Two departments, A and B, of an MBA coaching institute have different numbers of students. When a few students from department B shifted to department A, the strength of department A increased by \(22.5%\) and the strength of department B decreased by \(30%\). Now, what percentage of students from department A should be shifted to department B so that both departments have the same number of students?

At a management institute, \(60%\) of the students prefer case-study based learning, while the rest do not. Among those who actually prefer case-study based learning, \(80%\) say that they prefer it and the remaining students say that they do not. Among those who do not prefer case-study based learning, \(90%\) say that they do not prefer it and the remaining students say that they do. What percentage of students who say they do not prefer case-study based learning actually prefer it?

A snack manufacturer prepares a premium mixture in the ratio of peanuts:cashews:almonds as \(10:4:1\). Each packet can contain up to \(75\) nuts in total. What is the maximum percentage by which the manufacturer can reduce the number of peanuts in a packet while still ensuring that peanuts constitute more than half of the total nuts in the packet?

A manufacturing unit has two automated machines. Machine P completes one production cycle every \(18\) days, while Machine Q completes one production cycle every \(15\) days. Approximately by what percent is the number of production cycles completed by Machine Q more than the number of production cycles completed by Machine P over a \(3\)-year period?

In a college election, students vote for one among four student groups: A, B, C and D. \(25%\) of the students are committed to group B, \(25%\) to group C and \(10%\) to group D. \(10%\) of the total students are undecided and may vote for any group. \(50%\) of the students are female. Also, \(50%\) of the students committed to group D are male. Of the undecided students, half are female. Group B has no committed female supporters, while Group C has no committed male supporters. If all students except the undecided students cast their votes, what percent of the male votes will be won by group A?

In the first year of a startup venture, Partner A's earnings were \(40%\) of the combined earnings of the two partners. Partner A invested \(40%\) of her earnings in a scheme yielding \(5%\) annually, while Partner B invested \(30%\) of his earnings in a scheme yielding \(10%\) annually.

In the second year, the combined earnings of the partners increased by \(10%\) and Partner A's earnings became \(\frac{5}{6}\) of Partner B's earnings. Partner A invested \(48%\) of her earnings and Partner B invested \(50%\) of his earnings in the same schemes as before. The interest earned in the first year was withdrawn at the beginning of the second year, and no other investments were made.

By approximately what percent was the total interest earned in the second year greater than the total interest earned in the first year?

In a coaching institute, the number of female students is \(40%\) more than the number of male students. In a scholarship test, \(75%\) of the total students cleared the test. If \(4\) more male students had failed, the percentage of male students who cleared the test would have been \(85%\). If \(8\) more female students had failed, the overall percentage of students who cleared the test would have dropped to \(66\frac{2}{3}%\).

Approximately what percentage of the female students cleared the test?

A college library purchased a number of new books, all belonging to the management category, and did not acquire books from any other category. After the purchase, management books constituted \(37.5%\) of the new total number of books in the library. Before the purchase, only \(20%\) of the books in the library were management books.

By what percent did the number of management books in the library increase?

In a consumer research study, an index score is defined by the formula: \(Q=\frac{(41ab^2c^3)}{d^2}\)

where \(a\), \(b\), \(c\), and \(d\) are positive parameters. Brand Alpha's index score is \(150\%\) higher than that of Brand Beta. Also, the values of \(a\), \(b\), and \(c\) for Brand Alpha are \(60\%\) higher, \(40\%\) higher, and \(20\%\) lower respectively than those for Brand Beta. Approximately by what percent is the value of \(d\) for Brand Alpha higher or lower than that for Brand Beta?

A survey conducted in a city found that \(45%\) of all residents support a new public transport initiative, including \(60%\) of residents who have not completed school, \(50%\) of residents who have completed school but are not graduates, and \(20%\) of graduates. If \(25%\) of all residents have not completed school, what fraction of those who support the initiative are residents who have completed school but are not graduates?

