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:

If u : v : w = 3 : 6 : 8, then what will be the ratio of (u/v) : (v/w) : (w/u)?

 

A) 8 : 6 : 3   B) 8 : 4 : 3  
C) 5 : 9 : 12   D) 6 : 9 : 32
 
Answer & Explanation Answer: D) 6 : 9 : 32

Explanation:
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5 11812
Q:

Find the missing value denoted by '?'

 

3 : 243 :: 5 : ?

 

A) 625 B) 465
C) 3125 D) 425
 
Answer & Explanation Answer: C) 3125

Explanation:
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5 11723
Q:

Based on the analogy given, find the missing number from the given options.

 

11 : 13 :: 17 : ___

 

A) 29 B) 21
C) 19 D) 23
 
Answer & Explanation Answer: D) 23

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2 11563
Q:

If x : y = 1 : 3, then what will be the ratio of (3y2 + 3x2) : (2y2 - 8x2)?

 

A) 4 : 1   B) 2 : 1  
C) 3 : 1   D) 5 : 1
 
Answer & Explanation Answer: C) 3 : 1  

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1 11549
Q:

Two numbers are in the ratio 3 : 7. If 6 be added to each of them, then they are in the ratio 5 : 9. Find the numbers ?

A) 11 & 17 B) 7 & 17
C) 9 & 21 D) 13 & 23
 
Answer & Explanation Answer: C) 9 & 21

Explanation:

Let the two numbers be x and y

Given x : y = 3 : 7 .....(1)

Now, x+6 : y+6 = 5 : 9 .....(2)

From (1), x = 3y/7

From (2), 5y - 9x = 24

=> 5y - 9(3y/7) = 24

=> y = 21

=> From(1), x = 9

Hence, the two numbers be 9 and 21

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36 11547
Q:

Two solutions have milk & water in the ratio 7:5 and 6:11. Find the proportion in which these two solutions should Be mixed so that the resulting solution has 1 part milk and 2 parts water ?

A) 7 : 12 B) 8 : 13
C) 9 : 4 D) 2 : 5
 
Answer & Explanation Answer: B) 8 : 13

Explanation:

To get the solution that contains 1 part of milk and two parts of water,
they must be mixed in the ratio as
7x+6x/5y+11y = 1/2
26x = 16y
x/y = 16/26
x/y = 8/13

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19 11483
Q:

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats ?

A) 1 : 2 : 3 B) 2 : 3 : 4
C) 3: 4 : 5 D) 4 : 5 : 6
 
Answer & Explanation Answer: B) 2 : 3 : 4

Explanation:

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8.

Seats for Mathematics, Physics and Biology in a school are 5x, 7x and 8x.

There is a proposal to increase these seats by 40%, 50% and 75% respectively.

Then Seats for Mathematics, Physics and Biology in a school will be

1.4 X 5x, 1.5 X 7x and 1.75 X 8x and

ratio will be 7 : 10.5 : 14  => 2:3:4.

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21 11442
Q:

16 : 56 :: 32 : ?

A) 196 B) 148
C) 132 D) 112
 
Answer & Explanation Answer: D) 112

Explanation:

16 : 56 :: 32 : ?

Let the required number be 'n'

The given numbers follow a logic that,

16/56 = 2/7

=> 32/n = 2/7

=> 32 x 7/2 = n

=> n = 112.

 

Hence, 16 : 56 :: 32 : 112.

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44 11256