Q1. The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10km the charge paid is rs 165 and for a journey of 18km the charge paid is rs 277.
(a) The fixed charges and charges per km respectively are ?

(b) The taxi fare for a distance of 25 km would be ?

What type of solution the pair of linear equation -3x+4y=5 and 9/2 x6y+15/2 has ?

(d) What is the value of k for which 2x+3y=7 and (k-1)x+(k+2)y=3k have infinitely many solutions.

Q2. Mr. joe decided to go to an amusement park along with his family.The cost of an entry ticket is rs 25 for children and rs 50 for adults . on that particular day attendance at the circus is 2000 and the total gate revenue is rs 70,000.

(a) If we let the number of children and adults who bought ticket on that day as x and y respectively , form the pair of linear equations describing the above situation

(b) Find the number of children and adults who bought tickets on that particular day.

Q3. Raman usually go to a dry fruit shop with his mother. He observes the following two situations.
On 1st day: The cost of 2 kg of almonds and 1 kg of cashew was Rs 1600.
On 2nd day: The cost of 4 kg of almonds and 2 kg of cashew was Rs 3000.
Denoting the cost of 1 kg almonds by Rs x and cost of 1 kg cashew by Rs y, answer the following questions.

(i) Represent algebraically the situation of day-I.

(ii) Represent algebraically the situation of day- II.

(iii)The linear equation represented by day-I, intersect the x axis at

(iv)The linear equation represented by day-II, intersect the y-axis at

(v) Linear equations represented by day-I and day -II situations, are

It is common that Governments revise travel fares from time to time based on
various factors such as inflation (a general increase in prices and fall in the
purchasing value of money) on different types of vehicles like auto, Rickshaws,
taxis, Radio cab etc. The auto charges in a city comprise of a fixed charge
together with the charge for the distance covered. Study the following
situations:
Situation 1: In city A, for a journey of 10 km, the charge paid is Rs 75 and for
a journey of 15 km, the charge paid is Rs 110.
Situation 2: In a city B, for a journey of 8km, the charge paid is Rs91 and for a
journey of 14km, the charge paid is Rs 145.

1. If the fixed charges of auto rickshaw be Rs x and the running charges be
Rs y km/hr, the pair of linear equations representing the situation is

2)  A person travels a distance of 50km. The amount he has to pay is

Refer situation 2
3. What will a person have to pay for travelling a distance of 30km?

Assertion : Pair of linear equations : 9x+3y+12=0, 8x+6y+24 =0 have infinitely many solutions.
Reanson : Pair of linear equations \(a_{1}x+b_{1}y+c_{1} =0 and a_{2}x+b_{2}y+c_{2} =0\) have infinitely many solutions, if \(\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} =\frac{c_{1}}{c_{2}}\)

Assertion : x+y-4 =0 and 2x+ky-3=0 has no solution if k=2
Reason : $$a_{1}x + b_{1}y + c_{1} and a_{2}x + b_{2}y + c_{2}$$ are consistent if \(\frac{a_{1}}{a_{2}}\neq \frac{k_{1}}{k_{2}}\)

Assertion: System of linear equation given by x-7y+16=0 and 7x-49y112=0 are dependent.
Reason: Dependent system of equations can be obtained from each other by multiplying with a suitable constant.

Assertion: If 2x+3y=12 and 3x-2y=5 then x=3 , y=2.

Reason: Method of elimination involves writing y in terms of x from any one of two equations and then putting this value of y in other equation to get value of x. Finally substituting value of x in any one equation gives value of y.

Q8. Mr. RK Agrawal is owner of a famous amusement park in Delhi.
Generally he does not go to park and it is managed by team of staff.
The ticket charge for the park is Rs 150 for children and Rs 400 for
adults.
One day Mr. Agrawal decided to random check the park and went there.
When he checked the cash counter, he found that 480 tickets were sold
and Rs 134500 was collected.

i)Let the number of children visited be x and the number of adults
visited be y.
Which of the following is the correct system of equation that
models the problem?

ii)How much amount collected if 300 children and 350 adults attended?