# How To Solve Ratio And Proportion Questions Quickly

## How To Solve Ratio And Proportion Question

#### Ratio

In some situations, the comparison by a division process makes good sense when compared to performing their difference. Therefore, the comparison of two quantities by the process of division method is called as ‘Ratio’ between two numbers. The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things. The sign used to denote a ratio is ‘:’.

#### Proportion

Ratio and proportions are said to be faces of the same coin. When two ratios are equal in value, then they are said to be in proportion. In simple words, it compares two ratios. Proportions are denoted by the symbol  ‘::’ or ‘=’.

## How To Solve Compound Ratio Based On Individual Ratios

### Question 1.

Find the compound ratio of (9 : 10), (11 : 13), (15 : 19).

A. 156:157
B. 297:494
C. 221:431
D. 1:5

#### Solution:

If we compound two or more ratio, then, a : b and c : d will become ac:bd.

Therefore, (9 : 10), (11 : 13), (15 : 19) = 9/10 * 11/13 * 15/19 = 1485/2470

= 297/494

### Question 2.

Find the composite ratio of 2 : 3, 3 : 5, 5 : 7.

A. 11 : 24
B. 2 : 7
C. 14 : 23
D. 24 : 97

#### Solution:

The composite ratio is intended by 2/3 * 3/5 * 5/7 = 30/105

= 2/7

### Question 3.

Find the compounded ratio of (3 : 7), (9:5), and (11:21)

A. 99:245
B. 13:17
C. 114:221
D. 305:711

#### Solution:

If we compound two or more ratio, then, a : b and c : d will become ac:bd.

Therefore, (3 : 7), (9:5), and (11:21)= 3/7 * 9/5 * 11/21 = 297/735 = 99/245

## How To Solve- Distributing Any Quantity Based On Ratios

### Question 4.

If Rs. 450 is divided among three people in the ratio 1/3 : 3/5 : 5/7, then find how much the second person will get?

A. 150
B. 126
C. 50
D. 180

#### Solution:

Given ration = 1/3 : 3/5 : 5/7 = 35 : 21 : 15

Therefore, the second person will get, 21/75 * 450 = 126

### Question 5.

Rs. 27440 is divided among 5 females, 3 men, and 1 child. The ratio of each woman, man, and kid, are 9 : 3 : 2. What is the child’s share?

A. 550
B. 760
C. 980
D. 952

#### Solution:

Given, the ratio of females, males, and toddlers = 9 : 3 : 2

No. of females, men, and child are 5, 3, 1
Thus actual ratio of females, men, and child = 9 * 5 : 3 * 3 : 2 * 1 = 45 : 9 : 2
Therefore, part of child = (2/56) * 27440 = Rs. 980

### Question 6.

An amount of Rs. 58666 is divided among three employees in the ratio of 1/17, 1/19, and 1/21. Find the smallest share.

A. 17561.7
B. 17200.49
C. 17000
D. 11760.50

#### Solution:

Given, three shares = 1/17, 1/19, 1/21.

Therefore, the ratio will be 399/6783, 357/6783, 323/6783

Thus, the ratio is 399 : 357 : 323

The smallest share = 58666*323/1079

= 17561.7

## How To Solve Ratio and Proportions Questions- Coins Based Ratio Problems

### Question 7.

Sahil got old currencies from his cupboard worth Rs. 450 in the denomination of 2 paisa, 5 paisa, and 50 paisa in ratio 5 : 4 : 3. How many 2 paisa coins he got.

A. 1200
B. 1250
C. 1100
D. 1220

#### Solution:

Let the number of 2 paisa coins be 5x

Let the number of 5 paisa coins be 4x

Let the number of 50 paisa coins be 3x

Then, 2*5x/100 + 5*4x/100 + 50*3x/100 = 180x/100

Given, 180x/100 = 450

Therefore, 450*100/180 = x

x = 250

Hence, 2paisa coins = 5 * 250 = 1250

### Question 8.

A person has 180 rupees in the denomination of 5paisa, 10paisa, and 25paisa in ratio 5 : 3 : 1. Calculate how many 25 paisa coins he has.

A. 225
B. 200
C. 350
D. 300

Solution:

Let the number of 5 paisa coins be 5x

Let the number of 10 paisa coins be 3x

Let the number of 25 paisa coins be x

Then, 5*5x/100 + 10*3x/100 + 25x/100 = 80x/100

Given, 80x/100 = 180

Therefore, 180*100/80 = x

x = 225

Hence, 25 paisa coins = 1*225 = 225 coins

### Question 9.

Harish has 1500 rupees in the denomination of 5 paisa, 25 paisa, and 50 paisa in ratio 5 : 3 : 2. Calculate how many 25 paisa coins he has.

A.2800
B.2000
C.2500
D.2250

#### Solution:

Let the number of 5 paisa coins be 5x

Let the number of 25 paisa coins be 3x

Let the number of 1 rupee coins be 2x

Then, 5*5x/100 + 25*3x/100 + 50 * 2x/100 = 200x/100

Given, 200x/100 = 1500

Therefore, 1500*100/200 = x

x = 750

Hence, 25 paisa coins = 3*750 = 2250

## How To Solve Mixtures & Addition Based Ratio Problems

### Question 10.

Chetan and Shaheen’s salaries are in the ratio 5 : 9. If both of their salaries are raised by Rs. 4200, then the proportion changes to 22 : 27. Find Shaheen’s salary.

A. 9250.95
B. 8058.32
C. 7199.97
D. 13580.45

#### Solution:

Let Chetan and Shaheen’s salaries be 5x and 9x

Given, 5x + 4200 / 9x + 4200 = 22/27

135x + 113400 = 198x + 92400

63x = 21000

x = 333.33

Therefore, Shaheen’s salary = 333.33 * 9 + 4200 = 7199.97

### Question 11.

Salaries of Preeti and Bina are in the ratio 14 : 15. If both get an increment of Rs. 5300, the new ratio becomes 33 : 35. What is Preeti’s salary?

A. 24000
B. 34980
C. 30100
D. 10200

#### Solution:

Let Preeti’s salary be 14x, and Bina’s salary be 15x

Given, 14x + 5300 = 33

Given, 15x + 5300 = 35

= 14x + 5300/15x + 5300 = 33/35

= 490x + 185500 = 495x + 174900

5x = 10600

x = 2120

Therefore, Preeti’s salary = 14 * 2120 + 5300 = 34980

### Question 12.

400 g of 25% sugar syrup was added to 600 g of 40% sugar syrup. Find the percentage of the syrup in the mixture.

A. 22%
B. 34%
C. 31%
D. 38%

#### Solution:

Amount of sugar syrup in mixture 1 = 25/100*400= 100

Amount of sugar syrup in mixture 2 = 40/100*600 = 240

The total amount of sugar syrup = 340

Percentage of sugar syrup in the mixture = 340 * 100/ 1000 = 34%

Read Also: Formula for Ratio And Proportion Questions 