise questions. Kindly Make use of it.

__RATIO AND PROPORTION__

**Solved examples:**

**Type: 6**

**1). An amount of money to be divided between A, B and C in the ratio 2 : 3 : 5 respectively. If the amount received by C is Rs.6000/- more than the amount received by B. Then the total amount of money received by A and B together is**

**Solution:**

A : B : C = 2 : 3 : 5 and 5x – 3x = 6000 => x = 3000

A receives 3000 x 2 = 6000/- and B receives 3000 x 3 = 9000/-

Then total amount received by both A and B = 6000 + 9000 = Rs.15000/-

**Type: 7**

**2). The ratio of two numbers is 4: 5 when the first is increased by 20% and the second is decreased by 20%, the ratio of the resulting number is**

**Solution:**

Given ratio = 4 : 5 = 400 : 500

This increased by 20% => (400 + 80) : (500 : 100) = 480 : 600

This decreased by 20% => (480 – 96) : (600 – 120) = 384 : 480 = 4 : 5

**Type: 8**

**3). A started a business with a capital of Rs 1,00,000. One year later, B joined him with a capital of Rs 2,00,000. At the end of 3 years from the start of the business, the profit earned was 84,000. The share of B in the profit exceeded the share of A is**

**Solution:**

A’s investment = Rs 1,00,000 for 3 years

B’s investment = Rs 2,00,000 for 2 years

Ratio of profit share = 100000 x 3 : 200000 x 2 = 3 : 4

B’s share in profit = (4/7) x 84000 = 48000

A’s share in profit = 84000 – 48000 = 36000

Difference = 48000 – 36000 = 12000

**Type: 9**

**4). The monthly income of Sachin and Nitin are in the ratio of 4 : 3. Their monthly expenses are in the ratio of 3 : 2. However, both save 600/- per month. What is their total monthly income?**

**Solution:**

Difference between Income and Expenses is savings so 1 unit is 600/-

Then total monthly income is 7 x 600 = 4200

**Type: 10**

**5). In an examination, the number of those who passed and the number of those who failed were in the ratio 25:4. If five more had appeared and the number of failures was 2 less than earlier, the ratio of passers to failures would have been 22:3. The number of students who appeared at the examination, is**

**Solution:**

Ratio of Pass to fail = 25:4 = 25x : 4x

New ratio = 25x + 7 : 4x -2 = 22 : 3

No of students passed increased by 7 because 5 more appeared and 2 less failed.

75x + 21 = 88x – 44

13x = 65

x = 5

No of students appeared initially = 25x + 4x = 25 x 5 + 4 x 5 = 125 + 20 = 145

**More Types on Ratio& Proportion Problems will be discussed in the next Session, Kindly follow us daily.**

**Dear Aspirants, Here below we have given exercise questions on Ratio& Proportion based on the above types, solve these questions by yourself and comment your answers below. Correct Answers with explanation will be updated in the end of the day.**

__Exercise problems__**:**

**1). A sum of money is divided among P, Q, R and S in the ratio 3 : 5 : 7 : 11. If the share of R is Rs 5,004 more than the share of P, then what is the total amount of money of Q and S together?**

a) Rs 16,762

b) Rs 18,672

c) Rs 17,506

d) Rs 19,255

e) None of these

**2). Ramesh started a business with Rs.25,000. Kiresh joined him after 4 months with Rs.40,000. After 2 more months, Ramesh withdrew Rs.5,000 of his capital and 2 more months later, Kiresh brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?**

a) 27 : 40

b) 40 : 28

c) 12 : 17

d) 17 : 12

e) None of these

**3). A sum of money is divided between two people in the ratio of 4:7. If the share of one person is Rs 36 less than that of other, find the sum.**

a) Rs 118

b) Rs 154

c) Rs 146

d) Rs 132

e) None of these

**4). The monthly salaries of two persons are in the ratio of 3:7. If each receives an increase of Rs. 55 in the salary, the ratio is altered to 2:5. Find their respective salaries.**

