Ratio and Proportion MCQ Quiz - Objective Question with Answer for Ratio and Proportion - Download Free PDF

Given:

Ratio of girls to boys = 1 : 5

Number of girls = 249

Formula Used:

Number of boys = Ratio of boys × Number of girls

Calculation:

Ratio of boys = 5

⇒ Number of boys = 5 × 249

⇒ Number of boys = 1245

The number of boys participating in the sports is 1245.

Given:

x varies inversely as y3 - 1 .

x = 6 when y = 3 .

Formula Used:

x × (y3 - 1) = k , where k is a constant.

Calculation:

When y = 3 , x = 6

⇒ 6 × (3³ - 1) = k

⇒ 6 × (27 - 1) = k

⇒ 6 × 26 = k

⇒ k = 156

Now, find x when y = 7 .

⇒ x × (7³ - 1) = k

⇒ x × (343 - 1) = 156

⇒ x × 342 = 156

⇒ x = \(\frac{156}{342}\)

⇒ x = \(\frac{26}{57}\)

The value of x when y = 7 is \(\frac{26}{57}\) .

Given:

x varies inversely as y³ - 1.

x = 6 when y = 3.

Find x when y = 8.

Formula used:

For inverse variation: x × (y³ - 1) = k (constant).

x = k / (y³ - 1).

Calculations:

Step 1: Calculate the constant k when x = 6 and y = 3:

k = x × (y³ - 1)

k = 6 × (3³ - 1)

k = 6 × (27 - 1)

k = 6 × 26

k = 156

Step 2: Find x when y = 8:

x = k / (y³ - 1)

x = 156 / (8³ - 1)

x = 156 / (512 - 1)

x = 156 / 511

∴ The value of x when y = 8 is approximately 156/511.

Given:

Option 1: 19 : 36

Option 2: 29 : 42

Option 3: 11 : 60

Option 4: 17 : 33

Formula Used:

To compare ratios, convert them into fractions and then compare the fractions.

Calculation:

Option 1: 19 : 36

Fraction = 19 / 36

Option 2: 29 : 42

Fraction = 29 / 42

Option 3: 11 : 60

Fraction = 11 / 60

Option 4: 17 : 33

Fraction = 17 / 33

To compare the fractions, convert them to a common denominator or compare their decimal values.

19 / 36 ≈ 0.527

29 / 42 ≈ 0.690

11 / 60 ≈ 0.183

17 / 33 ≈ 0.515

⇒ The smallest value is 0.183

The correct answer is option 3.

Given:

First number (a) = 76

Second number (b) = 38

Third proportional (x) = ?

Formula Used:

Third proportional: If a, b, and x are in continued proportion, then b² = a × x

Calculation:

Using the formula for third proportional:

b² = a × x

38² = 76 × x

⇒ 1444 = 76 × x

⇒ x = 1444 / 76

⇒ x = 19

The value of x is 19.

Given:

u : v = 4 : 7 and v : w = 9 : 7

Concept Used: In this type of question, number can be calculated by using the below formulae

Calculation:

u : v = 4 : 7 and v : w = 9 : 7

To make ratio v equal in both cases

We have to multiply the 1st ratio by 9 and 2nd ratio by 7

u : v = 9 × 4 : 9 × 7 = 36 : 63 ----(i)

v : w = 9 × 7 : 7 × 7 = 63 : 49 ----(ii)

Form (i) and (ii), we can see that the ratio v is equal in both cases

So, Equating the ratios we get,

u ∶ v ∶ w = 36 ∶ 63 ∶ 49

⇒ u ∶ w = 36 ∶ 49

When u = 72,

⇒ w = 49 × 72/36 = 98

∴ Value of w is 98

Given:

₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins

The coins are in the ratio of 6 : 9 : 10

Calculation:

Let the number of coins of ₹ 2, ₹ 5 and ₹ 10 be 6x, 9x, and 10x respectively

⇒ (2 × 6x) + (5 × 9x) + (10 × 10x) = 785

⇒ 157x = 785

∴ x = 5

Number of coins of ₹ 5 = 9x = 9 × 5 = 45

∴ 45 coins of ₹ 5 are in the bag

Given:

