Simple Ratios MCQ Quiz - Objective Question with Answer for Simple Ratios - 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).

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:

Two quantities: 2 km and 600 m

Formula Used:

To find the ratio between two quantities, they must be in the same unit.

1 kilometer (km) = 1000 meters (m)

Ratio = Quantity 1 : Quantity 2

Calculation:

Convert 2 km to meters:

2 km = 2 × 1000 m = 2000 m

Ratio = 2000 m : 600 m

Ratio = 20 : 6

Ratio = 10 : 3

∴ The ratio of 2 km and 600 m is 10:3.

Given:

Amount distributed = x

A gets 25% of x = (25/100) × x = x/4

Twice the difference of B and C = Share of A

2(B - C) = A

Calculations:

A = x/4

2(B - C) = A

⇒ 2(B - C) = x/4

⇒ B = C + x/8

Total amount distributed:

⇒ A + B + C = x

⇒ x/4 + (C + x/8) + C = x

⇒ x/4 + x/8 + 2C = x

⇒ 3x/8 + 2C = x

⇒ 2C = x - 3x/8

⇒ C = (5x/16)

Now, B = C + x/8

⇒ B = (5x/16) + (2x/16) = 7x/16

A = x/4 = 4x/16

Now, ratio A : B : C = (4x/16) : (7x/16) : (5x/16)

⇒ 4 : 7 : 5

∴ The correct answer is option (2).

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:

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
 

Given: 

5p : 10p : 25p = 3 : 2 : 1 = 3x : 2x : x

Concept:

1 Rupee = 100 paise

Calculation:

60 Rupees = 60 × 100 = 6000 paise

⇒ 5 × 3x + 10 × 2x + 25 × 1x = 6000

⇒ 15x + 20x + 25x = 6000

⇒ 60x = 6000

⇒ x = 100

∴ Number of 5 paise coins = 3x = 3 × 100 = 300

Given:

Ratio of Speed of Deepak and Vinod = 19 : 12

Let the speeds of Deepak and Vinod be 19x km/hr and 12x km/hr

Speed of Vinod = 84 km/hr

Calculations:

Speed of Vinod = 84 km/hr

⇒ 12x = 84

⇒ x = 7

Speed of Deepak = 19x = 19 × 7 = 133 km/hr

∴ The speed of Deepak is 133 km/hr.

Shortcut Trick

P : Q : R = 5 : 3 : 6

Le P be 5x, Q be 3x and R be 6x

Then, (P/Q) ∶ (Q/R) ∶ (R/P) = (5x/3x) ∶ (3x/6x) ∶ (6x/5x)

Let us take the LCM (3, 6, 5) = 30

So, (P/Q) ∶ (Q/R) ∶ (R/P) = (5x/3x) × 30 ∶ (3x/6x) × 30 ∶ (6x/5x) × 30

∴ Required ratio is 50 ∶ 15 ∶ 36

Alternate Method

Given:

P : Q : R = 5 : 3 : 6

Le P be 5x, Q be 3x and R be 6x.

Concept:

If N is divided into a : b, then

First part = N × a/(a + b)

Second part = N × b/(a + b)

Calculations:

The required ratio = P/Q : Q/R : R/P

Multiplying the above ratio with PQR

⇒ Required ratio = P²R : Q²P : R²Q

Putting values of P,Q and R in above ratio, we get

⇒ Required ratio = (5x)²(6x) : (3x)²(5x) : (6x)²(3x)

⇒ Required ratio = (25x²)(6x) : (9x²)(5x): (36x²)(3x)

⇒ Required ratio = (25)(2) : (3)5: (36)

⇒ Required ratio = 50 : 15 : 36

∴ Required ratio is 50 ∶ 15 ∶ 36.

Given:

The ratio of the salaries of Ravi and Sarita is 3 ∶ 5.

If the salary of each is increased by ₹ 5,000, the new ratio becomes 29 ∶ 45.

Formula Used:

Initial salaries: R = 3x and S = 5x.

New salaries: R + 5000 and S + 5000.

New ratio: (R + 5000) / (S + 5000) = 29/45.

Calculation:

Substituting the values of R and S in the new ratio equation:

(3x + 5000) / (5x + 5000) = 29 / 45

Cross multiplying to solve for x:

⇒ 45 × (3x + 5000) = 29 × (5x + 5000)

⇒ 135x + 225000 = 145x + 145000

⇒ 145x - 135x = 225000 - 145000

⇒ 10x = 80000

⇒ x = 8000

Now, finding the current salary of Sarita:

S = 5x = 5 × 8000

S = 40000

The present salary of Sarita is ₹ 40,000.

Shortcut Trick 

Given:

Total Rs. = Rs.550

Calculation:

Let the number of denominations of 50p = 2x

the number of denominations of 25p = 3x

the number of denominations of 20p = 5x

Total paisa = 550 × 100 = 55000 paise

According to the question:

⇒ (50 × 2x) + (25 × 3x) + (20 × 5x) = 55000

⇒ 100x + 75x + 100x = 55000

⇒ 275x = 55000

⇒ x = 55000/275 = 200

Amount in (Rs.) of 50p = 100x = (100 × 200) = 20000 paise = Rs.200

Amount in (Rs.) of 20p = 100x = (100 × 200) = 20000 paise = Rs.200

Required difference = 200 - 200 = 0

∴ The correct answer is 0.