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 two numbers is 5 : 6. If their product is 1470, then what is the sum of both the numbers?

A) 210 B) 77
C) 132 D) 98
 
Answer & Explanation Answer: B) 77

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Q:

A sum of Rs. 69 was divided between Jason and Ruhana in the ratio 1:2. How much money did Ruhana get?

A) Rs. 45 B) Rs. 23
C) Rs. 46 D) Rs. 40
 
Answer & Explanation Answer: C) Rs. 46

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Q:

If angles of a quadrilateral are in the ratio 3:5:9:13, find the largest angle?

A) 165 B) 180
C) 156 D) 190
 
Answer & Explanation Answer: C) 156

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Q:

In what ratio is the segment joining (12,­1) and (-­3,4) divided by the Y­-axis?

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

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Q:

The diagonals of two squares are in the ratio 5:2.The ratio of their area is

A) 5:6 B) 25:4
C) 5:4 D) 125:8
 
Answer & Explanation Answer: B) 25:4

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Q:

Two whole numbers are such that the cube of first number exceeds the cube of second by 61 and the ratio of the numbers is 5:4. What is the value of larger number?

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

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Q:

The cash difference between the selling price of an article at a profit of 4% and 6% is Rs. 3. The ratio of two selling prices is:

A) 51:53 B) 55:53
C) 52:53 D) 54:53
 
Answer & Explanation Answer: C) 52:53

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Q:

The ratio of incomes of C and D is 3 : 2. Ratio of income of D and E is 5 : 4. If one-third of C’s income is Rs 4000 more than the half of E’s income, then what is the D’s income (in Rs)?

A) 40000 B) 43000
C) 50000 D) 60000
 
Answer & Explanation Answer: A) 40000

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