Formulae
1. Ratio:
The ratio of two quantities a and b in the same units, is the fraction \( a \over b \)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.
Eg. The ratio 5 : 9 represents \( 5 \over 9 \) 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.
Eg. 4 : 5 = 8 : 10 = 12 : 15. 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. Fourth Proportional:
If a : b = c : d, then d is called the fourth proportional to a, b, c.
Third Proportional:
a : b = c : d, then c is called the third proportion to a and b.
Mean Proportional:
Mean proportional between a and b is \( \sqrt {ab} \).
4. Comparison of Ratios:
We say that (a : b) > (c : d) ⇔ \( a \over b \) > \( c \over d \)
Compounded Ratio:
The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf).
5. Duplicate Ratios:
Duplicate ratio of (a : b) is (a2 : b2).
Sub-duplicate ratio of (a : b) is (√a : √b).
Triplicate ratio of (a : b) is (a3 : b3).
Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).
If \( a \over b \) = \( c \over d \) , then \( {a + b} \over {a - b} \) = \( {c + d} \over {c - d} \). [componendo and dividendo]
6. Variations:
We say that x is directly proportional to y, if x = ky for some constant k and we write, x ∝ y.
We say that x is inversely proportional to y, if xy = k for some constant k and
we write, x ∝ \( 1 \over y \)
Exercise : Ratio and Proportion MCQ Questions and Answers
Question 1
The triplicate ratio of 1:2 is?
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Correct Answer : C. 1:8
Description :
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50/50
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Question 2
If an amount of Rs 168480 is distributed equally among 72 persons. How much amount would each person get ?
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Correct Answer : B. Rs. 2340
Description :
Total amount = 168480
No. of persons = 72
each person get amount = 168480/72
= 2340
Question 3
If 12, 21, 72, 126 are in proportion, then:
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Correct Answer : D. 12 ? 126 = 21 ? 72
Description :
12 ? 126 = 21 ? 72
Question 4
In a class there are 20 boys and 15 girls. The ratio of boys to girls is:
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Correct Answer : B. 4 : 3
Description :
No answer description available for this question. Let us discuss.
Question 5
38 percent of first number is 52 percent of the second number. What is the respective ratio of the first number to the second number?
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Correct Answer : B. 26 : 19
Description :
No answer description available for this question. Let us discuss.
Question 6
If an amount of Rs. 5,86,700 is distributed equally amongst 25 persons, then how much would each person get ?
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Correct Answer : D. Rs. 23,468
Description :
Amount received by each person = 586700/25 = Rs. 23468
Question 7
Salary of B is 18% more than the salary of A and salary of C is 20% more than the salary of B. What is the total salary of A, B and C if the salary of ' B ' is ?18880 ?
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Correct Answer : A. Rs. 57536
Description :
Let the salary of A be x
∴ Salary of B = x + x x 18/100
= x + 9x/50 = 59x/50 = 18880
∴ x = 18880 x 50/59 = 16000
Salary of C = 18880 x 120/100 = 22656
∴ Total salary of A, B and C = 16000 + 18880 + 22656 = 57536
Question 8
If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number.
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Correct Answer : C. 5:3
Description :
No answer description available for this question. Let us discuss.
Question 9
If the product of the ages of A and B is 864 years and the ratio of their ages is 3 : 2, what is the age of 'B' ?
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Correct Answer : B. 24 years
Description :
Age of B = 2 x √864/3x2 = 2 √864/6
= 2√144 = 2 x 12 = 24 yrs
Question 10
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
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Correct Answer : D. 2000 Rs.
Description :
Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.
Then, 4x - 3x = 1000 => x = 1000.
B's share = Rs. 2x = 2 * 1000 = Rs. 2000.