CAT: Percentages Test

After receiving two successive increments, Rohan's monthly salary became 187.5% of his original salary. If the percentage increase given in the second increment was twice the percentage increase given in the first increment, then the percentage increase in the first increment was:

The population of a city in 2020 was 100,000. It decreased by y% from 2020 to 2021 and then increased by x% from 2021 to 2022, where x and y are natural numbers. If the population in 2022 was greater than that in 2020 and the difference between x and y is 10, then the lowest possible population of the city in 2021 was:

A candidate obtains 40% of the maximum marks in a test and initially fails by 35 marks. After a re-evaluation, her score increases by 50%, but she still falls short of the passing marks by 35 marks. If her revised score is further increased by 20%, she would score 7 marks above the passing marks. What is the percentage required to pass the test?

A stationery shop has a stock of notebooks, pens and pencils, with at least one item of each type. At the beginning of a day, notebooks constitute 40% of the total stock. During the day, the shop sells half of the notebooks, 96 pens and 40% of the pencils. By the end of the day, the shop has sold 50% of the total items that it had at the beginning of the day. The smallest possible number of items in the initial stock is:

A sum of money was distributed among Arjun, Bhavna, Karan and Divya. Arjun received 20% of the total amount, while Bhavna received 40% of the amount left after Arjun's share. If Divya received 20% less than Arjun, then the ratio of the amounts received by Arjun and Karan is:

Identical soap bars are packed in two different-sized boxes, small and large. The selling price of the large box is twice the selling price of the small box. However, the selling price per gram of soap in the large box is 12% less than that in the small box. The percentage by which the weight of soap in the large box exceeds that in the small box is nearest to: