Ratio & Proportion- 1 - CUET Commerce Free MCQ Practice Test with solutions

Work done will be directly proportional to number of men and days.
So according to the question:

• [(p)(p + 2)] / [(p + 4)(p - 1)] = 1/1 
• p² + 2p /  p² + 4p - p - 4 = 1
• p² + 2p =  p² + 3p - 4
• -p = -4
• p = 4

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 :

The ratio of the income of X and Y is 4 : 3.

The ratio of monthly expenses of X and Y is 3 : 2. 

X and Y save 6000 rupees each month.

Concept used :

Savings = Income - expense

Calculations :

Let the ratio of monthly income of X and Y be 4a and 3a respectively. 

Let the ratio of monthly expenses of X and Y be 3b and 2b respectively. 

Savings of X = 4a - 3b

4a - 3b = 6000      ....(1) 

Savings of Y = 3a - 2b 

3a - 2b = 6000      ....(2) 

Solving equation 1 and 2 

We get a = 6000 and b = 6000

Total monthly income of X and Y = 4a + 3a = 7a 

⇒ 7 × 6000 

⇒ 42000 rupees 

∴ Option 2 is the correct answer.

Let the incomes be 4x, 5x, 6x and the spending be 6y, 7y, 8y and savings are (4x–6y), (5x–7y) & (6x–8y)
Sheldon saves 1/4^th of his income.

Therefore:

⇒ 4x – 6y = 4x / 4
⇒ 4x – 6y = x
⇒ 3x = 6y
⇒ x / y = 2
∴ y = x / 2

Ratio of Sheldon’s Leonard’s & Howard’s savings:

= 4x – 6y : 5x – 7y : 6x – 8y
= x : 5x – 7y : 6x – 8y
= x : 5x – 7x / 2 : 6x – 8x / 2
= x : 3x / 2 : 2x
= 2 : 3 : 4 

Given:

A : B = 3 : 4

B : C = 5 : 6

C : D = 8 : 9

Sum to divided among them = Rs. 12,384

Concept used:

Ratio Proportion

Calculation:

A : B = 3 : 4 = 15 : 20

B : C = 5 : 6 = 20 : 24

C : D = 8 : 9 = 24 : 27

A : B : C : D = 15 : 20 : 24 : 27

Share of C = 24/(15 + 20 + 24 + 27) × 12384 = Rs. 3456

∴ The share of C is Rs. 3456.

• Story Books / Non Story Books = 4 / 3
• Therefore, Non Story Books = 3 / 4 x Story books = 3 / 4 x 1248 = 936
• Let M storybooks be added. So number of story books = 1248 + M
• Story Books / Non story books = 5 / 3
• 1248 + M / 936 = 5 / 3
• 1248 + M = 312 x 5
• M = 1560 - 1248 = 312

Let's denote the total weight of persons A, B, and C by S.

When person D joins:

• The new total weight becomes S + D.
• The new average weight becomes (S + D) / 4.
• We are told that this new average is x kg less than the original average (which is S/3). That gives us the equation:

  (S + D) / 4 = (S / 3) - x

When instead person E joins:

• The new total weight becomes S + E.
• The new average weight becomes (S + E) / 4.
• In this case, the average increases by 2x kg compared to the original average, so:

  (S + E) / 4 = (S / 3) + 2x

We are also told that E weighs 12 kg more than D, which means:

  E = D + 12

Step 1. Subtract the two equations

Subtract the equation for D from the equation for E:

  [(S + E) / 4] – [(S + D) / 4] = [(S / 3) + 2x] – [(S / 3) - x]

Simplify the left side:

  (E - D) / 4

Simplify the right side:

  (S / 3 cancels) and we get 2x + x = 3x

So we have:

  (E - D) / 4 = 3x

Multiply both sides by 4:

  E - D = 12x

Step 2. Substitute the known difference

We are given that E - D = 12 kg. So:

  12 = 12x

Divide both sides by 12:

  x = 1

Conclusion

The value of x is 1 kg.

Answer: 1

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

Step 1: Find the cost price (C.P.) of the mixture per kg.
Selling Price (S.P.) = Rs. 1.50
Gain = 25%

C.P. of mixture = S.P. ÷ (1 + Gain%)
= 1.50 ÷ 1.25
= 1.20 per kg

So the average C.P. of the mixture = Rs. 1.20

Step 2: Use alligation rule.

Cheaper sugar price = 1.15
Dearer sugar price = 1.24
Mean price = 1.20

Now subtract:

• (1.24 – 1.20) = 0.04

• (1.20 – 1.15) = 0.05

Ratio = 0.04 : 0.05 = 4 : 5

Let the number of total employees in the company be 100x, and the total salary of all the employees be 100y.

It is given that 20% of the employees work in the manufacturing department, and the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company.

Hence, the total number of employees in the manufacturing department is 20x, and the total salary received by them is (100y/6)

Average salary in the manufacturing department = (100y/6*20x) = 5y/6x

Similarly, the total number of employees in the nonmanufacturing department is 80x, and the total salary received by them is (500y/6)

Hence, the average salary in the nonmanufacturing department = (500y/6*80x) = 25y/24x

Hence, the ratio is:- (5y/6x): (25y/24x) 

=> 120: 150 = 4:5

The correct option is D