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

Correct answer B

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

Correct answer B

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

Correct answer A

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

Correct answer B

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

Correct answer C

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

Correct answer A

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

Correct answer B

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

Correct answer A

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

Correct answer D

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

Correct answer C

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

Correct answer B

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%

Correct answer B

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

how to solve ratio and proportions questions quickly

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