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Test: Ratio and Proportion- 1 - CLAT MCQ


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30 Questions MCQ Test Quantitative Techniques for CLAT - Test: Ratio and Proportion- 1

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Test: Ratio and Proportion- 1 - Question 1

If P : Q : = 8 : 15 and Q : R = 3 : 2, then find P : Q : R

Detailed Solution for Test: Ratio and Proportion- 1 - Question 1

Given that, P : Q = 8 : 15, Q : R = 3 : 2

P : Q : R = (8 x 3) : (15 x 3) : (15 x 2) = 24 : 45 : 30

∴ P : Q : R = 8 : 15 : 10 

Here, consequent of first ratio should be equal to the antecedent of second ratio.

Test: Ratio and Proportion- 1 - Question 2

If P:Q = 8:15, Q:R = 5:8, R:S = 4:5 Then P:S is

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Test: Ratio and Proportion- 1 - Question 3

Find the 4th proportional to 4, 16 and 7

Test: Ratio and Proportion- 1 - Question 4

Find the 3rd proportion to 15 and 30

Test: Ratio and Proportion- 1 - Question 5

Find the mean proportional between 9 and 64.

Detailed Solution for Test: Ratio and Proportion- 1 - Question 5

The correct option is B.
Step-by-step explanation:
Mean proportional=√9*√64
3*8
24

Test: Ratio and Proportion- 1 - Question 6

Find the compound ratio of 2:7, 5:3, 4:7

Detailed Solution for Test: Ratio and Proportion- 1 - Question 6



Test: Ratio and Proportion- 1 - Question 7

A : B is 3 : 4 and B : C  is 8 : 9 Find A : B : C

Detailed Solution for Test: Ratio and Proportion- 1 - Question 7

Test: Ratio and Proportion- 1 - Question 8

If 4a = 5 b and 7b = 9c then a : b : c = ?

Detailed Solution for Test: Ratio and Proportion- 1 - Question 8

The correct option is A.
Given that 4a = 5b
∴ a/b = 5/4
Also 7b = 9c
∴ b/c = 9/7
∴ a : b = 5 : 4 = (5 x 9) : (4 x 9) = 45 : 36
and b : c = 9 : 7 = (9 x 4) : (7 x 4) = 36 : 28
∴ a : b : c = 45 : 36 : 28
 

Test: Ratio and Proportion- 1 - Question 9

If P : Q : R = 2 : 3 : 4, then find P/Q : Q/R : R/P ?

Detailed Solution for Test: Ratio and Proportion- 1 - Question 9

Given that, P : Q : R = 2 : 3 : 4
Let P = 2K, Q = 3K, R = 4K
∴ P/Q = 2K/3K = 2/3,
Q/R = 3K/4K = 3/4,
R/P = 4K/2K = 2/1
∴ P/Q : Q/R : R/P = 2/3 : 3/4 : 2/1
= (2 x 12)/3 : (3 x 12)/ 4 : (2 x 12)/1
= (2 x 4) : (3 x 3) : 24
= 8 : 9 : 24

Test: Ratio and Proportion- 1 - Question 10

a : b = c : d = e : f = 1 : 2 then (3a + 5c + 7e) : (3b + 5d + 7f) = ?

Detailed Solution for Test: Ratio and Proportion- 1 - Question 10

The correct option is A.
A/b=c/d=e/f=1/2
so,b=2a, d=2c, f=2e
then,
=3a+5c+7e/[3(2a)+5(2c)+7(2e)]
=3a+5c+7e/6a+10c+14e
=3a+5c+7e/2(3a+5c+7e)
=1/2.

Test: Ratio and Proportion- 1 - Question 11

The average age of a person and his son is 30 years. The ratio of their age is 4 : 1 respectively. Find the age of son.

Detailed Solution for Test: Ratio and Proportion- 1 - Question 11

The correct option is A.
Let ,father's age=Y years
and,son's age=X years
Acc. to question, there average is 30
therefore,
=> (X + Y) / 2 = 30
=> X + Y = 60
=> X + 4X = 60 (RATIO IS 4:1)
=> 5X = 60
=> X = 12

Test: Ratio and Proportion- 1 - Question 12

If Rs. 782 be divided into three parts, proportional to 1/2 = 2/3 = 3/4  then the first part is:

Detailed Solution for Test: Ratio and Proportion- 1 - Question 12

Test: Ratio and Proportion- 1 - Question 13

A bag contains one rupee, 50 paise 25 paisa coins in the Ratio of 8:9:11. If the total money in the bag is Rs. 366, find the number of 25 paisa coins.

Detailed Solution for Test: Ratio and Proportion- 1 - Question 13

Let coins are
1 ruppe coin = 8X.
Value of 1 ruppe coin = 8X.
50 paise coins = 9X
Value of 50 paise coin = 9X/2
25 paise coins = 11X
Value of 25 paise coins = 11X/4.
Total Ruppes = 366
8X + 9X/2 + 11X/4 = 366
61X/4 = 366
61X = 1464
X = 24.
Number of 25p paise coin = 11X = 11* 24 = 264.

Test: Ratio and Proportion- 1 - Question 14

A mixture contains alcohol and water in the ratio of 4 : 3. If 14 L of water is added to the mixture the ratio of Alcohol and water becomes 3 : 4, find the quantity of alcohol in the mixture.

Test: Ratio and Proportion- 1 - Question 15

Rahul obtained 12 marks more than that of Tanvi. If the ratio of their marks is 4:3. Find the sum of their marks.

