$A$ shopkeeper sells a saree at $8 \%$ profit and a sweater at $10 \%$ discount,thereby,getting a sum of $Rs. 1008$. If she had sold the saree at $10 \%$ profit and the sweater at $8 \%$ discount,she would have got $Rs. 1028$. Find the cost price of the saree and the list price (price before discount) of the sweater (in $Rs.$).

If the following pair of equations has infinite solutions,then find the value of $k$:
$5x + 2y = k$
$10x + 4y = 3$

Four years ago,the sum of the ages of a mother and her two daughters was $x$ years. What will be the sum of their ages after two years?

Formulate the following problems as a pair of equations,and hence find their solutions:
Roohi travels $300 \ km$ to her home partly by train and partly by bus. She takes $4 \ hours$ if she travels $60 \ km$ by train and the remaining by bus. If she travels $100 \ km$ by train and the remaining by bus,she takes $10 \ minutes$ longer. Find the speed of the train and the bus separately.

In the pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if $\ldots \ldots \ldots \ldots$,then the system has infinitely many solutions.

$A$ two-digit number is obtained by either multiplying the sum of the digits by $8$ and then subtracting $5$,or by multiplying the difference of the digits by $16$ and then adding $3$. Find the number.