An amount was invested at a simple rate of interest p.a. for 5 years. It would have fetched Rs.300 more had it been invested at 2% higher rate. What was the amount invested?
This problem involves simple interest. We are given a scenario where a principal amount is invested for a certain period at a simple interest rate. We then consider a hypothetical situation where the interest rate is 2% higher, leading to an additional interest of Rs. 300. We need to find the original principal amount.
B) Rs. 3,000 is the amount invested.
This is an analogy question where we need to identify the relationship between the first pair of words and apply the same relationship to the second pair to find the missing word.
A Director is the person who is primarily responsible for the creative vision and overall execution of a movie, much like an Author is for a book. The Director guides the actors, crew, and technical aspects to bring the script to life on screen.
P is 4 times faster than Q in doing a job; Q takes 27 more days than P to finish the job. If they work together, in how many days will the work be finished?
6 \( \frac{4}{5} \) days
7 \( \frac{2}{5} \) days
7 \( \frac{3}{5} \) days
7 \( \frac{1}{5} \) days
This problem involves work and time. We are given the relative speeds of two individuals, P and Q, and the difference in the time they take to complete a job individually. We need to find the time taken if they work together. We will use the concept that efficiency is inversely proportional to the time taken to complete a job.
Establish the relationship between P and Q's efficiencies:
Given that P is 4 times faster than Q, their efficiency ratio is:
Determine the ratio of time taken:
Since efficiency is inversely proportional to the time taken to complete a job, the ratio of the time taken by P to the time taken by Q will be the inverse of their efficiency ratio:
Calculate individual times:
Let the time taken by P be \(x\) days. Then, the time taken by Q will be \(4x\) days.
We are given that Q takes 27 more days than P to finish the job. So,
Calculate their combined work rate:
P's one day's work \( = \frac{1}{9} \) of the job.
Q's one day's work \( = \frac{1}{36} \) of the job.
If they work together, their combined one day's work is:
Calculate the total time taken when working together:
The total time taken to finish the job together is the reciprocal of their combined work rate:
Convert the result to a mixed fraction:
\[ \frac{36}{5} = 7 \frac{1}{5} \text{ days} \]
D) 7 \( \frac{1}{5} \) days. This matches our calculated result.
To find the area of a square when its diagonal is given, we can use the formula that relates the area to the diagonal. The area of a square can be calculated as half the square of its diagonal.
Correct Option: A) 18 sq.cm. is the calculated area of the square.
The question asks to identify the individual who is NOT an international golfer from the given options. This requires knowledge of prominent personalities in the sport of golf and other sports.
Correct Option: C) Michael Bevan is a former Australian international cricketer, famous for his role as a middle-order batsman. He is not known as an international golfer.
To find the profit margin percentage, we first need to establish a relationship between the Cost Price (CP) and Selling Price (SP) based on the given information. Then, we can calculate the profit and express it as a percentage of the Selling Price.
Understand the given relationship:
The problem states that the Cost Price (CP) is 35% of the Selling Price (SP).
Calculate the Profit:
Profit is the difference between the Selling Price and the Cost Price.
Substitute CP in the Profit equation:
Substitute the expression for CP from step 1 into the profit equation:
Calculate the Profit Margin Percentage:
Profit margin is defined as profit as a percentage of the selling price.
Substitute Profit in the Profit Margin Percentage equation:
\[ \text{Profit Margin Percentage} = \left( \frac{0.65 \times \text{SP}}{\text{SP}} \right) \times 100\% \]\[ \text{Profit Margin Percentage} = 0.65 \times 100\% \]\[ \text{Profit Margin Percentage} = 65\% \]Re-read the question carefully:
The question asks for the "profit margin in percentage". In common business terms, "profit margin" usually refers to profit as a percentage of sales (Selling Price). However, in competitive exams, sometimes "profit percentage" is used interchangeably with "profit on cost price". Let's re-evaluate based on the options provided. If the question intended "profit percentage on cost price", the calculation would be different.
Let's calculate "Profit Percentage on Cost Price" just in case, as the options are high.
\[ \text{Profit Percentage on CP} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\% \]\[ \text{Profit Percentage on CP} = \left( \frac{0.65 \times \text{SP}}{0.35 \times \text{SP}} \right) \times 100\% \]\[ \text{Profit Percentage on CP} = \left( \frac{0.65}{0.35} \right) \times 100\% \]\[ \text{Profit Percentage on CP} = \left( \frac{65}{35} \right) \times 100\% \]\[ \text{Profit Percentage on CP} = \left( \frac{13}{7} \right) \times 100\% \]\[ \text{Profit Percentage on CP} \approx 1.85714 \times 100\% \]\[ \text{Profit Percentage on CP} \approx 185.71\% \]Compare with options:
The calculated value of approximately 185.71% matches option C. This implies that the question is asking for the profit percentage calculated on the cost price, which is often referred to simply as "profit percentage" in many contexts, especially when the value is greater than 100% of the selling price.
Correct Option: C) 185.71%
To classify an enterprise as public or private sector, we need to identify the fundamental characteristic that distinguishes these two types of organizations. This distinction primarily relates to who controls and owns the enterprise.
Correct Option: D) Ownership is the fundamental criterion used to classify an enterprise as belonging to the public or private sector. If the government owns a majority stake (or full ownership), it's public. If private individuals or entities own it, it's private.
The question asks about the components that constitute Prasar Bharati, an autonomous body in India. To answer this, one needs to know the foundational structure of Prasar Bharati as established by the Prasar Bharati Act.
Correct Option: B) both AIR and Doordarshan
The question asks for the most appropriate description of ObamaCare. To answer this, one needs to understand the primary goal and impact of the Affordable Care Act (ACA), commonly known as ObamaCare.
B) Affordable medical care is the most appropriate description. The Affordable Care Act (ObamaCare) was designed to make health insurance and medical care more accessible and affordable for millions of Americans through various provisions, including subsidies, expansion of Medicaid, and regulations on insurance companies.
To find the average speed of Car Q, we first need to determine the distance covered by Car P. Once we have the distance covered by Car P, we can calculate the distance covered by Car Q, as it covers 242 km more. Since both cars travel for the same duration, we can then use the total distance covered by Car Q and the given time to find its average speed.
Calculate the distance covered by Car P:
Given:
The formula for distance is \(\text{Distance} = \text{Speed} \times \text{Time}\).
\[ \text{Distance}_P = S_P \times T_P = 66 \text{ kmph} \times 11 \text{ hours} = 726 \text{ km} \]Calculate the distance covered by Car Q:
Car Q covers 242 km more than Car P.
\[ \text{Distance}_Q = \text{Distance}_P + 242 \text{ km} = 726 \text{ km} + 242 \text{ km} = 968 \text{ km} \]Determine the time taken by Car Q:
Car Q covers the distance in the same time as Car P.
\[ T_Q = T_P = 11 \text{ hours} \]Calculate the average speed of Car Q:
The formula for average speed is \[\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\].
\[ \text{Average Speed}_Q = \frac{\text{Distance}_Q}{T_Q} = \frac{968 \text{ km}}{11 \text{ hours}} = 88 \text{ kmph} \]Correct Option: C) 88 kmph