WBCS Mains 2018 Official Paper-VI

Through the publicity of road safety programmes, the street accidents in a state have decreased by $10\%$ in comparison to its previous year. In the present year, if the number of street accidents is $2187$, the number of street accidents that had been in the state $3$ years before was:

A hemispherical can with an internal radius of $9\text{cm}$ is completely filled with water. Someone is requested to fill this water into cylindrical bottles, each with a diameter of $3\text{cm}$ and a height of $4\text{cm}$. The number of bottles required to empty the can is:

The length of the radius of a spherical gas balloon increases from $7\text{cm}$ to $21\text{cm}$ as air is being pumped into it. The ratio of the surface areas of the balloon in the two cases is:

Total expenses of a hostel are partly constant and partly vary directly as the number of boarders. When the number of boarders is $120$ and $100$, the total expenses are $\text{Rs. }2000$ and $\text{Rs. }1700$ respectively. Find the total number of boarders if the total expense is $\text{Rs. }1880$.

Amal and Bimal started a business. Amal invested $\text{Rs. }500$ for $9$ months and Bimal invested some money for $6$ months. If they make a total profit of $\text{Rs. }69$ in a year and Bimal gets a profit share of $\text{Rs. }46$, the capital invested by Bimal in the business is: