Ratio and Proportion Test - 5

A+B+C = 147

A : B = 2 : 3

B : C = 5 : 8

Since both ratios considerB, write A : B : C as one ratio around B’s LCM of 15.

A : B ⇒ 10 : 15

B : C ⇒ 15 : 24

A : B : C = 10 : 15 : 24

10+15+24 = 49 “parts”, but we know A+B+C = 147so triple each value.

∴ A : B : C is actually 30 : 45 : 72

Hence, the answer is 45.

Given two numbersare in the ratio=12:26= 6: 13

Let the requirednumber be 6x and 13x

The LCM of 6x and13x is 78x

= 78x = 312

x = (312/78)

x = 4

Thus the numbersare 6x = 6 (4) = 24

13x = 13 (4) = 52

Inthis type of question, we will first try to calculate the ratio of two persons.Once we get ratio then we can easily get our answer. So lets solve this.

(8/30)A = (2/5)B

A : B = 3 : 2

B'sShare = 2/5 × 1210 = 484

Given x : y = 3 : 5

We can write aboveequation as

x/y = 3/5

5x = 3y

x = 3y/5

By substituting thevalue of x in given equation 3x + 4y : 8x + 5y we get,

3x + 4y : 8x + 5y =3 (3y/5) + 4y : 8 (3y/5) + 5y

= (9y+20y)/5 :(24y+25y)/5

= 29y/5 : 49y/5

= 29y : 49y

= 29 : 49

Let the number tobe added is xin the ratio =21:39=7:13

Then, (7 + x) + (13 + x) = (2/3)

(7 + x) 3 = 2 (13 +x)

21 + 3x = 26 + 2x

3x – 2x = 26 – 21

x = 5

Hence the required numberis 5

4:5= 4/5 = 0.8 and8: 10= 8/10= 0.8

Since both the ratiosare equal, they are said to be in proportion.

Given ratio are

4:6=2:3 and 80:114=40:57

Let the original Salaries of Ravi and Sumit is 2xand 3x.

Soas per question
(2x+4000)/(3x+4000)=40/57

57(2x+4000)=40(3x+4000)

6x=68000

3x=34000 

Sumit Salary =3x+4000=34000+4000

Given, 2/3 is theratio of any two numbers.

Let the two numbersbe 2x and 3x.

As per the givenquestion, the sum of these two numbers = 60

So, 2x + 3x = 60

5x = 60

x = 12

Hence, the twonumbers are;

2x = 2 × 12 = 24

and

3x = 3 x 12 = 36

24 and 36 are therequired numbers.

Multiplying thefirst ratio by 5, second by 3 and third by 6, we have

a:b = 10: 15

b:c = 15 : 6

c:d = 6 : 24

In the ratio’sabove, all the mean terms are equal, thus

a:b:c:d = 10:15:6:24

Given x: y = 8: 9

We can write aboveequation as

x/y = 8/9

9x = 8y

x = 8y/9

By substituting thevalue of x in the given equation (7x – 4y): 3x + 2y we get,

(7x – 4y): 3x + 2y= 7 (8y/9) – 4y: 3 (8y/9): + 2y

= (56y – 36y)/9:42y/9

= 20y/9: 42y/9

= 20y: 42y

= 20: 42

= 10: 21

Given ratiois 6:10=3:5

Let the requirednumbers be 3x and 5x

Given that if 8 isadded to each other then ratio becomes 4:6= 2: 3

That is 3x + 8: 5x+ 8 = 2: 3

(3x + 8)/ (5x + 8)= 2/3

3 (3x + 8) = 2 (5x+ 8)

9x + 24 = 10x + 16

By transposing

24 – 16 = 10x – 9x

x = 8

Thus the numbersare 3x = 3 (8) = 24

And 5x = 5 (8) = 40

Letthe first number is A and second number is B.
As per question

(40/100)A = 4/6 ofB

A/B = 2/3 × 100/40

A/B = 5/3

A : B = 5 : 3

8:10= 8/10= 0.8 and7:10= 7/10= 0.7

Since both the ratios arenot equal, they are not in proportion.

The ratio between girls and boys can be written as 3:5( Girls: Boys).The ratio can also be written in the form of factor like 3/5.

Fromquestion, lets assume that two numbers are 3x and 5x.

then, (3x−9)/(5x−9)=12/23

23(3x−9)=12(5x−9)

9x=99

x=11

∴The smallernumber=3×11=33