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 Ratios and Proportions Questions

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FACTS  AND  FORMULAE  FOR  RATIO  AND  PROPORTION  QUESTIONS

 

 

1. RATIO: The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a:b.

In the ratio a:b, we call a as the first term or antecedent and b, the second term or consequent.

Ex. The ratio 5: 9 represents 5/9 with antecedent = 5, consequent = 9.

Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio. Ex. 4: 5 = 8: 10 = 12: 15 etc. Also, 4: 6 = 2: 3.

 

2. PROPORTION : The equality of two ratios is called proportion. 

If a: b = c: d, we write, a: b :: c : d and we say that a, b, c, d are in proportion . Here a and d are called extremes, while b and c are called mean terms.

Product of means = Product of extremes.

Thus, a: b :: c : d <=> (b x c) = (a x d).

 

 3. (i) Fourth Proportional : If a : b = c: d, then d is called the fourth proportional to a, b, c.

     (ii) Third Proportional : If a: b = b: c, then c is called the third proportional to a and b.

     (iii) Mean Proportional : Mean proportional between a and b is ab

 

 4. (i) COMPARISON OF RATIOS : We say that (a: b) > (c: d) ⇔ (a/b)>(c /d).

     (ii) COMPOUNDED RATIO : The compounded ratio of the ratios (a: b), (c: d), (e : f)  is    (ace: bdf)

 

5. (i) Duplicate ratio of (a : b) is a2:b2.

    (ii) Sub-duplicate ratio of (a : b) is (√a : √b).

    (iii)Triplicate ratio of (a : b) is a3:b3.

    (iv) Sub-triplicate ratio of (a : b) is a13: b13.

    (V) If ab=cd, thena+ba-b=c+dc-d (Componendo and dividendo)

 

 6. VARIATION:

(i) We say that x is directly proportional to y, if x = ky for some constant k and we write, x∝y

(ii) We say that x is inversely proportional to y, if xy = k for some constant k and we write, x∝1y

Q:

What is the equivalent compound ratio of 5:6::7:10::6:5  ?

A) 7 : 9 B) 9 : 7
C) 7 : 4 D) 7 : 10
 
Answer & Explanation Answer: D) 7 : 10

Explanation:

Given 5:6 :: 7:10 :: 6:5

We know that compound ratio is calculated as
a:b :: c:d :: e:f
(axcxe):(bxdxf)

=> (5x7x6):(6x10x5)
=> (210):(300)
= 7:10

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11 7208
Q:

In the following question, select the related number from the given alternatives.

8 : 27 : : 64 : ?

A) 190 B) 144
C) 125 D) 72
 
Answer & Explanation Answer: C) 125

Explanation:
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0 7030
Q:

At a casino in mumbai, there are three tables A, B and C. The payoffs at A is 10:1, at B is 20:1 and at C is 30:1. If a man bets Rs 200 at each table and win at two of the tables, what is the maximum and minimum difference between his earnings can be?

A) Rs.2500 B) Rs.2000
C) Rs.4000 D) None of these
 
Answer & Explanation Answer: C) Rs.4000

Explanation:

Maximum earning will be only when he will won on the maximum yielding table.

     A ----> 10:1

     B ----> 20:1

     C ----> 30:1

 i.e, he won on B and C but lost on A

 20 x 200 + 30 x 200 -1 x 200 = 9800

 minimum earning will be when he won on  table A and B and lose on that table 3.

 

Therefore, 10 x 200 + 20 x 200 - 1 x 200  =  6000-200 = 5800

Therefore, Difference= 9800 - 5800 = 4000

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12 6810
Q:

Rs. 7444 is divided among 5 ladies, 3 gents and 3 girls. The ratio of share of a lady, a gents and a girl is 7: 4: 3. What is the share of gents ?

A) Rs. 1595.14 B) Rs. 1793.4
C) Rs. 595.14 D) Rs. 1551.5
 
Answer & Explanation Answer: A) Rs. 1595.14

Explanation:

Ratio of the share of a lady, a gents and a girl is 7 : 4 : 3
No of ladies, gents and girls are 5, 3, 3
Thus effective ratio of ladies, gents and girls is 7 x 5 : 4 x 3 : 3 x 3 = 35 : 12 : 9
so part of gents = (12/56) x 7444 = Rs. 1595.142
so part of 1 gents = 1595.142/3 = Rs. 531.71.

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9 6675
Q:

Out of 135 applicants for a post, 60 are graduates and 80 have experience. What is the ratio of minimum to maximum number
of graduates having experience?

A) 12:1 B) 5:1
C) 1:5 D) 1:12
 
Answer & Explanation Answer: D) 1:12

Explanation:

Given total applicants = 135
Given graduates are G=60
Otherthan graduates=135-60 = 75
Given experienced candidates = 80
1) For maximum number of graduates have experience
    Total graduates to have experience = 60

2) For minimum number of graduates have experience
    Remaining after taking other than graduates in experience= 80-75 = 5

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13 6503
Q:

6 pumps of kirlosker can fill a tank in 7 days and 2 similar pumps of USHA can fill the same tank in 18 days. what is the ratio of the efficiency of a kirlosker pump and a USHA pump?

A) 6:7 B) 7:6
C) 7:54 D) None of these
 
Answer & Explanation Answer: A) 6:7

Explanation:

The number of days required by a single kirlosker pump to fill the tank = 6 x 7 =42 days and the number of days required by a single USHA pump to fill the same tank = 2 x 18 =36 days.

Now , since efficiency is inversely proportional to the number of days. Hence,

Efficiency of one K - pumpEfficiency of U- pump=3642=67  

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7 6468
Q:

A company requires 12,100 strength. Present employees are 400 ladies and 6400 gents. To reach the target how many ladies required to maintain the same ratio ?

A) 400 B) 600
C) 900 D) 700
 
Answer & Explanation Answer: C) 900

Explanation:

6,400 gents, 2400 ladies in that company.
So total 8,800employees.
for 8,800 employees, we want 2400 ladies.
for 12,100employees we want how many ladies ?
=> (12,100/8,800) x 2400 = 3300.
So we want 3300 - 2400 = 900 more ladies.

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11 6458
Q:

Two vessel P and Q contain milk and water in ratio 3 : 2 and 5 : 3 respectively. If 10 liters of the mixture is removed from vessels P and poured in vessel Q then ratio of milk to water in vessel Q becomes 8 : 5. Find the initial quantity of water in vessel Q.

A) 10 lit B) 6 lit
C) 16 lit D) 12 lit
 
Answer & Explanation Answer: A) 10 lit

Explanation:

Given ratio of initial mixture of milk and water in Q = 5 : 3

Let the initial quantity of mixture in vessel Q = 8x

Let quantity of Milk = 5x and

Let quantity of water = 3x

According to the question,

5x + 10 x 353x + 10 x 25  = 85

=> 25x + 30 = 24x + 32

=> x = 2

Required Initial quantity of milk = 5x = 5 x 2 = 10 lit.

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