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 bus fare between two cities is increased in the ratio 11:18. What would be the increase in the fare, if the original fare is Rs 550?

A) Rs 350 B) Rs 900
C) Rs 180 D) Rs 360
 
Answer & Explanation Answer: A) Rs 350

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Q:

The ratio of the number of marbles that Joyee and Minati had was 5 : 8 while the ratio of the number of marbles that Jacob and Minati had was 7 : 12. What is the ratio of the number of marbles that Joyee and Jacob had?

A) 5 : 7 B) 7 : 5
C) 15 : 14 D) 2 : 3
 
Answer & Explanation Answer: C) 15 : 14

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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 ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If S divides PQ in the ratio 1:5 and length of QR is 15 cm, find ST?

A) 2.4 cm B) 3.6 cm
C) 2.5 cm D) 5.6 cm
 
Answer & Explanation Answer: C) 2.5 cm

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Q:

Two whole numbers are such that the square of first number exceeds the second by 112 and the ratio of the numbers is 4:3. What is thevalue of smaller number?

A) 3 B) 4
C) 12 D) 36
 
Answer & Explanation Answer: C) 12

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Q:

If Girish's salary is 4/9 times of Harishankar's and Shirish's salary is 5/6 times of Harishankar's, what is the ratio of Girish's salary to Shirish's.

A) 27:10 B) 10:27
C) 8:15 D) 15:8
 
Answer & Explanation Answer: C) 8:15

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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:

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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