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

Given:

The total amount is divided between A, B, and C in the ratio 8 : 4 : 3.

A divides his share between D and E in the ratio 9 : 7.

Formula used:

Profit = Time × Investment

Calculation:

Let the total amount of money be S.

A's share = (8 / (8 + 4 + 3)) × S = (8 / 15) × S

B's share = (4 / (8 + 4 + 3)) × S = (4 / 15) × S

C's share = (3 / (8 + 4 + 3)) × S = (3 / 15) × S

Now, A divides his share between D and E in the ratio 9 : 7.

So, D's share from A = (9 / (9 + 7)) × A's share = (9 / 16) × (8 / 15) × S

⇒ D's share = (72 / 240) × S = (3 / 10) × S

Now, we need to find the ratio of C's share to D's share:

C's share : D's share = (3 / 15) × S : (3 / 10) × S

⇒ Ratio = (3 / 15) × (10 / 3) = 2 / 3

∴ The ratio of C's share to D's share is 2 : 3.

Given:

The sum of money is divided between x and y in the ratio 4:3.

y's share = ₹2,400

Calculation:

Let the total sum of money be S.

y's share = (3 / (4 + 3)) × S

y's share = (3 / 7) × S = ₹2,400

⇒ (3 / 7) × S = ₹2,400

⇒ S = ₹2,400 × (7 / 3)

⇒ S = ₹5,600

∴ The total initial capital is ₹5,600.

Given:

We are asked to find the third ratio of (a + b) and (a + b)².

Formula used:

Third proportion of a and b = b²/a

Calculation:

Third ratio = ((a + b)²)²/(a + b)

Third ratio = (a + b)4/(a + b)

We can simplify this expression:

Third ratio = (a + b)³

∴ The third ratio is (a + b)³.

Given:

Monthly incomes of Chetan and Vipul are in the ratio 5 : 7

Each of them saves ₹96000 every month

The ratio of their monthly expenditure is 1 : 3

Formula used:

Income = Expenditure + Savings

Calculation:

Let the monthly income of Chetan be 5x and that of Vipul be 7x.

Let the monthly expenditure of Chetan be y and that of Vipul be 3y (since the ratio of their expenditures is 1:3).

For Chetan, Income = Expenditure + Savings

5x = y + 96000

For Vipul, Income = Expenditure + Savings

7x = 3y + 96000

Now, solve the system of equations:

1) 5x = y + 96000

⇒ y = 5x - 96000

2) 7x = 3y + 96000

Substitute y = 5x - 96000 into equation 2:

7x = 3(5x - 96000) + 96000

7x = 15x - 288000 + 96000

7x = 15x - 192000

⇒ 7x - 15x = -192000

⇒ -8x = -192000

⇒ x = 24000

Now, the monthly income of Chetan = 5x = 5 × 24000 = ₹120000

∴ The monthly income of Chetan is ₹120000.

Given:

19, 57, 81, and y are in proportion.

Formula Used:

If four numbers a, b, c, and d are in proportion, then a/b = c/d.

Calculation:

Here, a = 19, b = 57, c = 81, and d = y.

According to the formula:

⇒ 19 / 57 = 81 / y

Cross-multiplying:

⇒ 19y = 57 × 81

⇒ 19y = 4617

Dividing both sides by 19:

⇒ y = 4617 / 19

⇒ y = 243

The correct answer is option 4.

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:

Ratio of salaries of A and B = 6 : 7

B's salary increased by \(5\frac{1}{2}\%\)

Total salary of B = Rs. 147700

Calculation:

Let salary of A and B be Rs. 60x and Rs. 70x

Now,

Increased salary of B = 70x + 70x × \(5\frac{1}{2}\%\)

⇒ Rs. 73.85x

According to the question,

73.85x = 147700

⇒ x = 147700/73.85

⇒ x = 2000

So, actual salary of A = 60 × 2000

⇒ Rs. 120000

∴ The salary (in Rs.) of A is 120000.

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