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:

Sanjay's test marks in two subjects, English and Hindi are in the ratio 7 : 11. If he got 20 marks more in Hindi than in English, what are his marks in English?

A) 35 B) 55
C) 45 D) 65
 
Answer & Explanation Answer: A) 35

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Ratios and Proportions
Exam Prep: Bank Exams

5 3607
Q:

Rs 6300 is divided among A, B and C in the ratio of 1/2 : 1 : 3/5. What is the share (in Rs) of B?

A) 3300 B) 2700
C) 3000 D) 4200
 
Answer & Explanation Answer: C) 3000

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Ratios and Proportions
Exam Prep: Bank Exams

6 3474
Q:

If 3A = 2B = 4C; then what is A : B : C?

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

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Ratios and Proportions
Exam Prep: Bank Exams

4 3147
Q:

Divide Rs. 80 in the proportion of 3:6:7.

A) Rs. 10, Rs. 35, Rs. 40 B) Rs. 15, Rs. 30, Rs. 35
C) Rs. 15, Rs. 35, Rs.30 D) Rs. 10, Rs. 40, Rs. 35
 
Answer & Explanation Answer: B) Rs. 15, Rs. 30, Rs. 35

Explanation:

3/16 X 80, 6/16 X 80, 7/16 X 80
⇒ 15, 30, 35

Report Error

View Answer Report Error Discuss

Filed Under: Ratios and Proportions
Exam Prep: Bank Exams

7 2765
Q:

The ratio of the monthly salaries of A and B is in the ratio 5 : 16 and that of B and C is in the ratio 17 : 18. Find the monthly income of C if the total of their monthly salary is Rs. 1,87,450.

A) Rs. 66,240 B) Rs. 72,100
C) Rs. 62,200 D) Rs. 65,840
 
Answer & Explanation Answer: A) Rs. 66,240

Explanation:

So A : B : C = 1 5 × 1 7 : 1 6 × 17 : 16 × 18 = 255 : 272 : 288

Report Error

View Answer Report Error Discuss

Filed Under: Ratios and Proportions
Exam Prep: Bank Exams

2 2727
Q:

Rizwan has a box in which he kept red and blue marbles. The red marbles and blue marbles were in the ratio 5 : 4. After he lost 5 red marbles the ratio became 10 : 9. How many marbles does he have now?

A) 81 B) 86
C) 76 D) 91
 
Answer & Explanation Answer: C) 76

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Ratios and Proportions
Exam Prep: Bank Exams

0 2695
Q:

In PQR, straight line parallel to the base QR cuts PQ at X and PR at Y. If PX:XQ = 5:6, then the XY:QR will be

A) 5:11 B) 6:5
C) 11:6 D) 11:5
 
Answer & Explanation Answer: A) 5:11

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Ratios and Proportions
Exam Prep: Bank Exams
Job Role: Bank Clerk

1 2693
Q:

If A's wealth is 4/9 times of B's and C's is 7/6 times of B's, what is the ratio of C's wealth to A's?

A) (8:21) B) (21:8)
C) (27:14) D) (14:27)
 
Answer & Explanation Answer: B) (21:8)

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Ratios and Proportions
Exam Prep: Bank Exams

1 2672