Aarav earns a certain income this year. He decides to save some part of it and spend the remaining part. Next year, Aarav will have no income, but for every Rs. \(1\) that he saves this year, he will have Rs. \((1+r)\) available to spend next year.

In terms of \(r\), what fraction of his income should Aarav save this year so that the amount available to spend next year is equal to half the amount he spends this year?

A shopkeeper mixes two varieties of rice, A and B, and sells the mixture at Rs. \(40\) per kg. He earns a profit of \(10%\) when A and B are mixed in the ratio \(3:2\), and a profit of \(5%\) when they are mixed in the ratio \(2:3\).

The cost prices per kg of rice A and rice B are in the ratio:

On January \(1\), \(2076\), a village reservoir contains \(x\) litres of water. By December \(31\) of the same year, \(\frac{2}{7}\) of the \(x\) litres has evaporated.

This pattern continues, so by the end of each subsequent year, the reservoir loses \(\frac{2}{7}\) of the water that it contained at the beginning of that year.

During which year will the water in the reservoir be reduced to less than \(\frac{1}{4}\) of the original \(x\) litres?

Currently, a fraction \(f\) of the members of a fitness club pay an extra fee for \(24\)-hour access, where \(0
To double this fraction, the club could either convince \(x\) current members to start paying the extra fee or enroll \(y\) new members, of whom a fraction \(3f\) will pay the extra fee.

What is the value of \(y\) in terms of \(x\) and \(f\)?

Madhur Foods and Rasika Foods are two of the producers of jaggery, and each producer is either from Gujarat or Maharashtra. Each producer competes with every other producer in this group and with no one outside the group.

\(\frac{2}{3}\) of Madhur Foods's competitors are from Maharashtra, whereas more than \(\frac{2}{5}\) of Rasika Foods's competitors are from Gujarat.

Among the following choices, what is the smallest possible number of jaggery producers in this group?

A dairy shop has a mixture of milk and water. Water equal to \(10%\) of the initial mixture is added to it. After this, \(10%\) of the resulting mixture is removed.

If the final ratio of milk to water is \(3:1\), find the ratio of milk to water in the initial mixture.

Initially, \(\frac{1}{4}\) of the police officers in a city police department were women. After \(9\) women police officers joined the force, \(\frac{2}{5}\) of the police officers were women.

How many additional women police officers must join so that at least \(45%\) of the police officers are women?

Ananya bought a frying pan at a \(40%\) discount, a saucepan at a \(50%\) discount, and cutlery at a \(15%\) discount. She paid Rs. \(30\) for the frying pan and Rs. \(30\) for the saucepan, and she saved \(25%\) overall on the three items.

The amount Ananya saved on the cutlery was approximately what fraction of her total savings on the three items?

Everyone in Nandipur lives either to the east or to the west of a river. Since the turn of the century, the number of residents living to the east of the river has fallen by \(60%\), whereas the number of residents living to the west of the river has risen by \(540%\).

If the population of Nandipur is now \(240%\) of what it was at the turn of the century, what fraction of the current residents live to the east of the river?

At a currency exchange counter in Delhi, \(7\) Canadian dollars are worth \(5\) US dollars, and \(6\) US dollars are worth \(5\) euros.

One Canadian dollar is worth approximately how many euros?

At a Bengaluru-based company, the average age of all employees is \(40.0\) years, and half of the employees are men. Among employees under \(40\), the ratio of men to women is \(7:5\), and among the remaining employees, the ratio of women to men is \(3:2\).

If the average age of employees under \(40\) is \(37.0\) years, what is the average age of the remaining employees?

In a city named Surajpur, one-fourth of the houses are currently wheelchair accessible (WA). City regulations require that by \(2040\), at least one-half of the houses should be WA.

By then, one-third of the houses that are currently not WA will have been demolished, and no other houses will be demolished. Also, enough new houses will be built to increase the total number of houses in Surajpur by \(50%\).

Three-fifths of these new houses will be WA. To meet the regulation, what fraction of the houses that are currently not WA and that will not be demolished must be converted to WA?

