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

Given:

Total sum = Rs. 4350

A receives 25% more than C

B receives 20% more than A

Formula used:

Let the amount received by C = x

Amount received by A = x + 25% of x = 1.25x

Amount received by B = 1.25x + 20% of 1.25x = 1.25x + 0.25x = 1.5x

Calculations:

Total amount = x + 1.25x + 1.5x = 4350

3.75x = 4350

x = 4350 / 3.75

x = 1160

Amount received by B = 1.5x = 1.5 × 1160 = 1740

∴ The amount received by B is Rs. 1740.

Given:

An amount of ₹840 is divided among three persons in the ratio of 16 : 6 : 18.

Formula used:

Share of a person = (Ratio of the person / Sum of all ratios) × Total amount

Calculation:

Sum of all ratios = 16 + 6 + 18 = 40

Share of first person = (16 / 40) × 840

⇒ Share of first person = 0.4 × 840 = 336

Share of second person = (6 / 40) × 840

⇒ Share of second person = 0.15 × 840 = 126

Share of third person = (18 / 40) × 840

⇒ Share of third person = 0.45 × 840 = 378

Difference between the largest and smallest shares = 378 - 126

⇒ Difference = 252

∴ The correct answer is option (2).

Calculation

Total toffies B and C has = 60 – 25 = 35

Let total toffies B has = x

So, total toffies C has = x – 5

ATQ, [2x – 5] = 35

Or, 2x = 40, x = 20

Let y toffies added with C to found resultant ratio

So, [15 + y]/ 20 = [6/4]

Or, 15 + y = 30

So, y = 15

Given:

of a tank holds 135 litres of water.

The tank contains 180 litres of water.

Calculations:

If of the tank holds 135 litres,

Total capacity of the tank = 135 litres × 4

⇒ Total capacity = 540 litres

Part of the tank full = (Current amount of water) / (Total capacity of the tank)

⇒ Part of the tank full = 180 / 540

⇒ Part of the tank full = 1/3

∴ 1/3 part of the tank is full if it contains 180 litres of water.

Given:

The sum, difference, and product of two numbers are in the ratio 5 : 1 : 30.

Formula used:

Let the two numbers be x and y.

The sum of the numbers = x + y

The difference of the numbers = x - y

The product of the numbers = x × y

We are given that:

(x + y) : (x - y) : (x × y) = 5 : 1 : 30

Calculations:

Let (x + y) = 5k, (x - y) = k, and (x × y) = 30k.

Now, we have the following system of equations:

x + y = 5k

x - y = k

Adding these two equations:

(x + y) + (x - y) = 5k + k

⇒ 2x = 6k

⇒ x = 3k

Substitute x = 3k into x + y = 5k:

3k + y = 5k

⇒ y = 2k

Now, substitute x = 3k and y = 2k into the product equation:

x × y = 30k

⇒ (3k) × (2k) = 30k

⇒ 6k² = 30k

⇒ k = 5

Now, substitute k = 5 into x and y:

x = 3k = 15

y = 2k = 10

Finally, the product of the numbers is:

x × y = 15 × 10 = 150

∴ The product of the numbers is 150.

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:

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 : 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:

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,  = (5/4)/(4/5) = 25/16

∴  = 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 

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 × 

⇒ 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