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:

If 3A = 6B = 9C; What is A : B : C

A) 6 : 3 : 1 B) 6 : 3 : 2
C) 9 : 3 : 6 D) 9 : 3 : 1
 
Answer & Explanation Answer: B) 6 : 3 : 2

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Q:

If 25% of X is equal to 40% of Y, then what is the ratio of X and Y?

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

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5 1830
Q:

The radius of base of solid cone is 9 cm and its height is 21 cm. It cut into 3 parts by two cuts, which are parallel to its base. The cuts are at height of 7 cm and 14 cm from the base respectively. What is the ratio of curved surface areas of top, middle and bottom parts respectively?

A) 1 : 4 : 8 B) 1 : 3 : 5
C) 1 : 3 : 9 D) 1 : 6 : 12
 
Answer & Explanation Answer: B) 1 : 3 : 5

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Q:

A, B and C start a business and the ratio of their investment is 8 : 5 : 3. If at the end the ratio of their profits is 4 : 15 : 6, then what is the ratio of time period of their investment?

A) 1 : 6 : 5 B) 2 : 3 : 4
C) 1 : 6 : 4 D) 2 : 6 : 3
 
Answer & Explanation Answer: C) 1 : 6 : 4

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Q:

The incomes of P and Q are in the ratio 4 : 7 and their expenditures are in the ratio 3 : 7. If P saves Rs 10000 and Q saves Rs 7000, then what will be the income (in Rs) of P?

A) 28000 B) 23000
C) 30000 D) 19000
 
Answer & Explanation Answer: A) 28000

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0 1696
Q:

If 2A = 3B = 8C; What is A : B : C?

A) 8 : 3 : 2 B) 8 : 4 : 3
C) 2 : 3 : 8 D) 12 : 8 : 3
 
Answer & Explanation Answer: D) 12 : 8 : 3

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3 1693
Q:

A certain sum of money was divided between A, B and C in the ratio 5:6:9. If A received Rs. 450 the sum divided was

A) 2000 B) 1800
C) 2250 D) 1000
 
Answer & Explanation Answer: B) 1800

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1 1637
Q:

Priya's marks in History and Geography are in the ratio 5 : 7. If she got 14 marks more in Geography than in History, what are her History marks?

A) 49 B) 42
C) 56 D) 35
 
Answer & Explanation Answer: D) 35

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