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:

A discount of 45% on an article is equal to the discount of 65% on other article. What is the respective ratio of the marked price of both the articles?

A) 5 : 9 B) 3 : 4
C) 7 : 12 D) 13 : 9
 
Answer & Explanation Answer: D) 13 : 9

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Q:

Average of the height of 251 students of a school is 48. If the average of the height of the boys is 51 and the average of the height of the girls is 29, then what will be the ratio of the total height of boys and the total height of girls respectively?

 

A) 323 : 29 B) 31 : 441
C) 29 : 323 D) 441 : 23
 
Answer & Explanation Answer: A) 323 : 29

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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 cash difference between the selling price of an article at a profit of 2% and 18% is Rs. 3. The ratio of two selling prices is

A) 51:59 B) 51:53
C) 51:60 D) 55:59
 
Answer & Explanation Answer: A) 51:59

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Q:

The third proportional of the following numbers (x - ­y)2, (x2 - y2)2 is

A) (x+y)3 (x-­y)2 B) (x+y)4 (x­-y)2
C) (x+y)2 (x-­y)2 D) (x+y)2 (x-y)3
 
Answer & Explanation Answer: B) (x+y)4 (x­-y)2

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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:

Divide Rs. 368 in the ratio 1:5:8:9. The rupees in the respective ratios are given by

A) 16, 80, 127 7 145 B) 16, 80, 129 & 143
C) 16, 80, 128 & 144 D) 16, 80, 128 & 143
 
Answer & Explanation Answer: C) 16, 80, 128 & 144

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Q:

In what ratio should Darjeeling Tea costing Rs. 400 per kg be mixed with Assam Tea costing Rs. 300 per kg. So that by selling the mixture at Rs. 408 per kg, there is a gain of 20%?

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

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