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- Most Important Multiple Choice Questions
- Online Ratio and Proportion Exercise with Correct Answer Key and Solutions
- Useful for all Competitive Exams

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- Question 1 of 23
##### 1. Question

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?

##### Hint

Originally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x)

∴ Required ratio

=

- Question 2 of 23
##### 2. Question

In what proportion must a number be divided so that ¼ of the first part and ⅓ of the second part are together equal to ½ of the original number?

##### Hint

Let number be divided in ratio x : y. Then

First part ,

second part

Now,

- Question 3 of 23
##### 3. Question

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?

##### Hint

For 9 kg zinc, mixture melted = (9 + 11) kg.

For 28.8 kg zinc, mixture melted

=

- Question 4 of 23
##### 4. Question

The Binary Ice-cream Shopper sells two flavours : Vanilla and Chocolate. On Friday, the ratio of Vanilla cones sold to Chocolate cones sold was 2 : 3. If the store had sold 4 more Vanilla cones, then, the ratio of Vanilla cones sold to the Chocolate cones sold would have been 3 : 4. How many Vanilla cones did the store sell on Friday?

##### Hint

and …(1)

∴ C =

⇒ [From (1)]

where V denoted for vanilla and C for chocolate.

⇒ 4V + 16 =

⇒ 8V + 32 = 9V

⇒ V = 32

- Question 5 of 23
##### 5. Question

The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is:

##### Hint

A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15

and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24

Therefore, A : B : C = 10 : 15 : 24

Let the numbers be 10x, 15x and 24x.

Then, 10x + 15x + 24x = 98

⇒ 49x = 98

⇒ x = 2

⇒ Second number = 15x = 15 × 2 = 30

- Question 6 of 23
##### 6. Question

The ratio of number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents left, the ratio became 1 : 3. How many people were originally present at the party?

##### Hint

Let number of ladies = x

and, number of gents = 2x

Now,

⇒ x = 4

∴ Total number of people originally present = 4 + 8 = 12

- Question 7 of 23
##### 7. Question

A man divides his property so that his son’s share to his wife’s and the wife’s share to his daughter are both in the ratio 3 : 1. If the daughter gets Rs 10,000 less than the son, find the total worth of the property.

##### Hint

Let Son’s share = Rs S;

Daughter’s share = Rs D;

and Wife’s share = Rs W.

Also, S : W = W : D = 3 : 1

∴ S : W : D = 9 : 3 : 1

then S = 9x , D = x

and 9x – x = 10,000

⇒ x = Rs 1250

∴ Total worth of the property

= (9 + 3 + 1) x = 13x

= 13 × 1250 = Rs 16,250

- Question 8 of 23
##### 8. Question

Mrs X spends Rs 535 in purchasing some shirts and ties for her husband. If shirts cost Rs 43 each and the ties cost Rs 21 each, then what is the ratio of the shirts to the ties, that are purchased?

##### Hint

Let S denotes the shirts and T denotes the ties.

We have, 43S + 21T = 535

By hit and trial, S = 10, T = 5

⇒ 43 × 10 + 21 × 5 = 535

∴ Ratio of shirts to ties = 10 : 5 = 2 : 1

- Question 9 of 23
##### 9. Question

The ratio between the number of passengers travelling by I and II class between the two railway stations is 1 : 50, whereas the ratio of I and II class fares between the same stations is 3 : 1. If on a particular day, Rs 1325 revenue collected from the passengers travelling between these stations, then what was the amount collected from the II class passengers?

##### Hint

Let, the number of passengers travelling by I and II class be x and 50x and fares of I and II class be 3y and y.

∴ Revenue is x × 3y + 50x × y = Rs 1325

53xy = 1325

⇒ xy = 25

∴ Amount collected from the II class passengers

= 50xy

= 50 × 25

= Rs 1250.

- Question 10 of 23
##### 10. Question

Railway fares of 1st, 2nd and 3rd classes between two stations were in the ratio of 8 : 6 : 3. The fares of 1st and 2nd class were subsequently reduced by 1/6 and 1/12, respectively. If during a year, the ratio between the passengers of 1st, 2nd and 3rd classes was 9 : 12 : 26 and total amount collected by the sale of tickets was Rs 1088, then find the collection from the passengers of 1st, class.

##### Hint

Fare after reduction.

1st classes 2nd classes 3rd classes 8 – ⁸⁄₆ 6 – ⁶⁄₁₂ 3 ²⁰⁄₃ ¹¹⁄₂ 3 40 33 18 Ratio of revenue

1st 2nd 3rd 9 × 40 12 × 33 26 × 18 Ratio of revenue of all three classes

= 10 : 11 : 13

∴ Collection for 1st class

- Question 11 of 23
##### 11. Question

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?

