Practice Test: Ratio & Proportion- 1 - UPSC MCQ

# Practice Test: Ratio & Proportion- 1 - UPSC MCQ

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## 10 Questions MCQ Test CSAT Preparation - Practice Test: Ratio & Proportion- 1

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Practice Test: Ratio & Proportion- 1 - Question 1

### If the work done by p men in (p + 2) days is to the work done by (p + 4) men in (p – 1) days is in the ratio 1 : 1, then the value of p is:

Detailed Solution for Practice Test: Ratio & Proportion- 1 - Question 1

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
p = 4

Practice Test: Ratio & Proportion- 1 - Question 2

### If A is 25% less than B, then what will be the value of (2B - A)/A ?

Detailed Solution for Practice Test: Ratio & Proportion- 1 - Question 2

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Practice Test: Ratio & Proportion- 1 - Question 3

### The monthly incomes of X and Y are in the ratio of 4:3 and their monthly expenses are in the ratio of 3:2. However, each saves Rs. 6,000 per month. What is their total monthly income?

Detailed Solution for Practice Test: Ratio & Proportion- 1 - Question 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.

Practice Test: Ratio & Proportion- 1 - Question 4

The incomes of Sheldon, Leonard, and Howard are in the ratio of 4 : 5 : 6 respectively and their spending are in the ratio of 6 : 7 : 8 respectively. If Sheldon saves one fourth his income, then the savings of Sheldon, Leonard, and Howard are in the ratio:

Detailed Solution for Practice Test: Ratio & Proportion- 1 - Question 4

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 1/4th 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

Practice Test: Ratio & Proportion- 1 - Question 5

A sum of Rs. 12,384 is divided between A, B, C and D such that the ratio of the shares of A and B is 3 : 4, that of B and C is 5 : 6, and that of C and D is 8 : 9. What is the share of C ?

Detailed Solution for Practice Test: Ratio & Proportion- 1 - Question 5

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.

Practice Test: Ratio & Proportion- 1 - Question 6

In a library, the ratio of number of story books to that of non-story books was 4:3 and total number of story books was 1248. When some more story books were bought, the ratio became 5:3. Find the number of story books bought.

Detailed Solution for Practice Test: Ratio & Proportion- 1 - Question 6

Practice Test: Ratio & Proportion- 1 - Question 7

There are three persons A, B and C in a room. If a person D joins the room, the average weight of the persons in the room reduces by x kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by 2x kg. If the weight of E is 12 kg more than that of D, then the value of x is

Detailed Solution for Practice Test: Ratio & Proportion- 1 - Question 7

Practice Test: Ratio & Proportion- 1 - Question 8

A bag has ₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins. The coins are in the ratio of 6 : 9 : 10. How many coins of ₹ 5 are in the bag?

Detailed Solution for Practice Test: Ratio & Proportion- 1 - Question 8

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

Practice Test: Ratio & Proportion- 1 - Question 9

An alloy of gold and silver is taken in the ratio of 1 : 2, and another alloy of the same metals is taken in the ratio of 2 : 3. How many parts of the two alloys must be taken to obtain a new alloy consisting of gold and silver that are in the ratio 3 : 5?

Detailed Solution for Practice Test: Ratio & Proportion- 1 - Question 9

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.

Practice Test: Ratio & Proportion- 1 - Question 10

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the nonmanufacturing employees is

Detailed Solution for Practice Test: Ratio & Proportion- 1 - Question 10

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

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