The question asks for the best description of 'capital gains tax' in India. We need to understand what constitutes a capital asset and what kind of income is taxed under capital gains.
B) Tax on profit from sale of a capital asset during a year. This option accurately defines capital gains tax as a tax on the profit derived from the transfer or sale of any capital asset, regardless of its type or holding period (which determines if it's short-term or long-term capital gain).
To solve this problem, we need to determine the individual work rates of D and E. Then, we combine their work rates to find their combined work rate. Finally, we use the combined work rate to calculate the total time taken to complete the work together.
Determine the time taken by D:
D can do the work in 18 days.
Determine the time taken by E:
E can do the same work in half the time D takes. So, time taken by E is:
Calculate the one-day work of D:
If D completes the work in 18 days, then in one day, D completes \(\frac{1}{18}\) of the work.
Calculate the one-day work of E:
If E completes the work in 9 days, then in one day, E completes \(\frac{1}{9}\) of the work.
Calculate their combined one-day work:
When they work together, their one-day work is the sum of their individual one-day works:
To add these fractions, find a common denominator, which is 18:
\[ \text{Combined one-day work} = \frac{1}{18} + \frac{1 \times 2}{9 \times 2} = \frac{1}{18} + \frac{2}{18} = \frac{1+2}{18} = \frac{3}{18} = \frac{1}{6} \]So, together they complete \(\frac{1}{6}\) of the work in one day.
Calculate the total time taken to finish the work together:
If they complete \(\frac{1}{6}\) of the work in one day, then they will complete the entire work (1 whole) in the reciprocal of their combined one-day work:
Correct Option: D) 6
To find the profit percentage, we first need to calculate the total cost price (CP) of all laptops and the total selling price (SP) of all laptops. Then, we can find the profit and use the profit percentage formula: \[\text{Profit Percentage} = \frac{\text{Profit}}{\text{CP}} \times 100\].
Number of laptops = 15
Cost of each laptop = Rs. 15,000
\[ \text{Total CP} = \text{Number of laptops} \times \text{Cost of each laptop} \]\[ \text{Total CP} = 15 \times 15,000 = \text{Rs. } 225,000 \]All laptops were sold for Rs. 2.97 Lakh.
We know that 1 Lakh = 100,000.
\[ \text{Total SP} = 2.97 \times 100,000 = \text{Rs. } 297,000 \]Profit is the difference between the Selling Price and the Cost Price.
\[ \text{Profit} = \text{Total SP} - \text{Total CP} \]\[ \text{Profit} = 297,000 - 225,000 = \text{Rs. } 72,000 \]The formula for profit percentage is:
\[ \text{Profit Percentage} = \frac{\text{Profit}}{\text{Total CP}} \times 100 \]\[ \text{Profit Percentage} = \frac{72,000}{225,000} \times 100 \]\[ \text{Profit Percentage} = \frac{72}{225} \times 100 \]\[ \text{Profit Percentage} = 0.32 \times 100 = 32\% \]Correct Option: D) 32%
The question asks for the year Mahatma Gandhi returned to India from South Africa. This is a factual question related to modern Indian history. Recall the key dates associated with Mahatma Gandhi's life and his struggle in South Africa and India.
C) 1915 is the correct answer. Mahatma Gandhi returned to India from South Africa on January 9, 1915.
An amount is deposited at 8% p.a. compound interest. If the first year interest is Rs.72, find the interest amount for the 2nd year.
The problem involves compound interest. We are given the interest for the first year and the annual interest rate. We need to find the interest for the second year. In compound interest, the interest for the second year is calculated on the principal amount plus the interest earned in the first year.
For the first year, compound interest is the same as simple interest. Let the principal amount be \(P\).
\[ I_1 = \frac{P \times R \times T}{100} \]\[ 72 = \frac{P \times 8 \times 1}{100} \]\[ P = \frac{72 \times 100}{8} \]\[ P = 9 \times 100 \]\[ P = \text{Rs. } 900 \]This amount will serve as the new principal for calculating the interest for the second year.
\[ \text{Amount after 1 year} = P + I_1 \]\[ \text{Amount after 1 year} = 900 + 72 \]\[ \text{Amount after 1 year} = \text{Rs. } 972 \]The interest for the second year (\(I_2\)) is calculated on the amount at the end of the first year (Rs. 972) at the same rate of 8%.
\[ I_2 = \frac{\text{Amount after 1 year} \times R \times T}{100} \]\[ I_2 = \frac{972 \times 8 \times 1}{100} \]\[ I_2 = \frac{7776}{100} \]\[ I_2 = \text{Rs. } 77.76 \]Correct Option: C) Rs. 77.76
This is an analogy question where we need to identify the relationship between the first pair of words and then apply the same relationship to the second pair to find the missing word. The relationship is often one of antonyms (opposites), synonyms, cause-and-effect, part-to-whole, etc.
Correct Option: C) Confidence
N has Rs. p more than K. The total amount available with N and K together is Rs. q. How much does K have?
\( \frac{q}{2} \) + p
2(p + q)
\(\frac{p+q}{2}\)
\(\frac{q-p}{2}\)
This problem can be solved by setting up a system of two linear equations based on the given information and then solving for the amount K has. We will represent the amounts N and K have with variables and use algebraic manipulation to find K's amount.
D) \( \frac{q-p}{2} \) is the correct expression for the amount K has, as derived from the algebraic solution.
Find the value of 'x' in x : \( \frac{3}{7} \) :: \( \frac{7}{9} \) : \( \frac{5}{9} \)
\( \frac{4}{7} \)
\( \frac{3}{2} \)
\( \frac{3}{5} \)
\( \frac{9}{7} \)
The given expression is a proportion. A proportion states that two ratios are equal. If we have a proportion \(a : b :: c : d\), it means that the ratio \(a/b\) is equal to the ratio \(c/d\). This can be written as \[\frac{a}{b} = \frac{c}{d}\], or equivalently, the product of the extremes equals the product of the means, i.e., \(a \times d = b \times c\). We will use this property to solve for 'x'.
The given proportion is:
\[ x : \frac{3}{7} :: \frac{7}{9} : \frac{5}{9} \]Rewrite the proportion in fractional form:
\[ \frac{x}{\frac{3}{7}} = \frac{\frac{7}{9}}{\frac{5}{9}} \]Simplify the right side of the equation:
\[ \frac{\frac{7}{9}}{\frac{5}{9}} = \frac{7}{9} \times \frac{9}{5} = \frac{7}{5} \]Now the equation becomes:
\[ \frac{x}{\frac{3}{7}} = \frac{7}{5} \]To solve for 'x', multiply both sides by \(\frac{3}{7}\):
\[ x = \frac{7}{5} \times \frac{3}{7} \]Perform the multiplication:
\[ x = \frac{7 \times 3}{5 \times 7} \]Cancel out the common factor of 7:
\[ x = \frac{3}{5} \]C) \( \frac{3}{5} \) is the correct value for 'x'.
The mode of a data set is the value that appears most frequently. To find the mode, we need to count the occurrences of each unique number in the given data set.
Correct Option: C) 70 — The number 70 appears 3 times, which is the highest frequency among all the numbers in the given data set.
The problem presents an alphabetical series where each term consists of two letters. We need to identify the pattern in the progression of these letters to find the missing term.
A, D, H, ?, S
Let's find the difference in their alphabetical positions:
So, the first letter of the missing term is M.
C, G, L, ?, Y
Let's find the difference in their alphabetical positions:
So, the second letter of the missing term is R.
The missing term is MR.
D) MR