Solve: 

$217x+131y=913$

$131x+217y=827$ 

Use method of cross-multiplication to solve $2x+y=8$ and $3x-2y=5$

Use method of cross-multiplication to solve $x+4y=3$ and $2x+9y=5$

Seven times a two digit number is equal to four times the number obtained by reversing the order of digits. Find the number, if the difference between its digits is $3$.

$A$ and $B$ each have a certain number of mangoes. $A$ says to $B$, "If you give $30$ of your mangoes, I will have twice as many as left with you". $B$ replies, "If you give me $10$, I will have thrice as many as left with you". How many mangoes does each have?

A man rowing at the rate of $5 km$ an hour in still water takes thrice as much time in going $40 km$ down. Find the rate at which the river flows.

If $1$ is added to each of the two certain numbers, their ratio is $1:2$; and if $5$ is subtracted from each of the two numbers, their ratio becomes $5:11$. Find the numbers.