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 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:

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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Q:

If w : 0.80 :: 9 : 6, w = ?

A) 2.5 B) 1.1
C) 3.3 D) 1.2
 
Answer & Explanation Answer: D) 1.2

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9 1300
Q:

By increasing the price of entry ticket to a fair in the ratio 7:17, the number of visitors to the fair has decreased in the ratio 9:5. In what ratio has the total collection increased or decreased?

A) decreased in the ratio 85:63 B) increased in the ratio 35:153
C) increased in the ratio 63:85 D) decreased in the ratio 153:35
 
Answer & Explanation Answer: C) increased in the ratio 63:85

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6 1298
Q:

Two numbers are in the ratio 5:6 when 6 is added to each, the ratio becomes 7:8 then the numbers are

A) 10 & 12 B) 20 & 24
C) 15 & 18 D) 5 & 6
 
Answer & Explanation Answer: C) 15 & 18

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Q:

The income of S, T and U are in the ratio of 7 : 9 : 6 and their expenses in the ratio of 4 : 5 : 3. If S saves Rs 2000 out of an income of Rs 14000, then what will be the saving (in Rs) of T?

A) 2400 B) 1500
C) 3000 D) 2000  
 
Answer & Explanation Answer: C) 3000

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7 1291
Q:

Rs 9000 is divided among P, Q and R in the ratio of 5 : 6 : 7. What is the share (in Rs) of R?

A) 2500 B) 3500
C) 3000 D) 4000
 
Answer & Explanation Answer: B) 3500

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Q:

The ratio of salary of X, Y and Z is 15 : 3 : 8. If Z gets Rs. 3960 more than Y, then what is the salary (in Rs.) of X?

A) 11880 B) 12360
C) 9900 D) 10240
 
Answer & Explanation Answer: A) 11880

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