Maths Case study (4 Marks)

Ravish was wishing to buy a new car but he didnt had enough of money. One of his friend suggested him to take a loan from XYZ bank. Influenced by his idea, he decides to take a loan of Rs. 1,18,000 and decides to repay by Rs. 1000 per month. On a further note, he decides to increasethe installment by Rs. 100 every month. Answer the following questions.

(i) What is the amount paid by him in 30th installment?
(ii)What is the total amount paid by him in 30 installments?
OR
What is the ratio of first and last installment?
(iii) If the total number of installments is 40, what is the amount paid in the last installment?3

There are two routes to travel from source A to destination B by bus. First bus reaches at B via point C and second bus reaches from A to B directly. The position of A, B and C are represented in the following graph:

Based on the above information, answer the following questions.
(1) The distance between A and B is
(ii) The distance between A and C is
(iii) If the fare for first bus is 10/km, then what will be the fare for total journey by that bus?
OR
If the fare for second bus is 15/km, then what will be the fare to reach to the destination by
this bus?

Amit was playing a number card game. In the game, some number cards (having both +ve or-ve
numbers) are arranged in a row such that they are following an arithmetic progression. On his first turn, Amit picks up 6th and 14th card and finds their sum to be -76. On the second turn he picks up 8th and 16th card and finds their sum to be -96.ased on the above information, answer the following questions.
(i) What is the difference between the numbers on any two consecutive cards?
(ii) The number on first card is,
(iii) What is the number on the 19th card?
OR
What is the number on the 23rd card?

During the covid period, everyone started using his/her savings. Gauri and Sheetal also used her
savings which they both saved in the past few years. Here is the saving pattern of both of the girls for the last 15 weeks. Gauri saved in a pattern of Rs. 10 in first week, Rs. 12 in second week, Rs.14 in third week and so on while Sheetal saved Rs. 10 in first week, Rs. 13 in second week, Rs.16 in third week and so on.

(i)What is the amount saved by Gauri after 15 weeks?
(ii) What is the difference in total saving of Gauri and Sheetal 10th week?
OR
What is the difference in saving of Gauri and Sheetal at the end of 15 weeks?
(iii) Who saved more?

The diagram shows the plans for an area outside the city. The area is going to be built and
constructed to expand the main city's domain. The land is to be used carefully with a proper
planning and executions. A map as shown in the above figure is sketched to be built. It has
educational premises near the housing area. Also, a library and a skate park are planned for the
extra activities and refreshments for the people of the city. Refer to the information and image,imagining the outer area as a cartesian plane. (Distances measured are in units)

(i)How far apart is the school from home
(ii) Find the area for the figure formed from joining line segments between home, school and
library.
OR
Find the area for the figure formed from joining
line segments between skate park, school and library.
(iii) Locate the position of home from skate park.

Siya being a plant lover came up with an idea of opening a nursery during the lockdown and she
bought a few plants with pots. She wants to place pots in such a way that number of pots in row
one is 3, pots in row second is 5 and in third is 7 and so on.

(i) What is the difference in number of pots increasing per row?
(ii) If Siya wants to place 120 pots, how many rows will it require?
OR
Find the difference in number of pots placed in third and eighth row.
(iii)How many pots were placed in the 10th row?

A group of mosquitoes were buzzing around in the playground at the evening. The playground is
considered in the region of the cartesian coordinate system where we mark a point on a graph by
how far along and how far up it is. The left-right (horizontal) direction is commonly called X-axis.The up-down (vertical) direction is commonly called Y-axis. Now, if two mosquitoes travel by the same path of coordinates, they will eventually collide and could not fly ahead. So, to ensure that each mosquito has its own unique path of travel. Refer the point O as origin.

(i)What will be the coordinates for the mosquito that flies in the middle of the playground ?
(ii)What is the distance between the two mosquitoes marked on the graph ?
OR
What is the difference between the distance of the two points marked on the graph
(iii) What is the value of ordinate for the mosquito flying just 1 unit below (4,3) ?

Four friends Abhay, Ash, Debi and Chen planted their samplings of Lily, Rose, Tulip and
Orchid respectively as shown in the following figure. Ken also wanted to plant his sampling of aster in this area. The assistant instructed all five of them to plant their samplings in a rranged manner. So, they ended up planting their samplings in the rectangular shape .Here Lily, Rose, Tulip, Orchid and Aster are as Sampling A, B, C, D and E respectively. Refer to the image and information given above and answer the following questions.

