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.
 

Amit travels $760 \mathrm{km}$ to his office, partly by train and partly by car. He takes $8$ $\mathrm{hours}$ if he travels $160 \mathrm{km}$ by train and the rest by car. He takes $12$ $\mathrm{minutes}$ more if he travels$240 \mathrm{km}$ by train and the rest by car. Find the speed of the train and car separately.

A train which moves with uniform speed for a certain distance takes $6 \mathrm{hours}$less if its speed is increased by $6 \mathrm{km} \mathrm{per} \mathrm{hour},$ it would have taken $6 \mathrm{hours}$ more, had its speed been decreased by $4 \mathrm{km} \mathrm{per} \mathrm{hour}.$ Find the distance of the journey and the speed of the train.