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 ratio of incomes of P and Q is 5 : 3. Ratio of income of Q and R is 5 : 2. If one-fourth of P’s income is Rs 500 more than the R’s income, then what is the income (in Rs) of Q?

 

A) 7500 B) 15000
C) 30000 D) 18000
 
Answer & Explanation Answer: C) 30000

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6 1039
Q:

The flight fare between two cities is increased in the ratio 11:13. What is the increase (in Rs) in the fare, if the original fare was Rs 12100?

A) 14300 B) 2200
C) 22000 D) 1430
 
Answer & Explanation Answer: B) 2200

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1 1033
Q:

If 13A = 11B = 8C, find A : B : C

A) 143:104:88 B) 104:88:143
C) 88:104:143 D) 8:11:13
 
Answer & Explanation Answer: C) 88:104:143

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2 1029
Q:

If 7A = 5B = 2C; find A : B : C.

A) 35:14:10 B) 14:10:35
C) 2:5:7 D) 10:14:35
 
Answer & Explanation Answer: D) 10:14:35

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1 1020
Q:

If a : b is 32 : 35 and b : c is 21 : 32, then a : c is?

A) 5 : 3 B) 3 : 5
C) 1 : 1 D) 5 : 7
 
Answer & Explanation Answer: B) 3 : 5

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2 1016
Q:

A bag has Rs.51.25 in the form of 2-rupee, 50-paise and 25-paise coins in the ratio of 3:5:7. What is the total number of 50-paise coins?

A) 15 B) 35
C) 25 D) 5
 
Answer & Explanation Answer: C) 25

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1 1011
Q:

Rs. 782 is divided into 3 parts in the ratio 12:23:34, the first part is 

A) Rs. 182 B) Rs. 204
C) Rs. 190 D) Rs. 196
 
Answer & Explanation Answer: B) Rs. 204

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3 1006
Q:

According to the will, the wealth of Rs 11,50,000 was to be divided between the son and the daughter in the ratio 2/3 : 5/4. How much share did the son get (in Rs lakhs)?

A) 5 B) 6
C) 7 D) 4
 
Answer & Explanation Answer: D) 4

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2 1001