Simple Ratios MCQ Quiz - Objective Question with Answer for Simple Ratios - Download Free PDF

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:

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.

Calculation

Let B = x
A = [3x/4]

C = x − 125

Total amount is 5925.

[3x/4] + x + (x − 125) = 5925

⇒ 11x – 500 = 5925 x 4

⇒ 11x = 24200

⇒ x = 24200/11 = 2200

A’s amount = [3/4] × 2200 = 1650

C’s amount = 2200 – 125 = 2075

So, Required Difference = 2075 – 1650 = 425

Calculation:

a : b = 7 : 9 

⇒ a/b = 7/9                  ------(1)

b : c = 5 : 7

⇒ b/c = 5/7                  ------(2)

Multiplying (1) by (2)

⇒ a/b × b/c = 7/9 × 5/7

⇒ a/c = 5/9

∴ The correct answer is 5 : 9

Given:

Salaries of Asha, Sreerag, and Dileep are in the ratio 3:4:5.

Their salaries were decreased by 5%, 10%, and 13% respectively.

Formula used:

New salary ratio = Original ratio × (1 - Decrease %)

Calculation:

Let the original salaries be 3x, 4x, and 5x for Asha, Sreerag, and Dileep respectively.

New salary for Asha = 3x × (1 - 5/100) = 3x × (95/100) = 285x/100

New salary for Sreerag = 4x × (1 - 10/100) = 4x × (90/100) = 360x/100

New salary for Dileep = 5x × (1 - 13/100) = 5x × (87/100) = 435x/100

New ratio = 285x : 360x : 435x

⇒ Simplify the ratio by dividing by 5:

⇒ (285/5) : (360/5) : (435/5)

⇒ 57 : 72 : 87

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

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 :

(i) a : b = 3 : 2,

(ii) b : c= 2 : 1,

(iii) c : d = 1/3 : 1/7,

(iv) d : e = 1/4 : 1/5

Calculations :

To solve these type of questions fill the blank by side values and then multiply all the ratios

 a : b = 3 : 2 now check which options satisfied this ratio

1) a : b = 100 : 75 = 4 : 3 not equal to 3 : 2

2) a : b = 100 : 30 = 10 : 3 not equal to 3 : 2

3) a : b = 105 : 70 = 21 : 14 = 3 : 2 which is equal to 3 : 2

4) a : b = 105 : 35 = 21 : 7 = 3 : 1 which is not equal to 3 : 2

hence option 3 is correct option