The question asks to identify the Governor General of India during the Sepoy Mutiny (also known as the First War of Indian Independence or the Revolt of 1857). This requires knowledge of key historical figures and their tenures.
Correct Option: A) Lord Canning was the Governor General of India from 1856 to 1862. The Sepoy Mutiny, a major uprising against British rule, occurred in 1857, placing it squarely within his tenure. He later became the first Viceroy of India after the Government of India Act 1858.
This problem involves calculating the actual gain percentage when a trader not only sells goods at a profit but also uses faulty weights. We need to consider both sources of profit: the declared profit margin and the profit from using less weight.
Correct Option: A) 50%
The question asks to identify the personality in whose memory 'Statistics Day' is celebrated on June 29th in India. This requires knowledge of important figures in Indian statistics and their contributions.
Correct Option: B) Prasanta Chandra Mahalanobis
The Government of India celebrates 'Statistics Day' on 29th June every year to commemorate the birth anniversary of Professor Prasanta Chandra Mahalanobis. He is widely regarded as the "Father of Indian Statistics" for his pioneering work in statistical science and economic planning. His contributions include the Mahalanobis distance, large-scale sample surveys, and the design of the Second Five-Year Plan.
This is an alternating series problem. We need to identify two separate patterns within the given sequence of numbers. By analyzing the differences or relationships between alternate terms, we can predict the next number in the series.
C) 88 — The series follows two alternating patterns. The first pattern (odd-positioned terms: 7, 33, 60, ...) has differences increasing by 1 (26, 27, ...). The second pattern (even-positioned terms: 35, 63, 92, ...) also has differences increasing by 1 (28, 29, ...). The term after 92 is the next term in the first pattern, which is \(60 + 28 = 88\).
The question asks to identify the state for which Captain Amarinder Singh was the Chief Minister as of 2019. This is a factual question related to Indian politics and current affairs.
Correct Option: D) Captain Amarinder Singh was the Chief Minister of Punjab as of 2019. He served in this capacity from March 2017 to September 2021.
Express \( \frac{44}{5} \)% + \( \frac{4}{5} \)% + \( \frac{0.4}{5} \)% in decimal form.
The problem asks us to express the sum of three percentages in decimal form. We will first sum the given percentages and then convert the resulting percentage into a decimal.
The given percentages are \( \frac{44}{5} \%\), \( \frac{4}{5} \%\), and \( \frac{0.4}{5} \%\). Since they all have the same denominator, we can directly add their numerators.
\[ \text{Sum} = \left( \frac{44}{5} + \frac{4}{5} + \frac{0.4}{5} \right) \% \]\[ \text{Sum} = \left( \frac{44 + 4 + 0.4}{5} \right) \% \]\[ \text{Sum} = \left( \frac{48.4}{5} \right) \% \]Now, divide 48.4 by 5.
\[ \frac{48.4}{5} = 9.68 \]So, the sum is \(9.68\%\).To convert a percentage to a decimal, divide by 100.
\[ 9.68\% = \frac{9.68}{100} \]\[ \frac{9.68}{100} = 0.0968 \]B) 0.0968 is the correct decimal form of the given sum of percentages.
To solve this problem, we first need to determine the cost price (CP) of the article using the given selling price (SP) and profit percentage. Once the cost price is known, we can calculate the new selling price required to achieve a 30% profit.
C) Rs.260 is the correct answer. This is calculated by first finding the cost price from the initial selling price and profit, and then applying the new desired profit percentage to the cost price.
Choose the alternative that best replaces the question mark(?) in the given figure.
| 6 | 5 | 4 |
| 11 | 9 | 7 |
| ? | 56 | 33 |
Divide Rs.305 in three parts, so that \( \frac{3}{7} \) of the first, \( \frac{2}{3} \) of the second and \( \frac{4}{5} \) of the third are equal.
Find the share of the third one.
The problem asks us to divide a total amount into three parts such that specific fractions of each part are equal. We can set up equations based on this condition and then express each part in terms of a common constant. Finally, we use the total amount to find the value of this constant and then calculate the share of the third part.
Let the three parts be \(A\), \(B\), and \(C\).
The total amount is Rs.305, so we have the equation:
\[ A + B + C = 305 \]According to the problem statement, \(\frac{3}{7}\) of the first part, \(\frac{2}{3}\) of the second part, and \(\frac{4}{5}\) of the third part are equal. Let this common equal value be \(k\).
\[ \frac{3}{7}A = \frac{2}{3}B = \frac{4}{5}C = k \]From these equalities, we can express \(A\), \(B\), and \(C\) in terms of \(k\):
For the first part:
\[ \frac{3}{7}A = k \implies A = \frac{7k}{3} \]For the second part:
\[ \frac{2}{3}B = k \implies B = \frac{3k}{2} \]For the third part:
\[ \frac{4}{5}C = k \implies C = \frac{5k}{4} \]Substitute these expressions for \(A\), \(B\), and \(C\) into the total sum equation:
\[ \frac{7k}{3} + \frac{3k}{2} + \frac{5k}{4} = 305 \]To sum the fractions, find a common denominator for 3, 2, and 4, which is 12.
\[ \frac{7k \times 4}{3 \times 4} + \frac{3k \times 6}{2 \times 6} + \frac{5k \times 3}{4 \times 3} = 305 \]\[ \frac{28k}{12} + \frac{18k}{12} + \frac{15k}{12} = 305 \]\[ \frac{28k + 18k + 15k}{12} = 305 \]\[ \frac{61k}{12} = 305 \]Now, solve for \(k\):
\[ 61k = 305 \times 12 \]\[ k = \frac{305 \times 12}{61} \]\[ k = 5 \times 12 \]\[ k = 60 \]Finally, find the share of the third part, \(C\), using the value of \(k\):
\[ C = \frac{5k}{4} \]\[ C = \frac{5 \times 60}{4} \]\[ C = 5 \times 15 \]\[ C = 75 \]So, the share of the third part is Rs.75.
C) Rs.75 is the correct share for the third part, as calculated by determining the common constant \(k\) and then substituting it back into the expression for \(C\).