Close
###### 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 ratio of first and second class train fares between two stations is 40:1 and that of the number of passengers travelling between these stations by first and second class is 1:20. If on a particula

 A.   Rs.600/- B.   Rs.1800/- C.   Rs.900/- D.   Rs.600/-

Correct Answer : B. Rs.1800/-

Description :
No answer description available for this question. Let us discuss.

Question 2

A box contains rupee, fifty paise and twenty five paise coins whose values are in the proportion of 2:3:4. if the total number of coins are 480 find the value of each coins and total amount in rupees

 A.   20, 40, 60, and 650 B.   None of these. C.   40, 60, 80 and 180 D.   40, 60, 90 and 150

Correct Answer : C. 40, 60, 80 and 180

Description :
No answer description available for this question. Let us discuss.

Question 3

In 4 : 7 : : 16 : 28, 7 and 16 are called

 A.   none of these B.   all of these C.   extreme terms D.   middle terms

Correct Answer : D. middle terms

Description :
No answer description available for this question. Let us discuss.

Question 4

If a:b = 4:1, then find (a - 3b)/(2a - b)?

 A.   2/7 B.   5/7 C.   1/7 D.   3/7

Correct Answer : C. 1/7

Description :
a/b = 4/1 => a = 4b
(a - 3b)/(2a - b) = (4b - 3b)/(8b - b)
= b/7b => 1/7

Question 5

Divide Rs.118000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6?

 A.   A = 40000 B = 48000 C = 30000 B.   A = 30000 B = 40000 C = 48000 C.   A = 30000 B = 48000 C = 40000 D.   A = 48000 B = 40000 C = 30000

Correct Answer : B. A = 30000 B = 40000 C = 48000

Description :
Compound ratio of A:B:C
A:B = 3:4
B:C = 5:6
----------
A:B:C = 15:20:24
We can divide Rs.118000 in this ratio.
Share of A = 15/59 * 118000 = 30000
Share of B = 20/59 * 118000 = 40000
Share of C = 24/59 * 118000 = 48000

Question 6

Two numbers are in the ratio 7 : 9. If the sum of the numbers is 112, then the larger number is:

 A.   78 B.   63 C.   74 D.   56

Correct Answer : B. 63

Description :
No answer description available for this question. Let us discuss.

Question 7

If an amount of Rs 168480 is distributed equally among 72 persons. How much amount would each person get ?

 A.   Rs. 2040 B.   Rs. 2240 C.   Rs. 2340 D.   Rs. 2140

Correct Answer : C. Rs. 2340

Description :
Total amount = 168480
No. of persons = 72
each person get amount = 168480/72
= 2340

Question 8

The milk & water in two vessels A & B are in 4:3 and 2:3. In what ratio, the liquids be mixed in both the vessels so that the new liquid contains half milk and half water?

 A.   9 : 5 B.   1 : 5 C.   4: 5 D.   7 : 5

Correct Answer : D. 7 : 5

Description :
No answer description available for this question. Let us discuss.

Question 9

The average age of two persons A and B is 32 years. After four years, the ratio of the ages of A and B will be 5:13. What is the present age of B ?

 A.   51 years B.   49 years C.   48 years D.   50 years

Correct Answer : C. 48 years

Description :
Let the ages of A and B be x and y respectively.
x + y/2 = 32 ∴ x + y = 64 ....(1)
x + 4/y + 4 = 5/13
∴ 13x + 52 = 5y + 20or, 13x - 5y = -32 .....(2)
From equation (1) and (2)
x = 16, y = 48

Question 10

In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated

 A.   2:3 B.   3:4 C.   1:2 D.   1:4

Correct Answer : A. 2:3

Description :
Number of men in the colony = 4/7 (70) = 40
Number of women in the colony = 3/7 (70) = 30
Number of educated women in the colony = 1/5 (30) = 6
Number of uneducated women in the colony = 4/5 (30) = 24
Number of educated persons in the colony = 8/35 (70) = 16
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30
Number of educated men and uneducated men are in the ratio 10:30 => 1:3