Linear Equations Questions

If $3x+2y=7$ and $4x-y=24$, then find the value of $x-y$.

The value of $x$ for which the expressions $7x+13$ and $13x-7$ become equal is ______.

Two students appeared for an examination. One of them secured 24 marks more than the other and his marks were $65\%$ of the sum of their marks. The marks obtained by them are ______.

The average weight of $35$ apples is $50$ grams. If some apples of weight $40$ grams each were removed, then the average weight becomes $57.5$ grams. How many apples of weight $40$ grams were removed?

In a farm, in addition to $48$ hens, there are $42$ sheep and $11$ oxen with some shepherds. If the total number of feet is $224$ more than the number of heads, find the number of shepherds.

$\frac{7}{15}$ of $\frac{5}{3}$ of a number is greater than $\frac{7}{9}$ of $\frac{3}{5}$ of the same number by $9$. Find the quadruple of the number.

When Amar walks from $P$ to $Q$ and returns from $Q$ to $P$ on a cycle, it takes him $29$ minutes. By walking both ways, it takes him $49$ minutes. If he rides a cycle both ways, then what will be the total time (in minutes)?