Tricks To Solve Ratio and Proportion

Ratio and Proportion is one of the most important chapters in quant. In each bank exam (preliminary and mains) around 1 to 2 questions has been seen.  If you are aware about basic ideas, tricks and short cuts of ratio and proportion you can easily solve the problems within a few seconds.

Ratio, Proportion form an interesting part . The basic fundamentals of ratio and proportion are extensively used in solving many questions in chapters like time and work, time and distance ,DI etc. You are likely to get a few questions in the actual exams, based on these concepts.

Ratio is the comparison between two quantities of the same kind of units,different kinds can not be compared. The ratio of a and b is expressed as a : b or a/b.

Types of Ratios:-
There are various types of ratios, which are explained below

1. Duplicate Ratio:-  
If two numbers are in ratio, then the ratio of these two numbers squares is called duplicate ratio. 
If a and b are such two numbers, then the duplicate ratio of a and b = a² : b²

For example Duplicate ratio of 5:4=5²:4² = 25:16

2. Sub-duplicate Ratio:- 
If two numbers are in ratio, then the ratio of these two numbers square roots is called sub-duplicate ratio. 
If a and b are the two numbers, then the sub-duplicate ratio of a and b =  √a : √b

For example Sub-duplicate ratio of 5 : 3 is = √5:√3.

3. Triplicate Ratio:- 
If two numbers are in ratio, then the ratio of these two numbers cubes is called triplicate ratio. 
If a and b are the two numbers, then the triplicate ratio of a and b = a³ : b³.

For example Triplicate ratio of 2:5=2³:5³ = 8:125

4. Sub-triplicate Ratio:-
If two numbers are in ratio, then the ratio of these two numbers cube roots is called sub-triplicate ratio. 
If a and b are the two numbers, then the sub-triplicate ratio of a and b = ³√a : ³√b

For example Sub-triplicate ratio of 8 :125 = ³√8:³√125 = 2 : 5

5. Inverse Ratio:- 
If two numbers are in ratio and their antecedent and consequent are interchanged, then it is called inverse ratio .
If a and b are two numbers and their ratio is a:b then its inverse ratio will be b :a

For example Inverse ratio of 7:5 is 5:7.

Ratio and Proportion questions are asked in SBI Clerk Pre, IBPS Clerk Pre, IBPS RRB Pre, IBPS RRB Office Assistant Pre, IBPS RRB Scale 1 Pre, IBPS RRB Office Assistant Mains, IBPS RRB Scale 1 Mains, IBPS PO Pre, IBPS SO Pre, IBPS PO, SBI PO Pre, SBI SO Pre, SBI PO, LIC, NIACL, OICAL, SSC CGL,SSC CHSL, MAT, NIFT, CTET etc.

1. Question
If A : B = 3 : 7 and B : C = 4 : 1 ,then find A : B : C .
A) 9 : 28 : 5
B) 6 : 28 : 3
C) 12 : 28 : 7
D) 15 : 28 : 9
E) None of these
Answer :- C
Explanation :-
A : B = 3 : 7  ——-(×4)   = 12 : 28
B : C = 4 : 1  ——-(×7 )  = 28 : 7
A : B : C = 12 : 28 : 7

2.Question
If A : B = 1 : 2 , B : C = 4 : 3 and C : D = 6 : 7 ,then find  A : D. 
A) 4 : 7
B) 6 : 49
C) 2 : 7
D) 8 : 7
E) None of these
Answer:- A
Tricks :-
A/D = A/B × B/C × C/D
       = 1/2 × 4/3 × 6/7
       = 4 : 7

3. Question
Calculate the third proportional to 72 and 48.
A) 5
B) 32
C) 6
D) 9
E) 12
Answer :- B
Explanation :-
Let, Third proportional be = x
       72 : 48 = 48 : x
=>  72/48 = 48/x
=> x = 48×48/72
=> x = 32
Tricks :-
x = (48×48)/72 = 32  ( If A : B = B : C ,then C = B²/C)

4.Question
Calculate the fourth proportional to 85 , 17 and 25 .
A) 5
B) 12  
C) 6
D) 18
E) None of these
Answer :- A
Explanation :-
Let,fourth proportional = x
     85 : 17 = 25 : x
=>  85/17 = 25/ x
=>  85x = 25×17
=> x = (25×17)/85
=> x = 5

Tricks :-
If , a : b = c : d ,then d = bc/a
Here, x = (17×25)/85 = 5

5.Question
Find out the mean proportional between 27 and 75 .
A) 81
B) 3
C) 6
D) 45
E) None of these

Answer :- D
Explanation :-
Let, mean proportional = X
Then, 
   27 : X = X : 75
=> 27/X = X /75
=> X² = 75 × 27
=> X = √(75×27)
X = 45

Tricks :-
If a : X = X : b then mean proportional,X = √ab
Here, X = √(75×27)
         X = 45

6. Question
Find out the duplicate ratio of 9 : 11 .
A) 81 : 121
B) 121 : 81
C) 18 : 22
D) 729 : 1331
E) None of these
Answer :- A
Explanation :- 
Duplicate ratio of 9 : 11 = 9² : 11² 
                                        = 81 : 121

