Question for Practice Questions Level 1: Ratio & Proportion - 1
Try yourself:In a company, the salary of a person is directly proportional to his experience. The salary of a fresher is Rs. 20,000 per month and the salary of a person who has an experience of 2 years is Rs. 50,000. If the company follows the methodology, what will be the salary of a person who has an experience of 5 years?
Explanation
Let salary = 20,000 + k (experience)
If experience = 2 years
Salary = 50,000
50,000 = 20,000 + k(2)
⇒ k = 15,000
So, for 5 years of experience, salary will be:
20,000 + 15,000(5)
= 95,000
Question for Practice Questions Level 1: Ratio & Proportion - 1
Try yourself:The number of fruits purchased by Ms. Paul is given by the following two equations, where a, b and c are the number of apples, bananas and oranges, respectively: 3a - 4b + 2c = 0
4a - 2b - c = 0
Which of the following represents the ratio of the numbers of apples, bananas and oranges purchased by Ms. Paul?
Explanation
3a - 4b + 2c = 0 ... (1)
4a - 2b - c = 0 ... (2)
From equation (2),
c = 4a - 2b
Substituting the value of c = 4a - 2b in (1), we get
3a - 4b + 8a - 4b = 0
Or 11a = 8b
Further, c = 4a - 2b
Multiplying by 4 on both sides, we get
4c = 16a - 8b
Substituting 8b = 11a, we get
4c = 16a - 11a = 5a
Or a : b : c = a : 11a/8 : 5a/4 = 8 : 11 : 10 or 16 : 22 : 20
So, option 1 is the answer.
Question for Practice Questions Level 1: Ratio & Proportion - 1
Try yourself:The volume of a gas is directly proportional to temperature and inversely proportional to pressure. If the gas occupies 400 cubic feet volume at some pressure, then by what percentage does the pressure need to be increased so as to compress the gas into a 4 cubic feet tank at constant temperature?
Explanation
V α T/P
Since temperature is constant, therefore
V α T/P
⇒ V_{1}P_{1} = V_{2}P_{2}
400P_{1} = 4P_{2}
P_{2} = 100P_{1}
So, percentage increase
Question for Practice Questions Level 1: Ratio & Proportion - 1
Try yourself:The manager of a circus decides to buy some animals for the show. He buys 10 giraffes costing as much as 24 dogs, 16 dogs costing as much as 4 oxen and 6 oxen costing as much as 4 elephants. If the cost of 10 elephants is Rs. 1,70,000, what is the cost of a giraffe?
Explanation
Cost of a giraffe = P
10 giraffes = 24 dogs
16 dogs = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs. 1,70,000
P = Rs. [(24 × 4 × 4 × 1,70,000)/(10 × 16 × 6 × 10)]
P = Rs. (6,52,80,000/9600)
P = Rs. 6800
Question for Practice Questions Level 1: Ratio & Proportion - 1
Try yourself:Three friends, Sam, Michael and Puma went to a restaurant for lunch. Sam had $100 with him, Michael had $60 and Puma had $40. They got a bill for $104 and paid $16 as tip. They shared the total expenses in the ratio of the amounts of money each carried. If A is the difference between amount of money paid by Sam and Michael, and B is the difference between amount of money paid by Michael and Puma, then find the value of A : B.
Explanation
Ratio of amounts with Sam : Michael : Puma = 100 : 60 : 40 = 5 : 3 : 2
Let us assume that amounts spent are 5x, 3x and 2x, respectively.
A = 5x - 3x = 2x
B = 3x - 2x = x
Hence, A : B = 2 : 1 (Total expense is the redundant data in the question)
Question for Practice Questions Level 1: Ratio & Proportion - 1
Try yourself:The ratio of income of Aman to income of Raman is 4 : 3. Their expenditures are in the ratio 3 : 1. If their respective savings are Rs. 16,000 and Rs. 25,000, what is the income of Aman?
Explanation
Income of Aman = Rs. 4x
Income of Raman = Rs. 3x
Expenditure of Aman = Rs. 3y
Expenditure of Raman = Rs. y
According to question:
4x - 3y = 16,000 … (i)
3x - y = 25,000 … (ii)
Multiplying (ii) by 3 and then subtracting (ii) from (i), we get
x = 11,800
Aman's income = Rs. 4x
= Rs. 4 × 11,800
= Rs. 47,200
Question for Practice Questions Level 1: Ratio & Proportion - 1
Try yourself:Last year, the ratio between the salaries of A and B was 3 : 4. But, the ratios of their individual salaries between the last year and this year were 4 : 5 and 2 : 3, respectively. If the sum of their present salaries is Rs. 4160, then how much is the salary of A now?
Explanation
Let salary of A last year be Rs. 3s.
Salary of B last year = Rs. 4s
Let present salary of A be Rs. A and that of B be Rs. B.
So, 3s/A = 4/5 or A = 15s/4
4s/B = 2/3 or B = 6s
So, adding up the present salaries, we get (15s/4) + 6s = 4160
Or, s = 426.667
Present salary of A = Rs. A = Rs. (15/4)s = Rs. (15/4) × 426.667 = Rs. 1600
Thus, answer option (2) is correct.
Question for Practice Questions Level 1: Ratio & Proportion - 1
Try yourself:A sum of money is divided among A, B and C in the ratio 2 : 3 : 4. C gives Rs. 20 to B and B gives half of what he has now to A. Now, A and C have equal amount. What is the sum of money divided among the three?
Explanation
Suppose the shares of A, B and C are Rs. 2x, Rs. 3x and Rs. 4x, respectively.
When C gives Rs. 20 to B:
Amount with C = Rs. (4x - 20) and amount with B = (Rs. 3x + 20)
Now, B gives half of his amount to A.
Amount with A = Rs.
According to the question,
Or 4x + 3x + 20 = 8x - 40 or x = 60
Hence, total sum of money = Rs. (2x + 3x + 4x)
= Rs. 9x = Rs. (9 × 60) = Rs. 540
Question for Practice Questions Level 1: Ratio & Proportion - 1
Try yourself:The ratio of number of old employees to the new employees is 9 : 8 and the ratio of their initial to final wages is 14 : 15. What is the ratio of earlier bill of total wages to that of current bill of total wages?
Explanation
Ratio of the bill = 21 : 20
Question for Practice Questions Level 1: Ratio & Proportion - 1
Try yourself:In a factory, men, women and children were employed in the ratio 8 : 5 : 1 to finish a job and their individual wages were in the ratio 5 : 2 : 3. When 20 women were employed, the total daily wages of them all amounted to Rs. 318. Find the total daily wages paid (in rupees) to each category, respectively.