Download App

Maths Case study (4 Marks)

Linear Equations In Two Variables · CBSE STD 9 (CBSE - English Medium). 2 questions.

Questions

Case study (4 Marks)

Take a timed test

2 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks
Our excessive dependence on motorized road transport imposes significant economic costs on society. These include congestion, road casualties, physical inactivity and ill health caused by it eg.: obesity. Cycling could substantially reduce these risks, while strengthening local economies in both urban and rural areas, supporting local businesses and boosting the economic productivity.
A bicycle is being lent at fixed charges for the first three days of week and an additional charge of each day thereafter. If fixed charges are ₹ x and per day charges are ₹ y, then based on the above information, answer the following questions:
(i) Form the linear equation, if Mr. Sam paid ₹ 27 for a bicycle kept for 7 days.
(ii) Form the linear equation, if Mr. David paid ₹30 for a bicycle kept for 6 days.
(iii) If fixed charge is ₹ 15, then find the additional charge paid by Mr. Sam for each extra day.
(iv) If per day charge for lending the bicycle is ₹ 3, find the value of fixed charge paid by Mr. David.
Answer
(i) $x+4 y=27$ $\quad$(ii) $x+3 y=30$ $\quad$(iii) ₹ 3 $\quad$(iv) ₹ 21
View full question & answer→
Question 24 Marks
Teachers and students of class IX of a school had gone to Nandan Kannan for study tour. After visiting different places of Nandan Kannan, lastly, they visited bird's sanctuary and deer park. Rohan a clever boy and keen observer. He put the question to his friends "How many birds are there and how many deer are there (at particular time) in Nandan Kannan?" Rahul's friend, Nishith gave the correct ansuer us follows:
'Nishith answered that total animals have 1000 eyes and 1400 legs.'
Image
(i) If x and y be the number of birds and deer respectively, what is the equation of total number of eyes?
(a) $x+y=1000$ $\quad$(b) $x+y=500$ $\quad$(c) $x-y=1000$ $\quad$(d) $x-y=500$
(ii) What is the equation of total number of legs?
(a) $2 x+y=70$$\quad$(b) $x+2 y=500$$\quad$(c) $x+2 y=700$$\quad$(d) $2 x-y=500$
(iii) How many birds are there in the Zoo?
(a) 1000 $\quad$(b) 5000 $\quad$(c) 300 $\quad$(d) 200
(iv) How many deer are there in the Zoo?
(a) 500 $\quad$(b) 200 $\quad$(c) 300 $\quad$(d) 700
Answer
(i) (b): Each bird has two eyes and each deer has also two eyes.
$\therefore \quad \text { Total number of eyes }=2 x+2 y$
But, it is given that the total number of eyes is 1000 .
$\therefore \quad 2 x+2 y=1000 \Rightarrow x+y=500$
(ii) (c): A bird has two legs and a deer has four legs. Therefore, number of legs of $x$ birds and $y$ deer is $2 x+4 y$. It is given that there are 1400 legs.
$\therefore \quad 2 x+4 y=1400 \Rightarrow x+2 y=700$
(iii) (d): We have,
$\quad$$x+y=500$$\quad$...(i)$\quad$ and $x+2y=700$$\quad$...(ii)
Subtgracting (i) from (ii), we obtain
$(x+2 y)-(x+y)=700-500 \Rightarrow y=200$
Putting $y=200$ in (i), we obtain $x=300$. Thus, there are 300 birds.
(iv) (b): From (iii), we obtain $y=200$. Hence, there are 200 deer.

View full question & answer→
Generate Paper FreeAll Linear Equations In Two Variables topics
Case study (4 Marks) - Maths STD 9 Questions - Vidyadip