7. Question
what will be the sub- duplicate ratio of 400 : 9 ?
A) 800 : 18
B) 160000 : 81
C) 20 : 3
D) 3 : 20
E) None of these
Answer :- C
Explanation :-
Sub – duplicate ratio of 400 : 9 = √ 400 : √ 9
                                                   = 20 : 3

8. Question
What will be the triplicate ratio of 6 : 11 ?
A) 216 : 1331
B) 1331 : 216
C) 36 : 121
D) 121 : 36
E) None of these
Answer :-A
Explanation :-
Triplicate ratio of 6 : 11 = 6³ : 11³
                                        = 216 : 1331

9.Question
Find the subtriplicate ratio of 1331: 125 .
A) 121 : 25
B) 11 : 5
C) 7 : 10
D) 5 : 11
E) None of these
Answer :- B
Explanation :-
Sub – triplicate ratio of 1331 : 125 

= ³√1331 : ³√125

 = 11 : 5

10. Question
If P : Q = Q : R ,then what will be the ratio of P⁴ : Q⁴ ?
A) P² : R²
B) PR : Q²
C) Q² : PR
D) R² : P²
E) None of these

Answer :-A
Explanation :-
       P : Q = Q : R
=> P/Q = Q/R
=> Q² = PR
:. Q⁴ = P²R²
Now,  P⁴ : Q⁴ = P⁴ : P²R²
                      = P² : R²

11. Question

The ratio of tin and copper in a metal is 13 : 7. How much tin will be there in 220 kg of such a metal?
A) 120 kg
B) 135 kg
C) 155 kg
D) 143 kg
E) 160 kg
Correct Option: D
Tricks :-
Amount of tin=  (220 × 13/20 )kg = 143 kg.

Hence, option D is correct.

12.Question
In a private school the ratio of number of boys and girls  of 720 students is 11 : 7. How many more girls should be joined to the School to make the ratio 1 : 1? 
A) 160
B) 100
C) 120
D) 150
E) 170

Correct Option: A
Explanation :-
Number of boys = (720 × 11/18) = 440

Number of girls= (720 – 440) = 280

∴   Number of girls to be joined = (440 – 280) = 160.

Hence, option A is correct.

13.Question

In a factory, the ratio of boys to women is 7 : 5. If there are 240 workers in the factory, then how many women are there?
A) 50
B) 70
C) 80
D) 100
E) 90

Correct Option: D
Explanation :-
Let the number of boys and women are 7x and 5x, respectively.

Given, total number of workers= 240

⇒ 7x + 5x = 240 ⇒  12x = 240

∴   x = 20

∴    Required number of women = 5x = 5 × 20= 100.

Hence, option D is correct.

Tricks :-
(7 + 5) = 12 unit ——-> 240
                 1 unit ——–> 20
Thus, number of women = 5 × 20 = 100   

14.Question
Zinc and bronze are in the ratio 5 : 3 in 800 gm of an alloy. How much of zinc (in grams) should be added to make the ratio 7 : 3?
A) 150
B) 60
C) 70
D) 200
E) 250

Answer :- D
Explanation :-
Zinc = 5/8 × 800 = 500 gm
Bronze = 800 – 500 = 300 gm
Let, zinc should be added x gm.
(500 + x)/300 = 7/3
=> 1500 + 3x = 2100
=> 3x = 600
:. x = 200 gm
Thus, the required zinc = 200 gm

Tricks :-
8 unit = 800
1 unit = 100
Zinc should be added (7-5) = 2 unit = 2 × 100 
= 200 gm

15.Question
70 percent of a number is equal to 30 percent of another number. What is the respective ratio of these two numbers?

A) 3 : 7
B) 21 : 31
C) 7 : 10
D) 12 : 13
E) Can’t be determined

Correct Option: A
Explanation :-

Let, the first number = x 
and the second number = y.

According to the question,

70% of x = 30% of y   
⇒   70/100 * x = 30/100 * y
=> x/y = 30/70
So, required ratio = x : y = 3 : 7

Hence, option A is correct.

Tricks :-
   70% * 1st number = 30% * 2nd number
=> 1st number : 2nd number = 30 : 70 = 3 : 7          

16.Question

What must be added to each term of the ratio 3 : 5 so that it may equal to 5 : 7 ?
A) 5
B) 8
C) 3
D) 2
E) 7

Correct Option: D
Explanation :-
Let’s the added number = x. 
Then,

     (3 +x) /(5 + x) = 5/7
⇒ 21 + 7x = 25 + 5x
=> 2x = 4
=> x = 2
Required number = x = 2

Hence, option D is correct.

17. Question
Syrup is 15 times as heavy as water and alcohol is 7 times as heavy as water in what ratio should these  be mixed to get an alloy 10 times as heavy as water?
A) 2 : 5
B) 3 : 5
C) 1 : 3
D) 2 : 7
E) None of these

Correct Option: B
Tricks:-

Syrup = 15 water
Alcohol = 7 water
By allegation –

15       7
 \   /  
   10    
 /   \  
3       5

⇒ 3 : 5

Hence, option B is correct 

18. Question

The ratio of the two numbers is 7 : 4 and their sum is 440. Find the greatest number.

