Ratios and Proportions Questions

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, xy

(ii) We say that x is inversely proportional to y, if xy = k for some constant k and we write, x1y

Q:

Maneela, Raghu and Aravind have some jems with each of them. Five times the number of jems with Raghu equals seven times the number of jems with Maneela while five times the number of jems with Maneela equals seven times the number of jems with Aravind. What is the minimum number of jems that can be there with all three of them put together ?

A) 108 B) 107
C) 109 D) 110
 
Answer & Explanation Answer: C) 109

Explanation:

From given data,

R : M = 5 : 7

M : A = 5 : 7

R : M : A = 25 : 35 : 49

25 + 35 + 49 = 109

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15 4530
Q:

Rice worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, then the price of third variety of rice per kg?

A) Rs. 571.25 B) Rs. 175.5
C) Rs. 751.75 D) Rs. 850
 
Answer & Explanation Answer: B) Rs. 175.5

Explanation:

Let the price of required variety = Rs. P/kg

Then, respective amounts were m kg, m kg and 2m kg

= 126m + 135m + 2pm = 153 x 4m

=> 2p = 351

p = 175.5 / kg

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37 4409
Q:

If x : y = 1 : 3, then what will be the ratio of (3y2 + 3x2) : (2y2 - 8x2)?

 

A) 4 : 1   B) 2 : 1  
C) 3 : 1   D) 5 : 1
 
Answer & Explanation Answer: C) 3 : 1  

Explanation:
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1 4353
Q:

If (3/2)X = (5/7)Y = (6/5)Z, then what is X : Y : Z?

 

A) 105 : 50 : 84 B) 24 : 25 : 32
C) 15 : 21 : 25 D) 20 : 42 : 25
 
Answer & Explanation Answer: D) 20 : 42 : 25

Explanation:
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1 4326
Q:

If a=2b/3, b=2c/3, and c=2d/3, then find the ratio of b and d:

 

A) 8/9 B) 4/9
C) 4/3 D) 5/27
 
Answer & Explanation Answer: B) 4/9

Explanation:
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2 4180
Q:

Which of the following could not be the lengths of the sides of a right angled triangle?

A) 3, 4, 5 B) 5, 12, 13
C) 8, 15, 17 D) 12, 15, 18
 
Answer & Explanation Answer: D) 12, 15, 18

Explanation:

Using Pythagoras theorem we can see that 122 + 152 is not equal to 182
Neither is 102 + 242 = 252

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3 3915
Q:

If p : q : r = 2 : 3 : 5, then what will be the ratio of (p + q + r) : (3p + q – r)?

 

A) 5 : 2   B) 10 : 17  
C) 9 : 4 D) 5 : 4
 
Answer & Explanation Answer: A) 5 : 2  

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3 3900
Q:

If 6A = 4B = 9C; What is A : B : C?

A) 6 : 4 : 9 B) 9 : 4 : 6
C) 4 : 9 : 6 D) 6 : 9 : 4
 
Answer & Explanation Answer: D) 6 : 9 : 4

Explanation:
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