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:

One of the diagonal of a rhombus is 70% of the other diagonal. What is the ratio of area of rhombus to the square of the length of the larger diagonal?

A) 3 : 10 B) 3 : 20
C) 7 : 20 D) 7 : 10
 
Answer & Explanation Answer: C) 7 : 20

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Q:

If by increasing the price of a ticket in the ratio 8:11 the number of tickets sold fall in the ratio 23:21 then what is the increase (in Rs) in revenue if revenue before increase in price of ticket was Rs 36,800?

A) 21250 B) 9400
C) 7850 D) 12850
 
Answer & Explanation Answer: B) 9400

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Q:

The ratio of the sides of a triangular shaped park is 3 : 4 : 5 and the perimeter of the park is 170 m. What is the perpendicular distance in meters from the vertex, opposite to the largest side of the park?

A) 2400 √84 B) 2200 √84
C) 1400 √84 D) None
 
Answer & Explanation Answer: D) None

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Q:

If P/Q = R/S = T/U = 3/4 is (4P + 5R + 7T) : (3Q + 4S + 7U)?

A) 12:19 B) 6:7
C) 3:4 D) 5:8
 
Answer & Explanation Answer: B) 6:7

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Q:

A sum of Rs 125 is divided among u, v and w in such a way that u gets Rs 10 more than v and v gets Rs 5 more than w. What is the ratio of their shares?

 

A) 2 : 10 : 9   B) 10 : 8 : 7
C) 13 : 10 : 7   D) 5 : 4 : 3
 
Answer & Explanation Answer: B) 10 : 8 : 7

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Q:

Find two numbers such that their mean proportion is 8 and third proportion is 64.

A) 4 and 8 B) 8 and 16
C) 8 and 8 D) 4 and 16
 
Answer & Explanation Answer: D) 4 and 16

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Q:

In a college union, there are 48 students. The ratio of the number of boys to the number of girls is 5:3. The number of girls to be added in the union, so that the number of boys to girls in 6:5 is

A) 6 B) 7
C) 12 D) 17
 
Answer & Explanation Answer: B) 7

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Q:

The bus fare between two cities is increased in the ratio 29:31. What is the increase in the fare, if the original fare is Rs 725

A) Rs 50 B) Rs 775
C) Rs 155 D) Rs 310
 
Answer & Explanation Answer: A) Rs 50

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