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:

The ratio of three numbers is 2 : 5 : 7. If their product is 1890, then what is the sum of the three numbers?

A) 82 B) 140
C) 42 D) 72
 
Answer & Explanation Answer: C) 42

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1 1300
Q:

What is the fourth proportional to 6, 24 and 83?

A) 249 B) 332
C) 166 D) 498
 
Answer & Explanation Answer: B) 332

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Q:

The third proportional of two numbers 4 and 28 is _______.

A) 52 B) 56
C) 84 D) 196
 
Answer & Explanation Answer: D) 196

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1 1295
Q:

If Gadadhar's salary is 3/2 times of Haamid's and Sarvesh's is 4/3 times of Haamid's, what is the ratio of Gadadhar's salary to Sarvesh's?

A) 9:8 B) 1:2
C) 2:1 D) 8:9
 
Answer & Explanation Answer: A) 9:8

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1 1292
Q:

What is the fourth proportional to 24, 120 and 22?

A) 110 B) 120
C) 100 D) 90
 
Answer & Explanation Answer: A) 110

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0 1290
Q:

If A, B and C are denoting Mean, Median and Mode of a data and A : B = 9 : 8. Then the ratio of B : C is

A) 5:4 B) 8:9
C) 4:3 D) 7:6
 
Answer & Explanation Answer: C) 4:3

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Q:

The ratio of the amount of work done by (x-1) labours in (x+1) days and that done by (x+1) labours in (x+2) days is 5 : 6. Then the value of x is

A) 16 B) 15
C) 17 D) 14
 
Answer & Explanation Answer: A) 16

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Q:

What number should be added to each of the numbers 55, 100, 65 and 116, so that the resulting numbers are in continued proportion?

A) 20 B) 10
C) 5 D) 15
 
Answer & Explanation Answer: A) 20

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