How To Solve Ratio And Proportion Questions Quickly

How to Solve Ratio And Proportion Quickly – 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

Distributing Any Quantity Based On Ratios

Question 4.

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 5.

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

Coins Based Ratio Problems

Question 6.

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 7.

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 8.

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 Ratio And Proportion Quickly – Mixtures & Addition Based Ratio Problems

Question 9.

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 10.

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 11.

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%