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 a bag the ratio of red balls to green balls is 4 : 9. If 6 more green balls were added to the bag, the ratio of red balls to green balls would become 1 : 3. How many red balls are there in the bag?

A) 9 B) 10
C) 8 D) 12
 
Answer & Explanation Answer: C) 8

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2 1101
Q:

Find the 4th proportional to 9, 17 and 27.

A) 57 B) 48
C) 51 D) 53
 
Answer & Explanation Answer: C) 51

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8 1100
Q:

The ratio of two numbers is 6 : 11 and their difference is 65. What will be the smaller number among both the numbers?

A) 58 B) 65
C) 52 D) 78
 
Answer & Explanation Answer: D) 78

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1 1099
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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1 1094
Q:

Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of areas of triangle APQ: triangle ABC is 16:25. Then the ratio of AP:PB is?

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

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3 1093
Q:

The ratio between the weights of gold and silver in an alloy is 17:3. If the weight of silver in the alloy is 2.7 gm, find the weight of gold in the alloy?

A) 12.6 gm B) 15.3 gm
C) 18 gm D) 21.2 gm
 
Answer & Explanation Answer: B) 15.3 gm

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0 1090
Q:

Find two numbers such that their mean proportion is 12 and third proportion is 768.

A) 3 and 24 B) 3 and 48
C) 6 and 48 D) 6 and 24
 
Answer & Explanation Answer: B) 3 and 48

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6 1087
Q:

The bus fare between two cities is increased in the ratio 1:2. Find the increase in the fare, if the original fare is Rs. 175.

A) Rs 350 B) Rs 70
C) Rs 140 D) Rs 175
 
Answer & Explanation Answer: D) Rs 175

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1 1085