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:

According to the will the wealth of Rs 21,25,000 was to be divided between the son and the daughter in the ratio 7/6 : 5/3. How much did the son get (in Rs)?

A) 875000 B) 12,50,000
C) 10,00,000 D) 11,25,000
 
Answer & Explanation Answer: A) 875000

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Q:

Monthly salaries of Pia and Som are in the respective ratio of 5: 4. Pia, from her monthly salary, gives th to her mother. 15% towards her sister’s tuition fees, 18% towards a loan and she shops with the remaining amount which was Rs. 2,100. What is the monthly salary of Som ?

A) Rs.25,000 B) Rs.30,000
C) Rs.15,000 D) Rs.20,000
 
Answer & Explanation Answer:

Explanation:

Let monthly salary of Pia = Rs.500x => Monthly salary of Som = Rs.400x Amount given by Pia to her mother = 3/5 * 500x = 300x Amount for her sister tuition fees = 15*500x/100 = 75x Amount for loan = 18*500x/100 = 90x => Amount left = 500x −(300x +75x +90x) = 2100 => 500x - 465x = 35x = 2100 => x = 2100/35 = 60 Therefore, Som's salary = 400 x 60 = Rs. 24,000

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Q:

If 15% of x is three times of 10% of y, then x:y = 

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

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Q:

If a/b = c/d = e/f = 2/5, then what is (5a + 3c + 2e) : (5b + 3d + 2f)?

A) 2 : 5 B) 3 : 5
C) 16 : 25 D) 20:33
 
Answer & Explanation Answer: A) 2 : 5

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Q:

The incomes of X and Y are in the ratio 5 : 6 and their expenditure are in the ratio 6 : 5. If X saves Rs 7000 and Y saves Rs 15000, then what will be the income (in Rs) of X?

 

A) 28000 B) 20000
C) 25000 D) 24000
 
Answer & Explanation Answer: C) 25000

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Q:

The bus fare between two cities is increased in the ratio 17:20. Find the increase in the fare, if the original fare is Rs. 425

A) Rs 500 B) Rs 100
C) Rs 200 D) Rs 75
 
Answer & Explanation Answer: D) Rs 75

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Q:

A bag has Rs 20 in the form of 1­-rupee, 50­-paise and 10­-paise coins in the ratio of 2:3:5. Find the number of 50­-paise coins.

A) 25 B) 10
C) 15 D) 5
 
Answer & Explanation Answer: C) 15

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Q:

A bag has Rs 43 in the form of 5-rupee, 50-paise and 10-paise coins in the ratio of 1:5:11. What is the total number of 50-paise coins?

A) 5 B) 25
C) 55 D) 50
 
Answer & Explanation Answer: B) 25

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