##### Hint

Let income of A = Rs 3x,

income of B = Rs 2x

and expenditure of A = Rs 5y,

expenditure of B = Rs 3y

Now, saving = income – expenditure

∴ 3x – 5y = 2x – 3y = 200

⇒ x = 2y and y = 200

∴ x = 400

∴ A’s income = Rs 1200

- Question 12 of 23
##### 12. Question

A sum of money is divided among A, B and C in the ratio of 3¾ : 4 : 5.5. If the lowest share is Rs 30, then the total amount of money is

##### Hint

Let A’s share ,

B’s share = Rs 4x and

C’s share = Rs 5.5x

Given

∴ Total amount = 30 + 32 + 44 = Rs 106

- Question 13 of 23
##### 13. Question

At a start of a seminar, the ratio of the number of male participants to the number of female participants was 3 : 1. During the tea break 16 participants left and 6 more female participants registered. The ratio of the male to the female participants now became 2 : 1. What was the total number of participants at the start of the seminar?

##### Hint

Let the number of male and female participants be 3x and x respectively.

therefore total no. of participants are 4x.

During the tea break, the number of male participants are

… (i)

and the number of female participants are

… (ii)

Now,

⇒ 3x – 12 = 2x + 4

⇒ x = 16

Therefore, the total number of participants = 4 × 16 = 64.

- Question 14 of 23
##### 14. Question

The ratio of the present ages of Sushma and Karishma is 6:7 respectively. The ratio of their ages 8 years hence would be 8:9 respectively. What would be the respective ratio of their ages after 12 years?

##### Hint

Let the present ages of Sushama and Karishma be 6x and 7x respectively.

∴

or 56x + 64 = 54x + 72

Required ratio

=

= 9 : 10

- Question 15 of 23
##### 15. Question

The ratio of the present ages of Smita and Kavita is 3:8 respectively. Seven years hence the respective ratio of their ages will be 4:9. What is Kavita’s present age?

##### Hint

Let the present ages of Smita and Kavita be 3x and 8x years respectively

According to questions,

⇒ 32 x + 28 = 27x + 63

⇒ 32x – 27x = 63 – 28

⇒ 5x = 35

⇒ x = = 7

∴ Kavita’s present age = 8x = 8 × 7 = 56 years

- Question 16 of 23
##### 16. Question

The average age of a man and his son is 48 years. The ratio of their ages is 5 : 3 respectively. What is the son’s age?

##### Hint

Let the ages of man and his son be 5x and 3x respectively.

5x + 3x = 2 × 48

⇒ 8x = 96

⇒ x = = 12

∴ Son’s age = 12 × 3 = 36 years

- Question 17 of 23
##### 17. Question

The ages of Nishi and Vinnee are in the ratio of 6 : 5 respectively. After 9 years the ratio of their ages will be 9 : 8. What is the difference in their ages?

##### Hint

Difference in age

= 3 years

- Question 18 of 23
##### 18. Question

The difference between the present ages of Arun and Deepak is 14 years. Seven years ago the ratio of their ages was 5 : 7 respectively. What is Deepak’s present age?

##### Hint

Let Arun’s present age be x years.

Then, Deepak’s present age = (x + 14) years

Then,

⇒ 7x – 5x = 35 + 49

∴ Deepak’s present age

= 42 + 14 = 56 years

- Question 19 of 23
##### 19. Question

At present Meena is eight times her daughter’s age. Eight years from now, the ratio of the ages of Meena and her daughter will be 10 : 3 respectively. What is Meena’s present age?

##### Hint

Present age of Meena

=

=

= 32 years

- Question 20 of 23
##### 20. Question

The ratio of the ages of a father and son is 17 : 7 respectively. 6 years ago the ratio of their ages was 3 : 1 respectively. What is the father’s present age?

##### Hint

Let the present age of father and son be 17x and 7x respectively.

Then,

⇒ 21x – 17x = 18 – 6

⇒ x = 12 ÷ 4 =3

∴ Father’s present age

= 17 × 3 = 51 years.

- Question 21 of 23
##### 21. Question

The respective ratio of the present ages of Swati and Trupti is 4: 5. Six years hence the respective ratio of their ages will be 6 : 7. What is the difference between their ages?

##### Hint

Let the present ages be 4x and 5x respectively.

Then,

⇒ 30x – 28x = 42 – 36

⇒ x = ⁶⁄₂ = 3

∴ Difference in age

= 5x – 4x = x = 3 years

- Question 22 of 23
##### 22. Question

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:

##### Hint

Total age of 3 boys

= (25 × 3) years

= 75 years

Ratio of their ages = 3 : 5 : 7.

Age of the youngest boy

= years

= 15 years

- Question 23 of 23
##### 23. Question

A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is Rs 35, how many coins of each type are there?

##### Hint

Let number of each type of coin = x. Then,

1 × x + 0.50 × x + 0.25 x = 35

⇒ 1.75x = 35

⇒ x = 20 coins

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