The area of a rectangle gets reduced by $80$$\mathrm{square} \mathrm{units}$ if its length is reduced by $5$ $\mathrm{units}$ and the breadth is increased by $2$$\mathrm{units}.$ If we increase the length by $10$ $\mathrm{units}$ and decrease the breadth by $5 \mathrm{units}$ then area increased by $50$ $\mathrm{square} \mathrm{units}.$ Find the length and breadth of the rectangle.
 

If in a rectangle, the length is increased by $2$ units and breadth is reduced by $2$ $\mathrm{units}$ , then the area is reduced by $28$ $\mathrm{square} \mathrm{units}.$ If the length is reduced by $1$$\mathrm{unit}$, and the breadth increased by $2$ $\mathrm{units},$ then the area increases by $33$ $\mathrm{square} \mathrm{units}.$ Find the dimensions of the rectangle.

A part of monthly hostel charges in a college is fixed and the remaining depend on the number of days one has taken food in the mess. When a student $\mathrm{A}$ takes food for $22$ days, he has to pay $₹1380$ as hostel charges whereas a student $\mathrm{B}$, who takes food for $28$ days, pays $₹1680$ as hostel charges. Find the fixed charge and the cost of food per day.

The total expenditure per month of a household consists of a fixed rent of the house and mess charges depending upon the number of people sharing the house. The total monthly expenditure is $₹3900$for $2$ people and $₹7500$ for $5$ people. Find the rent of the house and the mess charges per head per month.

A taxi's charges consist of fixed charges and the remaining depending upon the distance travelled in kilometers. If a person travels $10 \mathrm{km}$, he pays$₹68$and for travelling $15 \mathrm{km}$, he pays $₹98$. Express the above statements with the help of simultaneous equations and hence, find the fixed charges and the rate per $\mathrm{km}$.

Scooter charges consist of fixed charges and remaining depending upon the distance travelled in $\mathrm{kms}$. If a person travels $12 \mathrm{km}$, he pays$₹45$ and for travelling $20 \mathrm{km}$, he pays $₹73$. Express the above statements in the form of simultaneous equations and hence, find the fixed charges and the rate per $\mathrm{km}$.

A part of the monthly expenditure of a family is constant and the remaining varies with the price of wheat. When the price of wheat is $₹880$ per quintal, the total monthly expenditure is $₹6000$ and when it is $₹1000$ per quintal, the total monthly expenditure are $₹6360$. Find the total monthly expenditure of the family when the cost of wheat is $₹1200$ per quintal (Assuming the consumption of wheat to be same).

A man travels $370 \mathrm{km}$partly by train and partly by car. If he covers $250 \mathrm{km}$ by train and the rest by car, it takes him $4 \mathrm{hours}$. But if he travels $130 \mathrm{km}$ by train and the rest by car, he takes $18$$\mathrm{minutes}$ longer. Find the speed of the train and that of the car.