Test: Ratio & Proportion (February 5) - CAT MCQ

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 :

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.

• 
• 1248 + M = 312 x 5
• M = 1560 - 1248 = 312

Given:

The ratio of the income of A and B = 7 : 8

The ratio of the income of B and C = 8 : 11

The difference in the income earned by A and C = Rs. 800

Calculation:

According to the question,

The ratio of the income of A and B = 7 : 8

The ratio of the income of B and C = 8 : 11

By combining the ratios, we get,

The ratio of the income of A, B and C = 7 : 8 : 11

Income of C = 11k

Income of A = 7k

The difference in the income earned by A and C = 11k - 7k = 4k

Again according to the question,

⇒ 4k = 800

⇒ k = 200

The income of A, B and C = 7k + 8k + 11k = 26k

Sum of income of A, B and C = 26 × 200 = Rs. 5200

Therefore, 'Rs. 5200' is the required answer.

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

Let x and y be mass of two alloys mixed.
In first alloy:

Gold = x × 1 / (1 + 2) = x/3
Silver = x × 2 / (1 + 2) = 2x/3

In second alloy:

Gold = y × 2 / (2 + 3) = 2y/5
Silver = y × 3 / (2 + 3) = 3y/5

In resulting alloy: 

Gold / Silver = 3 / 5
(x/3+2y/5) / (2x/3+3y/5) = 3 / 5
(x/3+2y/5) × 5 = (2x/3+3y/5) × 3
5x/3 + 2y = 2x + 9y/5
5x/3 - 2x = 9y/5 - 2y
-x/3 = -y/5
x / y = 3 / 5

Therefore, two alloys should be taken in ratio of 3 : 5.

► If new values of x, y, z are x′, y′ and z′, and respectively then x′ :  y′ = 4 : 5, y′ :  z′ = 3 : 4

⇒ x′ :  y′ :  z′ = 12 : 15 : 20
⇒ x + y + z = 5000
⇒ x′ + 50 + y′ + 100 + z′ + 150 = 5000 x′ + y′ + z′ = 4700
⇒ 12k + 15k + 20k = 4700 k = 100

► x = 1200 + 50 = 1250
► y = 1500 + 100 = 1600 z = 2000 + 150 = 2150
► x + y = 1250 + 1600 = 2850