Objective Function

Q. A three-wheeler scooter charges Rs. 10 for the first kilometer and Rs. 4.50 each for every subsequent kilometer. For a distance of x km, an amount of Rs. y is paid. Write the linear equation representing the above information.

Q. Every six months, price of petrol increases at the rate of Rs 4 per litre. Taking price of petrol in Dec, 2011 as x and present price of petrol as y, form a linear equation showing amount spent on petrol in Dec, 2011. Also, due to continuous rise in the petrol price, people are shifting towards CNG whose price increases at the rate of Rs 3 per litre in a year. Form a linear equation taking price of CNG in Dec, 2011 as a and in Dec, 2012 as b.

Q. Write a linear equation in two variables to represent the statement Four times the cost of a table is equal to seven times the cost of a chair. From the graph of above linear equation, find the cost of one chair if the cost of the table is ₹1050.

Q. A number is 27 more than the number obtained by reversing its digits. If its units and tens digit are x and y respectively, write the linear equation representing the above statement.

Q.

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

(Take the cost of a notebook to be Rs x and that of a pen to be Rs y.)

Q. A three-wheeler scooter charges Rs 15 for first kilometer and Rs 8 each for every subsequent kilometer. For a distance of x km, an amount of Rs y is paid. Write the linear equation representing the above information.

Q.

Form the pair of linear equations in the following problem and find their solution (if they exist) by any algebraic method:

Yash scored $40$ marks in a test, getting $3$ marks for each right answer and losing $1$ mark for each wrong answer. Had $4$ marks been awarded for each correct answer and $2$ marks been deducted for each incorrect answer, then Yash would have scored $50$ marks. How many questions were there in the test?

Q.

A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:

Each machine is available for a maximum of 6 hours per day. The profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5. We want to maximize the profit. Let x and y toys of type A and type B respectively be manufactured in a day. What is the objective function for this linear programming problem?

1. 7.5x + 5y

2. 2x+y -60

3. 2x+y<60

4. 2x+3y-120

Q.

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Aarushi paid $Rs.27$ for a book kept for seven days. If fixed charges are $Rs.x$ and per day charges are $Rs.y$. Write the linear equation representing the above information.

Q. Charges for borrowing a cycle is Rs.20 per day for the first 5 days and later Rs.50 per day.If the total amount is y and no.of days x ​, write linear equation for this.

Q. The ratio of the present ages of mother and son is 12 : 5. The mother's age, at the time of birth of the son was 21 years. Find their present ages.

Q. The total runs scored by two batsmen in a one-day cricket match is 215. Express this information in the form of a linear equation in two variables.