Analysts predicted that \(70%\) of the eligible voters in a district would cast their votes in a municipal election and that the leading candidate would secure \(45%\) of the votes polled. In the actual election, the voter turnout rate was \(5\) percentage points higher than expected, and the leading candidate received half of the votes cast. As a result, the candidate received \(19{,}800\) more votes than analysts had predicted. If \(60%\) of the district's residents are eligible voters, how many residents does the district have?

The population of an Indian city increased from \(2\) million in the year \(2000\) to \(2.5\) million in \(2015\), while the Gross Domestic Product (GDP) of the city in \(2000\) was \(\frac{3}{8}\) less than its GDP in \(2015\). What was the approximate percentage change in the per capita GDP of the city from \(2000\) to \(2015\)?

An investor purchased units of a mutual fund on December 31st, 2010, and held them for five years. The value of the investment increased by \(20\%\) in the first year, decreased by \(25\%\) in the second year, increased by \(16\frac{2}{3}\%\) in the third year, decreased by \(11\frac{1}{9}\%\) in the fourth year, and increased by \(33\frac{1}{3}\%\) in the fifth year. On which of the following dates was the value of the investment closest to its original value?

Under a corporate health insurance scheme, an employee is required to bear the first Rs. \(450\) of medical expenses and then pay \(20\%\) of the additional expenses, subject to a maximum annual payment of Rs. \(1,350\). Any remaining expenses are fully covered by the insurance provider. Last year, if an employee paid the maximum possible amount under this scheme, what is the least amount that the insurance provider could have paid?

In a management institute, \(45%\) of the students are women. Among the students who have attended an international academic exchange programme earlier, \(25%\) are women, while among those who have not attended any such programme, \(25%\) are men. If the difference between the number of students who attended the exchange programme and those who did not is \(120\), what is the total number of students in the institute?

\(P\) is \(x%\) more than \(Q\), and \(Q\) is \((x-10)%\) less than \(R\). If \(P>R\), what is the range of values that \(x\) can take?

quantity \(A\) is \(x\%\) more than quantity \(B\) and \(A\) is also \(x\%\) of the sum of \(A\) and \(B\). What is the value of \(x\)?

Four partners A, B, C, and D divide a fund. A receives \(a\%\) of the total fund. B receives \(b\%\) of the remaining fund after A takes his share. C receives \(c\%\) of the remaining fund after A and B take their shares, and D receives the rest. D receives \(a\%\) less than what A receives, B and C receive equal amounts, and \(b=2a\).

1. What percentage of A's share is C's share? 2. If the total fund is Rs. \(1000\), what is the difference between A's share and D's share?

quantity \(A\) is \(x\%\) less than quantity \(B\), and quantity \(A\) is \(y\%\) less than quantity \(C\). Also, quantity \(C\) is \(k\%\) more than quantity \(B\). Express \(k\) in terms of \(x\) and \(y\).

A bucket contains \(a\) balls in total, made up of small balls and large balls. Overall, \(b\%\) of the balls are black. Among the small balls, \(c\%\) are black, and among the large balls, \(d\%\) are black. Find the number of small balls in the bucket.

A student plans a trip within India. During the first \(10\%\) of the total trip days, while staying in the city, he spends \(12\%\) of his total budget. He knows that he has to spend another \(35\%\) of the trip days in the city, after which he will travel to the countryside. What should be the minimum decrease in his countryside spending rate, as a percentage of his city spending rate, so that he completes the trip within the initial budget?

five employees A, B, C, D, and E earn integer amounts less than Rs. \(100\). A earns \(25\%\) more than B. C earns \(25\%\) more than A. A earns \(20\%\) more than D. E earns \(20\%\) more than A. What is the total amount earned by all five of them together?

Section B has \(50\%\) more students than Section A. The number of girls in Section A is equal to the number of boys in Section B. Also, the percentage of girls is the same in both sections. What percentage of the combined student group are boys?

A two-digit number \(ab\) is \(60\%\) of \(x\). The two-digit number formed by reversing the digits of \(ab\) is \(60\%\) more than \(x\). Find \(x\).

Three employees A, B, and C have positive salaries. A earns \(x\%\) more than B, and B earns \(y\%\) less than C. If A earns more than C, which relation between \(x\) and \(y\) must be true?