Practice question on ratio and proportion (Aptitude)

ratio and proportion

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Question no. 1

If 0.75: x: : 5:8, then x is equal to:

looks_one 1.12

looks_two 1.20

looks_3 1.25

looks_4 1.30

Option looks_two 1.20

Solution :

Question no. 2

A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs 1000 more than D, what is B’s share?

looks_one Rs 500

looks_two Rs 1500

looks_3 Rs 2000

looks_4 None of these

Option looks_3 Rs 2000

Solution :
let x is the proportionality constant
A = 5x , B = 2x , C = 4x , D = 3x
4x= 3x + 1000
x = 1000
B = 2x = 2*1000 = 2000

Question no. 3

There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5:7, then the nurses at the hospital are

looks_one 20

looks_two 60

looks_3 100

looks_4 none of these

option looks_4 none of these

Solution :
let x is the proportionality constant
D(Doctor) = 5x , N(Nurse) = 7x
5x + 7x = 240
12x = 240
x = 20
N(Nurse) = 7 *20 = 140

Question no. 4

The ratio of the number of boys and girls in a school is 2 : 5. If there was 350 students in the school, find the number of girls in the school.

looks_one 200

looks_two 225

looks_3 250

looks_4 275

Option looks_3 250

Solution :
let x is the proportionality constant
B(Boys) = 2x , G(girls) = 5x
2x + 5x = 350
7x = 350 ⇒ x = 50
G = 5x = 5*50 = 250

Question no. 5

The salaries of A,B,C are in the ratio 2: 3: 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?

looks_one 3 : 3 : 10

looks_two 10 : 11 : 20

looks_3 23 : 33 : 60

looks_4 None of these

Option looks_3 23 : 33 : 60

Solution :
let x is the proportionality constant
A= 2x , B = 3x , C = 5x
New A = 2x + 0.15*2x = 2.3x
New B = 3x + 0.1*3x = 3.3x
New C = 5x + 0.2*5x = 6x
ratio = 2.3 : 3.3 : 6
ratio = 23 :33 : 60

Question no. 6

Salaries of A, B and C were in the ratio 3 : 5: 7, respectively. If their salaries were increased by 50%, 60% and 50% respectively, what will be the new ratio of the their respective new salaries ?

looks_one 4:5:7

looks_two 9 :16 :7

looks_3 9 : 15 : 18

looks_4 None of these

Option looks_4 None of these

Solution :
let x is the proportionality constant
A = 3x , B = 5x , C = 7x
New A = 3x + 0.5*3x =4.5x
New B = 5x + 0.6 * 5x = 8x
New C = 7x + 0.5 * 7x = 10.5x
New ratio = 4.5 : 8 : 10.5
New ratio = 9 : 16 : 21

Question no. 7

The ratio of the number of boys and girls in a college is 7: 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

looks_one 8 : 9

looks_two 17 : 18

looks_3 21 : 22

looks_4 none of these

Option looks_3 21 : 22

Solution :
let x is the proportionality constant
B(boys) = 7x , G(girls) = 8x
New B = 7x + 0.2*7x = 8.4x
New G = 8x + 0.1*8x = 8.8x
New ratio = 8.4 : 8.8
New ratio = 21 : 22

Question no. 8

The income of A and B are in the ratio 3:2 and expenses are in the ratio 5:3. If both save Rs 200, what is the income of A?

looks_one Rs 1000

looks_two Rs 1200

looks_3 Rs 1500

looks_4 Rs 1800

Option looks_two Rs 1200

Solution :
let x and y is the proportionality constant
A_I = 3x , B_I = 2x
A_e = 5y , B_e = 3y
According to Question
3x - 5y = 200 .....(1)
2x - 3y = 200 ......(2)
Solve for x and y
x = 400
income of A = 3x = 3 *400 = 1200

Question no. 9

The average age of three boys is 25 years and their ages are in the proportion 3: 5: 7. The age of the youngest boy is:

looks_one 21

looks_two 18

looks_3 15

looks_4 9

Option looks_3 15

Solution :
let x is the proportionality constant
B₁ = 3x , B₂ = 5x , B₃ = 7x
(3x + 5x + 7x)/3 = 25
15x = 75 ⇒ x = 5
youngest boy = 3x = 3*5 = 15

Question no. 10

In a mixture of 45 litres, the ratio of milk and water is 4 : 1. How much water must be added to make the mixture ratio 3 : 2?

looks_one 72

looks_two 24

looks_3 15

looks_4None of these

Option looks_3 15

Solution :
let x is the proportionality constant
milk(M) = 4x , water(W) = x
M + W = 45
4x + x = 45
5x= 45
x = 9
let W₁ is the water added to make the mixture ratio = 3 : 2

Question no. 11

A sum of money is to be divided among A, B and C in the ratio 2: 3: 7. If the total share of A and B together is Rs 1,500 less than C, What is A’s share in it?

looks_one Rs 1000

looks_two Rs 1500

looks_3 Rs 2000

looks_4 None of these

Option looks_two Rs 1500

Solution :
let x is the proportionality constant
A = 2x , B = 3x , C = 7x
according to Question
A + B = C - 1500
2x + 3x = 7x - 1500
2x= 1500
x = 750
A = 2x = 2*750 = 1500

Question no. 12

Out of a total amount of Rs 4,898, B receives 20% more than A and 25% more than C. What is B’s share?

looks_one Rs 930

looks_two Rs 1860

looks_3 Rs 1400

looks_4 Rs 1540

Option looks_two Rs 1860

Solution :
A + B + C = 4898
B = 1.2 A ⇒ A = 5B/6
B = 1.25 C ⇒ C = 4B/5
5B/6 + B + 4B/5 = 4898
79B/30 = 4898
B = 1860

Question no. 13

In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with the remaining meal ?

looks_one 20

looks_two 30

looks_3 40

looks_4 None of these

Option looks_two 30

Solution :

Question no. 14

Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it?

looks_one 58 kg

looks_two 60 kg

looks_3 64 kg

looks_4 70 kg

Option looks_3 64 kg

Solution :
let x is the proportionality constant
Zn = 9x , Cu = 11x
9x = 28.8 ⇒ x = 3.2
Cu = 11 * 3.2 = 35.2
Total mixture = 28.8 + 35.2 = 64

Question no. 15

A bag contains Rs 216 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 2: 3: 4. The number of 50 paise coins is

looks_one 96

looks_two 144

looks_3 141

looks_4 114

Option looks_two 144

Solution :
let x is the proportionality constant
one rupee = 2x , 50 paise = 3x , 25 paise = 4x
according to question
2x + (3/2)x + 4x/4 = 216
2x + 3x/2 + x = 216
9x = 216*2
x = 48
No. of 50paise coins = 3x = 3 *48 = 144