Mathematics Paper 2 (Ratio and Proportion) - CTET & State TET MCQ

Given:

A : B : C = 5 : 11 : 6

Total salary = Rs. 2,750

Calculation:

Salary received by C =  × 2750 = Rs. 750

∴ The salary received by C is Rs. 750.

Given:

The sum of the three numbers = 370

The first number = 1/4th of the third number

The ratio of the second number to the third = 3 : 5

Calculation:

According to question

Let, 2^nd number = 3X & 3^rd number = 5X

And, 1^st number = (1/4) × 5X = 5X/4

Now, (5X/4) + 3X + 5X = 370 

⇒ (5X/4) + 8X = 370 

⇒ 37X/4 = 370 

⇒ X = (370 × 4)/37 = 40

The third number = 5 × 40 = 200

∴ Correct answer is 200

Given:

A ∶ B ∶ C = 2 ∶ 3 ∶ 4

Calculation:

Let A = 2x , B = 3x and C = 4x

Finds the value of this given expression   ∶  ∶  ,

The value of 

⇒  = (2x/3x)

⇒  = (2/3)

The value of 

⇒  = (3x/4x)

⇒  = (3/4)

The value of 

⇒  = (4x/2x)

⇒  = (2/1)

Given:

There are ₹10 notes, ₹20 notes and ₹50 in a ratio of 3N ∶ 5N ∶ 7N.

The total amount of notes is ₹3,360.

Calculation:

According to question,

(10 × 3N) + (20 × 5N) + (50 × 7N) = 3360

⇒ 30N + 100N + 350N = 3360

⇒ 480N = 3360

⇒ N = 3360/480

⇒ N = 7

Now,

The number of ₹20 notes = 5 × 7 = 35

The number of ₹50 notes = 7 × 7 = 49

₹20 notes and ₹50 notes taken together:

⇒ 35 + 49 = 84

∴ The number of ₹20 notes and ₹50 notes taken together is 84.

Given:

a/b = 7/11

b/c = 12/17

Concept used:

If ratio a : b₁ and b₂ : c has b₁ = b₂ = b

Then, the ratio can be written as a : b : c

Calculation:

We have b common in both fractions

Equating b by multiplying a/b with 12 and b/c with 11

a/b = (7/11) × 12 = 84/132

b/c = (12/17) × 11 = 132/187

So, a : b : c = 84 : 132 : 187

Now, a + b = 84 + 132 = 216 units

And, b + c = 132 + 187 = 319 units

⇒ (a + b)/(b + c) = 216/319

Hence, the value of (a + b)/(b + c) is 216/319.

Given:

Ravi, Ramesh and Suresh can work together for ₹1,680

Ravi and Ramesh together are to do  of the work

Formula used:

The amount paid is directly proportional to the fraction of work done.

Efficiency = 1/time.

Solution:

According to the above formula:

The amount paid to Ravi and Ramesh together = 9/16 × 1680 = 945

The amount paid to Suresh = 1680 - 945 = 735

∴ The share of Suresh is 735.

Given:

Total students = 2400

Ratio of boys to girls = 7: 5

Concept used:

Total ratio units = sum of the ratio parts

Number of girls = (total students × girl's ratio units) / total ratio units

Calculation:

Total ratio units = 7 + 5 = 12

⇒ Number of girls = (2400 × 5) / 12

⇒ Number of girls = 12000 / 12

⇒ Number of girls = 1000

∴ The number of girls is 1000.

Alternate Method

Concept used:

Use the concept of proportional ratios.

Calculation:

Set up the ratio equation for girls (G) based on the given ratio:

Boys (B) : Girls (G) = 7 : 5

Express the ratio in terms of a variable (let x be the common multiplier):

B = 7x & G = 5x

Sum of the ratios equals the total number of students:

7x + 5x = 2400

Combine like terms:

12x = 2400

⇒ x = 200

Find the number of girls (G):

G = 5 × 200

⇒ G = 1000

∴ The number of girls is 1000.

Given:

Direct variation relationship = x ∝ y².

Inverse variation relationship = x ∝ 1/z^(1/3).

Concept used:

In variation problems, establishing the constant of proportionality allows transformation into equality.

Calculations:

x = k (y²/z^(1/3)) where k is the constant of proportionality.

Substituting x = 2, y = 4, and z = 8

⇒  2 = k((4²) ÷ (8^(1/3)) 

⇒ k = 0.25

Now substituting x = 3, z = 27, and k = 0.25 

⇒ 3 = 0.25(y²/(27^(1/3))).

⇒ 3 = 0.25(y²/3)

⇒ y² = 900/25

⇒  y² = ±36.

⇒ y = ±6.

∴ y can be either 6 or -6.

Given:

Original ratio of two numbers = 4 : 5

Modified ratio of two numbers = 3 : 4

Each number when reduced by 25

Calculation:

Let the original numbers be 4x and 5x.

According to the question,

 = 

⇒ 16x - 100 = 15x - 75

⇒ 16x - 15x = 100 - 75 

⇒ x = 25

Larger number = 5x = 5 × 25 = 125

∴ The largest number is 125.

Shortcut Trick

Men : Women = 5 : 7

Total number of workers = 840

⇒ The value of 12 → 840

⇒ The value of 1 → 70

Since more men are joining. But the women are the same. 

⇒ The value of 2 → 70 × 2 = 140

Hence, 140 more men should be joined to make the ratio 1 : 1.

Alternate Method

Let the men and women in the ice-cream factory be 5x and 7x respectively.

⇒ 5x + 7x = 840

⇒ 12x = 840

⇒ x = 70

Thus, Men = 5x = 5 × 70 = 350

And women = 7x = 7 × 70 = 490

Let y more men should be joined to make the ratio 1 : 1.

⇒ 350 + y = 490

⇒ y = 140

Hence, 140 more men should be joined to make the ratio 1 : 1.