a) 495 and 1155

b) 805 and 1405

c) 185 and 3085

d) 265 and 3565

e) None of these

**5). In business, X and Z invested amounts in the ratio 3:1, whereas the ratio between amounts invested by X and Y was 2:3, If Rs 89250 was their profit, how much amount did Y receive?**

a) Rs 48000

b) Rs 47000

c) Rs 47250

d) Rs 48450

e) None of these

**6). The doctors in three states are in the ratio 2: 4: 5. If 22 doctors are increased in each state the ratio changes to 4: 6: 7. What was the total number of doctors in the three states before the increases?**

a) 140

b) 121

c) 132

d) 100

e) Cannot be determined

**7). A, B and C start a business with each investing Rs 15,000. After 5 months A withdraws Rs 5000, B withdraws Rs 4000 and C invests Rs 6000 more. At the end of the year, a total profit of Rs 73698 was recorded. Find the share of A. (approx)**

a) 20600

b) 20700

c) 20500

d) 20400

e) 21600

**8). The income of Arun and Babu are in the ratio 5 : 3. The expenses of Arun, Babu and Chandru are in the ratio 8 : 5 : 2. If Chandru spends Rs 2000 and Babu saves Rs 700, then Arun saves?**

a) Rs 500

b) Rs 1000

c) Rs 1500

d) Rs 250

e) None of these

**9). Pari and David have together three times what David and Farhath have, while Pari, David, Farhath together have forty two rupees more than that of Pari. If David has 5 times that of Farhath, then Pari has ?**

a) Rs 60

b) Rs 91

c) Rs 77

d) Rs 49

e) Rs. 85

**10). The total marks obtained by Aravind in Science and Economics are 180. If the difference between his marks in Science and Economics subjects is 10, then the ratio between his marks in Science and Economics is….**

a) 7 : 18

b) 8 : 17

c) 9 : 18

d) 19 : 7

e) None of these

__Answers with Explanation:__**1). Answer: e)**

Let P, Q, R and S get money respectively is

3x, 5x, 7x, 11x.

Share of R is Rs. 5004 more than Share of P.

7x = 3x + 5004

4x = 5004

x = 1251.

Amount of Q = 5x = 5 *1251 = Rs. 6255.

Amount of S = 11x = 11 * 1251 = Rs. 13761.

Total amount of Q and S = 6255 + 13761 = Rs. 20016.

3x, 5x, 7x, 11x.

Share of R is Rs. 5004 more than Share of P.

7x = 3x + 5004

4x = 5004

x = 1251.

Amount of Q = 5x = 5 *1251 = Rs. 6255.

Amount of S = 11x = 11 * 1251 = Rs. 13761.

Total amount of Q and S = 6255 + 13761 = Rs. 20016.

**2). Answer: a)**

Ramesh invested 25000 for initial 6 months and 20000 for the next 6 months. Hence his term of ratio

= (25000 × 6 + 20000 × 6)

Kiresh invested Rs.40000 for 4 months and Rs.60000 for next 4 months. Hence his term of ratio

= (40000 × 4 + 60000 × 4)

Ramesh : Kiresh

=(25000 × 6 + 20000 × 6) : (40000 × 4 + 60000 × 4)

= (25 × 6 + 20 × 6) : (40 × 4 + 60 × 4)

= (25000 × 6 + 20000 × 6)

Kiresh invested Rs.40000 for 4 months and Rs.60000 for next 4 months. Hence his term of ratio

= (40000 × 4 + 60000 × 4)

Ramesh : Kiresh

=(25000 × 6 + 20000 × 6) : (40000 × 4 + 60000 × 4)

= (25 × 6 + 20 × 6) : (40 × 4 + 60 × 4)

= (25 × 3 + 20 × 3) : (40 × 2 : 60 × 2)

=135 : 200 = 27 : 40.

**3). Answer: d)**

Let the share of one person be x then the share of other person is x + 36.

