Ratio and Proportion- Aptitude Questions and Answers

Let the number of 10, 20 and 50 notes be X, 2X and 3X, respectively. Then ,
10*X + 40*X + 150*X = 1000
X = 5
So, the number of 10 notes are, X = 5

A = B*(2/3) => A/B = 2/3
B = C *(4/5) => B/C = 4/5

So, A:B = 2:3 and B:C =4:5
Hence A:B:C =(2*4) :(3*4) :(3*5)
=8:12:15

Let the monthly salary of A, B and C are X, 3X and 7X, then

X+7x=800000
X=100000
Hence ,the monthly salary of B = 3*100000 / 12 => 25000

Let the successful candidates is 6X and unsuccessful candidates is X , then

Therefore, 6X+6 / X - 6 = 9/1
6X+6 = 9X- 54
3X=60
X=20
Hence , Total candidates= 6X+ X =7X
=> 7*20 =>140

Let the numbers is 4X and 7X , then
4X+4 / 7X+ 4 = 3/5
20X+20 = 21X+12
X=8
Hence , greater number is= 7X=7*8 = 54

Let the P's number is 2X and Q's number is 5X , then
2X = 120

Hence , Q's number = 5X=5*60 = 300

Let the number of girls be 4x and boys be 3x.
4x + 3x =49
7x=49
x=7

So,number of girls, 4x = 4*7 = 28 and number of boys, 3x = 3*7 = 21

Now 4 girls leave thus number of girls = 28 - 4 = 24
Hence, new ratio of girls to boys = 24/21 = 8/7

Let,Om and Pihu monthly salary be7x
and 9x respectively.
Now, saving of Om = 7x* 20/100 =7x/5
and saving of Pihu = 9x* 40/100 =18x/5

Om’s investement in PPF=7x/5 * 1/2 =7x/10
and Pihu’s investment in PPF=18x/5 * 7/9 =14x/5

Now, according to the question,
7x/10 + 14x/5 = 17500
7x/10 + 28x/10 = 17500
35x/10 = 17500
x = 175000/35
x = 5000
Pihu’s monthly salary = 9x = 9 * 5000 = 45000

Total collection = Price of each entry ticket * number of visitors
Increase in ratio = 16 * 3 : 13 * 7 = 48 : 91

2x = 3y => x=3y/2

4y = 5z => z= 4y/5

Hence, x:z = (3y/2) : (4y/5) = 15:8

Let the X is quantity , then -
(a + b) + x / (a – b) + x = (a + b)²/(a – b)²
⇒ (a + b)(a – b)² + (a – b)².x = (a + b)²(a – b) + (a + b)².x
⇒ (a + b)².x - (a – b)².x = (a + b)(a – b)² - (a + b)²(a – b)
⇒ [a² + b² + 2ab - (a² + b² - 2ab )]x = (a + b)(a – b)(a – b) - (a + b)(a + b)(a – b)
⇒ [a² + b² + 2ab - (a² + b² - 2ab )]x = [ (a² - b²)(a – b) – (a² - b²) (a +b) ]
⇒ 4ab.x = (a² - b²) [(a – b) – (a +b) ]
⇒ 4ab.x = -2b (a² - b²)
⇒ x = (b² - a² ) / 2a

Let total people be x
number of boys = 4x/9

So,number of girls = 1 - 4/9 = 5x/9
Then, 5x/9 = 125
x = 125* 9/5 = 25*9
x = 225 students

So number of boys = 4x/9 = 4/9 *225 = 100

As is given B/C = 5/6
Then, B = (5/6)*C
Substitute B value in A/B=3/4,
Then,
A/(5/6)*C = 3/4
A = (3/4)*(5/6)*C
A/C = (3/4)*(5/6)
A/C = 15/24
A/C = 5/8
So A : C = 5/8

Given, X:Y = 3:4
X = 3Y / 4

Now, Y:Z = 4 : 5
5Y = 4Z
Z = 5Y / 4

So, X : Y : Z = 3Y / 4 : Y : 5Y / 4
= 3Y / 4 : 4Y / 4 : 5Y / 4
= 3Y : 4Y : 5Y
Therefore the ratio X:Y:Z = 3 : 4 : 5

Or

X : Y = 3 : 4 = 3*4:4*4 = 12/16
Y : Z = 4 : 5 = 4*4:5*4 = 16/20

Therefore the ratio X:Y:Z = 12:16:20 = 3:4:5

Given, A:B = 2:3
A=2B/3

Now, B:C = 9:5
5B=9C
C=5B/9

So, A:B:C = 2B/3 : B : 5B/9
= 9*2B/3 : 9*B : 9*5B/9
= 6: 9 : 5

Or

A:B = 2:3 = 2*9:3*9 = 18/27
B:C = 9:5 = 9*3:5*3 = 27/15

Therefore the ratio A:B:C = 18 : 27 : 15 = 6:9:5

A:B = 3/5:5/7 = 3*7:5*5 = 21 : 25
B:C = 3/4:2/5 = 3*5:4*2 = 15 : 8

Therefore for the ratio A:B:C

A:B = 21*15:25*15
B:C = 15*25:8*25

A:B:C =21*15 : 25*15 : 8*25
=21*3:25*3:8*5
=63:75:40