WBCS Mains 2020 Official Paper-VI

Sneha wants to buy a piece of furniture worth $\text{Rs. }12,500$. She gets a discount of $10\%$ on it. After getting the discount, she pays $18\%$ GST. Find the total amount she will have to pay for the furniture.

If $2x^2+5y^2+2z^2-2xy-6yz=0$, then $x:y:z$ is:

A pipe can fill a tank in $16$ hours. Due to a leak in the bottom, it is instead filled in $24$ hours. If the tank is completely full, how much time will the leak take to empty it?

A man travels three-fifth of a distance $AB$ at a speed of $3x$ and the remaining distance at a speed of $2y$. If he goes from $B$ to $A$ and returns at a uniform speed of $5z$ in exactly the same total time, then which one of the following relations is correct?

A man buys milk at $\text{Rs. }60$ per litre, adds water to it, and then sells the mixture at $\text{Rs. }50$ per litre. What is the ratio of milk and water if his profit in the deal is $20\%$?