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:

In an army selection process, the ratio of selected to unselected was 3:1. If 60 less had applied and 30 less selected, the ratio of selected to unselected would have been 5:1. How many candidates had applied for the process?

A) 240 B) 480
C) 120 D) 720
 
Answer & Explanation Answer: A) 240

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Q:

In an army selection process, the ratio of selected to unselected was 5:1. If 100 less had applied and 20 less selected, the ratio of selected to unselected would have been 6:1. How many candidates had applied for the process?

A) 5520 B) 2760
C) 1380 D) 8280
 
Answer & Explanation Answer: B) 2760

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Q:

In an army selection process, the ratio of selected to unselected was 6:1. If 90 less had applied and 30 less selected, the ratio of selected to unselected would have been 8:1. How many candidates had applied for the process?

A) 3150 B) 6300
C) 4725 D) 1575
 
Answer & Explanation Answer: D) 1575

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Q:

If the three numbers in the ratio 3:2:5 be such that the sum of the squares is equal to 1862 then which number is the middle one.

A) 16 B) 14
C) 13 D) 15
 
Answer & Explanation Answer: B) 14

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Q:

 In the triangle ABC, the internal bisector of angle A meets the side BC at D. If BD=7.5 cm and BC=9 cm. Then calculate the value of AB:AC.

 

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

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Q:

If a cone is divided into two parts by drawing a plane through the midpoints of its axis, then the ratio of the volume of the 2 parts of the cone is

A) 1 : 2 B) 1 : 4
C) 1 : 7 D) 1 : 8
 
Answer & Explanation Answer: C) 1 : 7

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Q:

What number should be added to each of 4, 16, 18 and 58 so that the resulting numbers will be in proportion in the given order?

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

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Q:

The third proportional of two numbers 24 and 36 is

A) 48 B) 54
C) 72 D) 108
 
Answer & Explanation Answer: B) 54

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