(A) 170

(B) 200

(C) 245

(D) 280

Answer :- D
Explanation :-
Let, the numbers are 7x and 4x.
According to the question,
7x + 4x = 440
=> 11x = 440
=> x = 40
Thus,the greatest number = 7×40 = 280

Tricks :-
(7+4) =11 units —-> 440
              1    ———–> 40
            :. 7   ———–> 40×7 = 280

19.Question
The ratio of the two numbers is 11 : 6 and their sum is 850. Find the smallest number.

(A) 170

(B) 200

(C) 245

(D) 300

(E) None of these 

Answer :- D
Explanation :-
Let, the numbers are 11x and 6x.
According to the question,
11x + 6x = 850
=> 17x = 850
=> x = 50
Thus,the smallest number = 6×50 = 300

Tricks :-
(11+6) =17 units —-> 850
              1    ———–> 50
            :. 6   ———–> 50×6 = 300

20.Question
Five books and four pens cost as much as three books and nine pens. Find the ratio of the cost of one book to that of one pen .

(A) 3 : 2

(B) 5 : 3

(C) 5 : 2

(D) 1 : 3

(E) None of these

Answer :- C
Explanation :-
Let, cost of one book = x
       Cost of one pen = y
According to the question,
     5x + 4y = 3x + 9y
=> 2x = 5y
=> x : y = 5 : 2
Thus ,the required ratio is = 5 : 2

21.Question
The speeds of three bikes are in the ratio 6 : 4 : 5 . Find the ratio between the times taken by them to cover the same distance .

(A) 5 : 4 : 6

(B) 6 : 4 : 5

(C) 10 : 15 : 12

(D) 12 : 15 : 10

(E) None of these

Answer:-C
Explanation :-
Speed ratio = 6 : 4 : 5
We know, speed and time are inversely proportional .

Time ratio = 1/6 : 1/4 : 1/5    (LCM of 6 , 4 & 5 = 60)
                  = 60/6 : 60/4 : 60/5
                  = 10 : 15 : 12

22.Question

A and B two numbers are respectively 25% and 50% more than a third number C. Find the ratio of A and B.

A) 3 : 5
B) 2 : 5
C) 4 : 5 
D) 5 : 6
E) 5 : 4

Answer: D
Explanation:

Let the third number be x.

Then, A= 125% of x =125x/100 = 5x/4

B =150% of x = 150x/100 = 3x/2

A : B = 5x/4 : 3x/2 = 5x : 6x = 5 : 6

23.Question
There are Rs 840 consisting of Rs 1, 50 paise, 25 paise and 10 paisa coins. The ratio of their numbers in that order is 5 : 4 :2 : 9. Find the number of 50 paisa coins.

(a) 200
(b) 115 
(c) 400
(d) 500
(e) None of these

Answer :- C
Explanation:-

Let the number of coins of Rs 1, 50 paise , 25 paise 
and 10 paisa be 5x, 4x 2x and 9x respectively.

According to the question, 
(1) (5x) + (0.50)(4x) + (0.25)(2x) + (.10)(9x)= 840
=> 5x + 2x + x/2 + 9x/10 = 840
=> 50x + 20x + 5x + 9x = 840 × 10       [ Multiplied both sides by 10]
=> 84x = 840 × 10
=> x = 100

Therefore, number of coins of 50 paisa 
= 4x   = 4 × 100  = 400

24. Question
A thief took 5 leaps for every 4 leaps of a police but 3 leaps of the police were equal to 4 leaps of the thief. What is the ratio of the speeds of the thief to that of the police?
A) 15 : 16
B) 16 : 15
C) 9 : 17
D) 12 : 13
E) None of these

Answer :-A
Tricks:-

 4 leaps of thief = 3 leaps of police
=> 1 leap of thief = 3/4 leaps of police
Now, required ratio of speed 
= ( 5 × thief’s leap) : ( 4 × police’s leap)
= (5 ×3/4 police’s leap) : ( 4 × police’s leap)
= 15 : 16          

25. Question
In an IT company, the ratio of the numbers of employees of three types P, Q and R is 9:13:18 and their wages are in the ratio of 10: 7:4. If number of employees of type R is 54 and wages of every employee of type Q is 1400, then find the total wages of all the employees of type P.

(a) Rs 52000

(b) Rs 53000

(c) Rs 54000

(d) Rs 56000

(e) Rs 60000

Answer :-C
Explanation :-
Let,
Number of P’s employees = 9x
                   Q’s employees = 13x
                   R’s employees = 18x
Now, According to the question
18x = 54
=> x = 3
the number of employees of type P 
= 9×3 = 27
the wages of every employees in P
= 1400× 10/7 
= 2000 Rs.
Thus ,the required total wages = 27×2000 = 54000