Ratio and Proportion Aptitude Test Paper 3

11) The ratio of income in two consecutive years is 2: 3 respectively. The ratio of their expenditure is 5: 9. Income of second-year is Rs 45000 and Expenditure of first-year is Rs 25000. Find the Savings in both years together.

5000
7000
6075
8025

Answer: A

Explanation:

Let the First-year income = 2x
And, Second-year income = 3x
But ATQ, the second-year income = 45000
So, x = 45000/3 = 15000
Then, first-year income = 2*15000=30000

Similarly,
Let the first-year expenditure = 5y
But ATQ, the first-year expenditure =25000
So, y = 25000/5 = 5000
Second-year expenditure = 9y= 9* 5000 = 45000

Apply formula:

Income = expenditure + savings
Or, savings = income - expenditure
Or, first-year savings = 30000- 25000 = 5000
Similarly,
Second-year savings = 45000- 45000 = 0

Now, total saving in two years = first-year savings + second-year savings
Or, Total saving = 5000+0 = 5000.

12) Pervez, Sunny, and Ashu Bhati alone can complete a piece of work in 30, 50, and 40 days. The ratio of their salaries of each day is 4: 3: 2 respectively. The total income of Parvez is Rs 144. Find the total income of Sunny.

Answer: A

Explanation:

Note: Total income = total days * per day salary

Let per day salary of Pervez = 4
Pervez can complete a piece of work in 30 days and his per day salary is 4
So, the total income of Pervez = 30* 4 = 120

Let per day salary of Sunny = 3

Similarly, Sunny can complete the same work in 50 days and his per day salary is 3
So, the total income of Sunny = 50 * 3 = 150

Let per day salary of Ashu Bhati = 2
Ashu Bhati can complete the same work in 40 days and his per day salary is 2
So, the total income of Ashu Bhati = 40* 2 = 80

Or, the ratio of total income of Pervez: Sunny: Ashu Bhati = 120: 150: 80 = 12: 15: 8
That means total income of Pervez = 12, but according to the question it is 144.
On multiplying 12 by 12, we get the original value.
So, multiply each by 12.
Hence, the total income of Pervez = 144
Total income of Sunny = 15*12 = 180
Total income of Ashu Bhati = 8*12 = 96

13) A person covers the different distances by train, bus, and car in the ratio of 4: 3: 2. The ratio of the fair is 1: 2: 4 per km. The total expenditure as a fair is Rs 720. Find the total expenditure as fair on the train.

Answer: C

Explanation:

Distance covered in the ratio T: B: C = 4: 3: 2
Fair ratio per km. T: B: C = 1: 2: 4
So, the ratio of total fair T: B: C = 4: 6: 8

Sum of the ratio of total fair = 18
But ATQ, it is 720, so multiply 18 by 40.
Now, multiply each and every ratio with 40.
The total expenditure as fair on a train = 4*40=160

14) The price of silver-biscuit is directly proportional to the square of its weight. A person broke down the silver-biscuit in the ratio of 3: 2: 1, and faces a loss of Rs 4620. Find the initial price of silver-biscuit.

7520
7530
7450
7560

Answer: D

Explanation:

Given ratio = 3: 2: 1
Or, 3x: 2x: x
The initial price= (6x)² = 36x²
After broke down the price = (3x)²: (2x)²: x² = 9x²: 4x²: x² = 14x²
After breakdown, a loss of Rs. 4620 occurs.
i.e., loss = initial price - final price
Loss = 36x² - 14x² = 22x²
22x² = 4620
Or, x2 =4620/22 = 210
The initial price of silver-biscuit = 36*210 = 7560

15) B is inversely proportional to the cube of A. If B=3, A=2. If B = 8/9. Find the value of A.

Answer: A

Explanation:

As per the question, B is inversely proportional to A³
i.e., B α 1/A³
Or, B =k/ A³
Given that, B=3, A=2
So, 3 = k/ 8, or k=24
Given that, B = 8/9
So, 8/9 = 24/A³
A³ = (9*24)/8 = 27
So, A = ³√ 27 = 3