It is given that,

It is given that,

x / (x + 36) = 4 : 7

7x = 4(x + 36)

7x = 4(x + 36)

7x = 4x + 144

3x = 144

x = 48

And (x + 36) = 48 + 36 = 84

And therefore the sum is 84 + 48 = Rs . 132

And (x + 36) = 48 + 36 = 84

And therefore the sum is 84 + 48 = Rs . 132

**4). Answer: a)**

Let the salaries be 3x and 7x

Therefore,

(3x + 55) / (7x+55) = 2 / 5

5 × (3x + 55) = 2 × (7x + 55)

15x + 275 = 14x + 110

x = 165

Therefore, their salaries are 3 × 165 and 7 × 165 i.e.,

**495**and**1155****5). Answer: c)**

X : Y = 2 : 3 = 6 : 9

X : Z = 3:1 = 6 : 2

X : Y : Z = 6 : 9 : 2

Y’s share = (9/17)*89250

= 47250

X : Z = 3:1 = 6 : 2

X : Y : Z = 6 : 9 : 2

Y’s share = (9/17)*89250

= 47250

**6). Answer: b)**

Let the number be 2x, 4x and 5x.

It is given that if 22 doctors in each state are increased then the ratio becomes 4: 6:7

It can written as (2x +22) : (4x +22) : (5x + 22) = 4 : 6 : 7

Taking the first two ratio

we have,

(2x +22) / (4x +22) = 4/6

6(2x +22) = 4(4x +22)

12x + 132 = 16x + 88

4x = 44

x =11

Therefore, the doctors in each state before the increase are 2×11, 4×11, 5×11 = 22, 44, 55

And total doctors = 121

It is given that if 22 doctors in each state are increased then the ratio becomes 4: 6:7

It can written as (2x +22) : (4x +22) : (5x + 22) = 4 : 6 : 7

Taking the first two ratio

we have,

(2x +22) / (4x +22) = 4/6

6(2x +22) = 4(4x +22)

12x + 132 = 16x + 88

4x = 44

x =11

Therefore, the doctors in each state before the increase are 2×11, 4×11, 5×11 = 22, 44, 55

And total doctors = 121

**7). Answer: a)**

A : B : C =(15000×5+10000×7):(15000×5+11000×7):(15000×5+21000×7)

=(15 × 5 +10 × 7):(15 × 5 +11 × 7): (15 × 5 + 21 × 7)

= 145 : 152 : 222

A’s share = 73698 × 145 / (145+152+222)

=(15 × 5 +10 × 7):(15 × 5 +11 × 7): (15 × 5 + 21 × 7)

= 145 : 152 : 222

A’s share = 73698 × 145 / (145+152+222)

= 73698 × 145 / 519 = 20590 ≈ 20600

**8). Answer: c)**

Ratio of incomes of Arun and Babu = 5 : 3 = 5x : 3x

Ratio of expenses of Arun, Babu and Chandru = 8y : 5y : 2y

Chandru’s expenditure = 2y = 2000

y = 1000

Therefore Arun’s expenditure = 8y = 8000

Given that Babu’s saving = 700

3x – 5y = 700

3x = 700 + 5000

3x = 5700

x = 1900

Arun’s income = 5x = 5 x 1900 = 9500

Arun’s saving = 9500 – 8000 = 1500

**9). Answer: b)**

Let Pari’s share = a

Let David’s share = b

Let Farhath’s share = c

a + b = 3(b + c) ——-(1)

a + b + c = 42 + a

Therefore, b + c = 42 ——-(2)

b = 5c ——–(3)

Substituting b + c = 40 from eqn 2 in eqn 1

a + b = 3(42)

Therefore, a + b = 126 ———-(4)

Substituting b = 5c from eqn 3 in eqn 2

5c + c = 42

c = 7

From (2), b = 42 – c = 42 – 7 = 35

a + b = 126

a + 35 = 126

a = 126 – 35 = 91

So a = 91, b = 35, c = 7

**10). Answer: e)**

Let S = Science, E – Economics

Total marks S + E= 180

Difference S – E = 10

(S+E)/(S-E)= 180/10 —— (1)

Adding 1 to both sides of equ 1:

2S/(S-E) = 19 ——- (2)

Subtracting 1 from both sides equ 1:

2E/ (S-E) = 17 ——– (3)

Dividing equ 2 by equ 3:

S/E = 19 / 17 => This is the desired ratio.

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