CUET UG 2024 — Arithmetic

A mixture contains apple juice and water in the ratio $10: \mathrm{x}$. When $36$ litres of the mixture and $9$ litres of water are mixed, the ratio of apple juice and water becomes $5: 4$. The value of $x$ is :

Arun's speed of swimming in still water is $5 \mathrm{~km} / \mathrm{hr}$. He swims between two points in a river and returns back to the same starting point. He took $20$ minutes more to cover the distance upstream than downstream. If the speed of the stream is $2 \mathrm{~km} / \mathrm{hr}$, then the distance between the two points is :

Two pipes A and B together can fill a tank in $40$ minutes. Pipe A is twice as fast as pipe B. Pipe A alone can fill the tank in :

In a $700 \mathrm{~m}$ race, Amit reaches the finish point in $20$ seconds and Rahul reaches in $25$ seconds. Amit beats Rahul by a distance of :

The least non-negative remainder when $3^{51}$ is divided by $7$ is :