Test: Ratio and Proportion- 1 - Question 16

One half of a certain number is equal to 65% of the second number. Find the ratio of Ist number to 2nd number.

Test: Ratio and Proportion- 1 - Question 17

If  , then find the value of 

Detailed Solution for Test: Ratio and Proportion- 1 - Question 17

The correct option is C.
a/3 = b/5 = c/7 = p
a = 3p
b = 5p
c = 7p
=> a+b+c/b => 3p+5p+7p/5p => 15p/5p
=> 3/1 
The answer is 3 

Test: Ratio and Proportion- 1 - Question 18

Monthly income of P and Q are in the ratio 2 : 3 and their monthly expenses are in the ratio of 5 : 9. If each of them saves Rs 300 per month, find their respective monthly income

Test: Ratio and Proportion- 1 - Question 19

What number has to be added to each term of 3 : 5 to make the ratio 5 : 6?

Detailed Solution for Test: Ratio and Proportion- 1 - Question 19

The correct option is D.
Let the no be x
Implies
3+x/5+x=5/6
Implies 6(3+x)=5(5+x)
18+6x=25+5x
6x-5x=25-18
Implies x=7
7 should be added
Proof-
3+7/5+7=10/12=5/6

Test: Ratio and Proportion- 1 - Question 20

The ratio between two numbers is 3 : 4. If each number is increased by 3, the ratio becomes 4 : 5. Find the difference between the numbers.

Test: Ratio and Proportion- 1 - Question 21

In a class, the number of boys and girls is in the ratio of 4 : 5. If 10 more boys join the class, the ratio of boys to girls becomes 6 : 5. How many girls are there in the class.

Test: Ratio and Proportion- 1 - Question 22

The sum of the ages of a father and his son is 100 yrs now. Five years ago their ages were in the ratio 2 : 1. Find the ratio of ages of father and son after 10 years.

Detailed Solution for Test: Ratio and Proportion- 1 - Question 22

The correct option is B.
Let present age of father - x
present age of son. - y
X + Y = 100. y = 100 - x
five years ago their ages = x -5/y-5 =2/1
- x - 5 = 2y - 10 , x - 5 = (100-x)2 - 10
x - 5 = 200 - 2x - 10 , 3x = 195 ,
x = 195/3 = 65,
y = 100 - 65 = 35
Ratio after 10 years= 65+10/35+10 = 75/45 =5/3.
 

Test: Ratio and Proportion- 1 - Question 23

The average age of a woman and her daughter is 19 years. The ratio of their ages is 16 : 3. What is the age of the daughter? 

Detailed Solution for Test: Ratio and Proportion- 1 - Question 23

Woman’s age = 16x years 
Her daughter’s age = 3x years 
∴ 16x + 3x = 2 × 19 = 38 
⇒ 19x = 38 ⇒ x = 2
∴  Daughter’s age = 3 × 2 

Test: Ratio and Proportion- 1 - Question 24

The ages of A and B are in the ratio 12 : 7. After 6 years the ratio will become 3 : 2. What is the difference in their ages

Test: Ratio and Proportion- 1 - Question 25

The average age of a man and his two sons, born on the same day, is 30 yr. The ratio of the ages of father to one of the sons is 5 : 2. What is the father’s age.

Test: Ratio and Proportion- 1 - Question 26

The ratio of present ages of Seeta and Geeta is 8 : 9. The sum of their ages is 68. What will be the ratio of their ages after 10 years?

Test: Ratio and Proportion- 1 - Question 27

The ratio between the present ages of Punit and suresh is 4 : 5. After 7 years Punit’s age will be 31 years. What was Suresh’s age four years ago

Detailed Solution for Test: Ratio and Proportion- 1 - Question 27

Let the present ages of Punit and Suresh be 4x and 5x
According to the question-
4x+7=31
4x=31-7
4x=24
X=6
Now, present age of suresh= 5x ⇒ 5(6)
30 years

so, his age 4 years ago=30-4=26 years

Test: Ratio and Proportion- 1 - Question 28

In a town 80% of the population are adults of which men and women are in the ratio of 9 : 7 respectively. If the number of adult women is 4.2 Lakh, what is the total population of the town.

Detailed Solution for Test: Ratio and Proportion- 1 - Question 28
Let the number of adult men be N.
Then, ratio of the numbers of adult men and adult women
9 : 7 = N : 4.2
⇒ N = (9/7) x 4.2 = 5.4 Lakh
Total adult population = 4.2 + 5.4 = 9.6 lakh.

If the population of the town be M Lakh,
then, 80M/100 = 9.6
⇒ M = (9.6 x 100)/80 = 12 lakh
Test: Ratio and Proportion- 1 - Question 29

If the positions of the digits of a two digit no. are interchanged the number newly formed is smaller than the original number by 45. Also the ratio of new number to original number is 3 : 8. What is the original number

Test: Ratio and Proportion- 1 - Question 30

There are two triangles A and B. The angles of triangle A are in the ratio 3 : 4 : 5 and the angles of triangle B are in the ratio of 5 : 6 : 7. What is the difference between the largest angle of triangle A and the smallest angle of triangle B.

Detailed Solution for Test: Ratio and Proportion- 1 - Question 30
The sum of all angles of triangle is 180 degrees .
so , in triangle A , let the sides be 3x,4x,5x
3x+4x+5x=180
12x=180 therefore x=15.
so, the angles are 3x = 45, 4x=60, 5x=75
Similarly in triangle B 
5x+6x+7x=180 
so x=10 
angles are 50,60,70 
largest angle of triangle A is 75 and smallest of B is 50 and the difference is 25 .
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