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 Ratios and Proportions Questions

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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, x∝y

(ii) We say that x is inversely proportional to y, if xy = k for some constant k and we write, x∝1y

Q:

A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year  ?

A) 21:29 B) 41:54
C) 32:45 D) 37:51
 
Answer & Explanation Answer: C) 32:45

Explanation:

             A              :               B
(8000x4)+(4000x8) : (9000x6)+(6000x6)
         64000           :      90000
=>        32 : 45

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28 25939
Q:

In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is

A) 100 B) 250
C) 260 D) 416
 
Answer & Explanation Answer: D) 416

Explanation:

Let the number of boys and girls be 8x and 5x.
Total number of students = 13x = 13 * 32 = 416.

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97 24049
Q:

The number of oranges in three baskets are in the ratio of 3 : 4 : 5. In which ratio the no. of oranges in first two baskets must be increased so that the new ratio   becomes 5 : 4 : 3?

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

Explanation:

Let,   B1 : B2 : B3 = 3x : 4x : 5x 

 

again  B1 : B2 : B3 = 5y : 4y : 3y

 

Since there is increase in no.of oranges in first two baskets only, it means the no. of oranges remains constant in the third basket

 

Therefore,   5x = 3y

 

Hence    3x : 4x : 5x   =>   9y5:12y5:15y5 = 9y:12y:15y

 

and       5y : 4y : 3y   =>   25x : 20x : 15x

 

Therfore, increment in first basket = 16

 

Increment in second basket = 8

 

Thus, required ratio = 16/8 = 2:1

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88 23154
Q:

The concentration of petrol in three different mixtures (petrol and kerosene) is 1/2 , 3/5 and 4/5 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. what is the ratio of petrol and kerosene in the new mixture?

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

Explanation:

Concentration of petrol in    A        B        C

                                                1/2      3/5     4/5

Quantity of petrol taken from A = 1 litre out of 2 litre

Quantity of petrol taken from B = 1.8litre out of 3 litre

Quantity of petrol taken from C = 0.8 litre out of 1 litre

Therefore, total petrol taken out from A, B and C = 1+1.8+0.8 =3.6 litres

So, the quantity of kerosen =(2+3+1) - 3.6 =2.4 litre

Thus, the ratio of petrol to kerosene = 3.6/2.4 = 3/2

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96 22440
Q:

In the following question, select the related number from the given alternatives.

8 : 27 : : 64 : ?

A) 190 B) 144
C) 125 D) 72
 
Answer & Explanation Answer: C) 125

Explanation:
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0 21211
Q:

In a competitive exam, the number of passed students was four times the number of failed students. If there had been 35 fewer appeared students and 9 more had failed, the ratio of passed and failed students would have been 2 : 1, then the total number of students appered for the exam ?

A) 175 B) 165
C) 155 D) 145
 
Answer & Explanation Answer: C) 155

Explanation:

Let the number of failed students be x

=> Number of passed students = 4x 

So total number of students was 5x

From the given data,

If total number of students be 5x – 35

=> 4x-35-9/x+9 = 2/1

=> 4x – 44 = 2(x + 9)

=> 4x – 2x = 18 + 44

=> x = 31

Total number = 31×5

= 155

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43 21033
Q:

The incomes of two persons A and B are in the ratio 3 : 4. If each saves Rs.100 per month, the ratio of their expenditures is Rs. 1 : 2. Find their incomes.

A) Rs. 100 and Rs.150 B) Rs. 150 and Rs.200
C) Rs.200 and Rs.250 D) Rs.250 and Rs.300
 
Answer & Explanation Answer: B) Rs. 150 and Rs.200

Explanation:

Let the incomes of A and B be 3P and 4P.

If each saves Rs. 100 per month, then their expenditures = Income - savings = (3P - 100) and (4P - 100).

 

The ratio of their expenditures is given as 1 : 2.

Therefor, (3P - 100) : (4P - 100) = 1 : 2

Solving, We get P = 50. Substitute this value of P in 3P and 4P.

Thus, their incomes are : Rs.150 and Rs.200

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43 20529
Q:

If A : B = 2 : 3 and B : C = 4 : 5, then what is (A + C) : B?

 

A) 8 : 5 B) 7 : 3
C) 23 : 12 D) 25 : 14
 
Answer & Explanation Answer: C) 23 : 12

Explanation:
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