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QUESTION: 1

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

Solution:

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.

QUESTION: 2

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

Solution:

QUESTION: 3

Find the 4^{th} proportional to 4, 16 and 7

Solution:

QUESTION: 4

Find the 3^{rd} proportion to 15 and 30

Solution:

QUESTION: 5

Find the mean proportional between 9 and 64.

Solution:

The correct option is B.

Step-by-step explanation:

Mean proportional=√9*√64

3*8

24

QUESTION: 6

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

Solution:

QUESTION: 7

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

Solution:

QUESTION: 8

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

Solution:

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

QUESTION: 9

If P : Q : R = 2 : 3 : 4 then

Solution:

QUESTION: 10

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

Solution:

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.

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.

Solution:

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

QUESTION: 12

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

Solution:

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.

Solution:

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.

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.

Solution:

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.

Solution:

QUESTION: 16

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

Solution:

QUESTION: 17

If , then find the value of

Solution:

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

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

Solution:

QUESTION: 19

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

Solution:

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

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.

Solution:

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.

Solution:

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.

Solution:

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.

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?

Solution:

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

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

Solution:

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.

Solution:

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?

Solution:

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

Solution:

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

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.

Solution:
Let the number of adult men be N.

Then, ratio of the numbers of adult men and adult women

9 : 7 = N : 4.2

â‡’ 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

â‡’ M = (9.6 x 100)/80 = 12 lakh

Then, ratio of the numbers of adult men and adult women

9 : 7 = N : 4.2

â‡’ 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

â‡’ M = (9.6 x 100)/80 = 12 lakh

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

Solution:

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.

Solution:
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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