One year ago, Arjun invested \(60%\) of his savings in a mutual fund and kept the rest in a savings account. Over the past year, the value of the mutual fund increased by \(20%\), while the amount in the savings account remained unchanged.

To buy a car today, Arjun withdraws the same amount from the mutual fund and the savings account. After the withdrawals, \(\frac{2}{3}\) of the savings that remain are in the mutual fund.

What fraction of his current savings does Arjun withdraw?

Yesterday, the ratio of male to female employees working at a company in Gurugram was \(2:3\). Today, the company hired an additional \(81\) employees, and the ratio of males to females is now \(6:5\). No employees left or were fired.

What is the least number of males that could have been working at the company yesterday?

At an Indian company, each employee is either a manager or a specialist. Each manager earns \(400%\) more per year than each specialist. The ratio of the total earnings of all managers to the total earnings of all specialists is \(1:10\).

If the annual salary of each specialist is Rs. \(77,000\), which of the following is closest to the average annual salary of all employees at the company?

At a pet park in Mumbai, the ratio of small dogs to medium dogs to large dogs is \(2:5:8\). Later in the evening, the ratio of small dogs to medium dogs doubles, and the ratio of small dogs to large dogs increases.

If the new percentage of small dogs and the new percentage of medium dogs are both integers, and there are fewer than \(30\) total dogs at the park, which of the following represents a possible new percentage of large dogs?

Mr. Sharma bought some white chocolates, which cost Rs. \(2.50\) each, and some brown chocolates, which cost Rs. \(3.50\) each, for a family celebration. The total amount paid by Mr. Sharma to the shopkeeper was Rs. \(40\).

What is the ratio of the number of white chocolates to the number of brown chocolates?

In a fictional time system, a day is divided into \(10\) new-hours. Each new-hour is divided into \(100\) new-minutes, and each new-minute is divided into \(100\) new-seconds.

In terms of actual time elapsed, what is the ratio of one new-second to one ordinary second?

Among the customers who bought at least one of tables or chairs at a furniture store in Pune, the ratio of customers who bought tables to customers who bought chairs is \(3:2\).

If half of the customers who bought chairs also bought tables, what percent of these customers bought tables?

For three positive integers \(p\), \(q\), and \(r\), the ratio of \(p\) to \(q\) is twice the ratio of \(q\) to \(r\).

Which of the following statements cannot be true?

In a flower nursery, there are two types of flowers, roses and tulips, and each flower is either blue or red. The ratio of the number of blue roses to the number of red tulips is \(3:7\). The ratio of the number of red roses to the number of blue tulips is \(2:1\).

If the ratio of the number of blue flowers to the number of red flowers is \(35:76\), then what is the ratio of the number of roses to the number of tulips?

A trader earns profits from selling bags of wheat, maize, and dry fruits. The profit from one bag of wheat is one-third of the profit from one bag of maize.

If one bag of maize generates five-fourths of the profit from one bag of dry fruits, then the profit from one bag of dry fruits is what fraction of the profit from one bag of wheat?

Mrs. Sharma has a certain number of chocolate candies that she wants to distribute among her five granddaughters. If she distributes the candies among them in the ratio \(1:4:5:7:9\), then \(1\) candy is left out. If she distributes the candies in the ratio \(2:3:3:4:5\), then \(3\) candies are left out. However, if she distributes the candies among them in the ratio \(1:2:3:7:8\), then no candy is left over.

What is the minimum number of candies that any of the five granddaughters can receive in any of the three cases?

On Sunday, at Meera's riding school in Pune, the ratio of the number of ponies to the number of horses was \(4:5\). On Monday, she bought \(35\) more animals, consisting only of ponies and horses, and the ratio of ponies to horses became \(5:8\).

Assuming that no animal left the stable or died, what is the least number of horses that were there in the stable on Sunday?

On a certain principal, the ratio of the simple interest to the compound interest, compounded annually, for \(2\) years is \(12:13\).

If the ratio of the compound interest to the simple interest for \(3\) years is \(m:n\), where \(m\) and \(n\) are co-prime, what is the value of \((m+n)\)?