(i) Find the distance between Lily and Tulip's sampling.
(ii) Find the area of the parallelogram formed
OR
Find the area of ∆???
(iii) Find the distance between Lily and Orchid's sampling.

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Read the above information and answer the below questions.
(i) What is the height of the building ?
(ii)Find the distance he walked towards the building?
OR
Draw a schematic diagram for the above instruction
(iii)What is the distance between the foots of the building and the point before he
started walking

The Class X students of a secondary school in Krishinagar have been allotted a
rectangular plot of land for their gardening activity. Sapling of Gulmohar is planted
on the boundary of the plot at a distance of 1 m from each other. There is a triangular
grassy lawn inside the plot as shown in Fig. The students have to sow seeds of flowering
plants on the remaining area of the plot.

Based on the above information, answer the following questions.
(i) Considering A as the origin, what are the coordinates of A?
(ii) What are the coordinates of P?
(iii) What are the coordinates of R?
OR
What are the coordinates of D?

RPVV, Suraj Mal organised Sports Day in which one of the event is 100 m race. Participants
have to run in the rows which are marked at a distance of 1 metre as shown in the figure. At
one time the participants are at position A, B, C, D. A has covered half the distance PQ, B has
covered 1/4th distance PQ, C has covered the distance PQ, D has covered half the distance
PQ. Considering P as origin, answer the questions given below the diagram.

Based on the above information, answer the following questions.
(i) On joing A, B, C, D which figure you will get?
(ii) What area is enclosed by ABCD ?
(iii) If another participant at E could not run due to some shoe problem, what are the co-odinates of E
OR
In what ratio B divides AE?

The ECO Club of a senior secondary school in Rohini have to make a Herbal
Garden in a rectangular plot of a land (See figure). Saplings of Tulsi are planted
on the boundary at a distance of 1 m from each other. There is a square land
inside the plot as shown in the figure for planting ‘ALOEVERA’. The students
are to sow seeds of other herbal pants on the remaining area of the plot.
Answer the questions given below the diagram:

Based on the above information, answer the following questions.
(i) Considering A as the origin, what are coordinates of M?
(ii) What are the coordinates of D?
(iii) What is the distance MO?
OR
The mid point of PN is

Siya being a plant lover came up with an idea of opening a nursery during the lockdown and she
bought a few plants with pots. She wants to place pots in such a way that number of pots in row
one is 3, pots in row second is 5 and in third is 7 and so on.

(i) What is the difference in number of pots increasing per row?
(ii) If Siya wants to place 120 pots, how many rows will it require?
OR
Find the difference in number of pots placed in third and eighth row.
(iii)How many pots were placed in the 10th row?

Alia and Shagun are friends living on the same street in Patel Nagar. Shagun's house is at
the intersection of one street with another street on which there is a library. They both study
in the same school and that is not far from Shagun's house. Suppose the school is situated
at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C.

Based on the above information, answer the following questions.
(i) How far is the library from Shagun's house?
(ii) How far is the library from Alia's house?
(iii) How far is the school from Alia's house than Shagun's house?
OR
Tell the type of Triangle ABC forms on the basis of side.

A round clock is traced on a graph paper as shown below The boundary intersect the
coordinate axis at a distance of 4/3 units from origin.

Based on the above information, answer the following questions.
(i) Circle intersect the positive y-axis at
(ii)The radius of the circle is
(iii)The area of the circle is
OR
If (1,√7/3)is one of the ends of a diameter, then its other end is

Satellite image of a colony is shown below. In this view, a particular house is pointed out by a flag, which is situated at the point of intersection of x and y-axes. If we go 2 cm east and 3 cm north from the house, then we reach to a Grocery store. If we go 4 cm west and 6 cm
south from the house, then we reach to a Electrician's shop. If we go 6 cm east and 8 cm
south from the house, then we reach to a food cart. If we go 6 cm west and 8 cm north from
the house, then we reach to a bus stand:

Based on the above information, answer the following questions.
(i) The distance between grocery store and food cart is
(ii) The distance of the bus stand from the house is
(iii) If the grocery store and electrician's shop lie on a line, the ratio of distance of house from grocery store to that from electrician's shop, is
OR
The ratio of distances of house from bus stand to food cart is

Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is.
The left-right (horizontal) direction is commonly called X-axis. The up-down (vertical) direction
is commonly called Y-axis. Answer the questions for the given info
.(i) Find the area of triangle shown in the image.
(ii) Can you say that O, R and S are collinear ? Prove it.
OR
Calculate the ratio in which P divides the line (0,2) and Q?
(iii) Find the area of the figure shown in the image.