A : B = 7 : 8

B : C = 7 : 9

Concept:

If N is divided into a : b, then

First part = N × a/(a + b)

Second part = N × b/(a + b)

Calculation:

A/B = 7/8      ----(i)

Also B/C = 7/9      ----(ii)

Multiply equation (i) and (ii) we get,

⇒ (A/B) × (B/C) = (7/8) × (7/9)

⇒ A/C = 49/72

∵ A : B = 49 : 56

∴ A : B : C = 49 : 56 : 72

 Alternate Method

A : B = 7 : 8 = 49 : 56

B : C = 7 : 9 = 56 : 72

⇒ A : B : C = 49 : 56 : 72

Given:

Total coin = 220

Total money = Rs. 160

There are thrice as many 1 Rupee coins as there are 25 paise coins.

Concept used:

Ratio method is used.

Calculation:

Let the 25 paise coins be 'x'

So, one rupees coins = 3x

50 paise coins = 220 – x – (3x) = 220 – (4x)

According to the questions,

3x + [(220 – 4x)/2] + x/4 =160

⇒ (12x + 440 – 8x + x)/4 = 160

⇒  5x + 440 = 640

⇒ 5x = 200

⇒ x = 40

So, 50 paise coins = 220 – (4x) = 220 – (4 × 40) = 60

∴ The number of 50 paise coin is 60.

Given:

A = 75% of B

Calculation:

A = 3/4 of B

⇒ A/B = 3/4

Let the value of A be 3x and B be 4x

So (2B – A)/A = (2 × 4x – 3x)/3x

⇒ (2B – A)/A = 5x/3x

∴ (2B – A)/A = 5/3

Short Trick:

Ratio of A : B = 3 : 4

∴ (2B – A)/A = (8 – 3) /3 = 5/3

Given:

x : y = 5 : 4

Explanation:

(x/y) = (5/4)

(y/x) = (4/5)

Now, \(\left( {\frac{x}{y}} \right):\left( {\frac{y}{x}} \right)\) = (5/4)/(4/5) = 25/16

∴ \(\left( {\frac{x}{y}} \right):\left( {\frac{y}{x}} \right)\) = 25 : 16

Given :

Ratio of two numbers is 4 : 7 

Calculations :

Let the number added to denominator and numerator be 'x' 

Now according to the question 

(4 + x)/(7 + x) = 2 : 3 

⇒ 12 + 3x = 14 + 2x 

⇒ x = 2 

∴ 2 will be added to make the term in the ratio of 2 : 3.

Given:

Ratio of two numbers is 14 : 25

Difference between them is 264

Calculation:

Let the numbers be 14x and 25x

⇒ 25x – 14x = 264

⇒ 11x = 264

∴ x = 24

⇒ Smaller number = 14x = 14 × 24 = 336

∴ The smaller of the two numbers is 336.

Given:

A and B invested money in a business in the ratio of 7 ∶  5.

15% of the total profit goes for charity, and A's share in the profit is Rs. 5,950

Calculation:

The total profit of A and B will be 5950 × 12 / 7 = Rs 10200

The total profit including charity is 10200 × 100/85 = Rs 12000

∴ The correct option is 2

Given:

x : y = 6 : 5

And z : y = 9 : 25

Calculation :

x/y = 6/5     ---- (i)

And z/y = 9/25

⇒ y/z = 25/9     ---- (ii)

Multiply equation (i) and (ii) we get,

(x/y) × (y/z) = (6/5) × (25/9)

⇒ x/z = 10/3

∴ x : z = 10 : 3

Alternate Method 

x : y = 6 : 5     ----- (i)

And z : y = 9 : 25     ---- (ii)

As y is in both the ratios, Multiply (i) × 5 to make equal value of y in both the ratios

x : y = (6 : 5) × 5 = 30 : 25    ---- (iii)

from (ii) and (iii), Since y is same in both the ratios

x : z = 30 : 9 = 10 : 3