Mathematics
Case study:
Jasjit goes from Connaught Place to Qutub Minar, a distance of 13 km, by a taxi and after spending some time there, he returned back to Connaught Place by a route which is 16 km long in some other taxi.
![Jasjit goes from Connaught Place to Qutub Minar, a distance of 13 km, by a taxi and after spending some time there, he returned back to Connaught Place by a route which is 16 km long in some other taxi. Simultaneous (Linear) Equations [Including Problems], Concise Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/cm9/q1-case-study-c6-icse-class-9-concise-maths-upd-2027-1200x435.png)
Case 1: If the taxi takes a fixed charge of ₹ x and per kilometer charges as ₹ y, calculate the total fare for going from Connaught Place to Qutub Minar and then returning back.
Case 2: If the taxi takes a fixed charge of ₹ x for the first kilometer and an additional charge of for ₹ y per km for subsequent kilometers, calculate the total fare for going from Connaught Place to Qutub Minar and then returning back.
Answer
Given,
Distance (Connaught Place to Qutub Minar while going) = 13 km
Distance (Connaught Place to Qutub Minar while returning) = 16 km
Case 1:
Charges applied:
Fixed charge = ₹ x
Per km charge = ₹ y
Total fare = Fixed charge + (Distance × per km charge)
For trip while going (13 km):
Total fare = x + (13 × y) = x + 13y
For trip while returning (16 km):
Total fare = x + (16 × y) = x + 16y
Total fare of whole journey = (x + 13y) + (x + 16y)
= 2x + 29y.
Hence, total fare = ₹ (2x + 29y).
Case 2:
Charges :
Fixed charge = ₹ x for first kilometer
Per km = ₹ y for remaining distance
Going (13 km):
Charge for first km = ₹ x
Remaining distance = 12 km
Charge for remaining distance = 12y
Total fare = x + 12y
Returning (16 km):
First km = ₹ x
Remaining distance = 15 km
Charge for remaining distance = 15y
Total fare = x + 15y
Total fare of whole journey = (x + 12y) + (x + 15y)
= 2x + 27y.
Hence, total fare = ₹ (2x + 27y).
Related Questions
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Geeta paid ₹ 27 for a book kept for seven days, while Mohit paid ₹ 21 for the book he kept for five days. Find the fixed charges and the charge for each extra day.
The area of rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. However, if the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
It takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool ?
Case study:
The school administration planned to renovate the common room and asked Rohan to calculate its dimensions so that the new furniture could be arranged properly. The common room is cuboidal in shape.After collecting the necessary data, Rohan found that :
The volume of the common room is 144 cubic units.
The total surface area of the common room is 192 sq. units.
The height of the room is 3 units.
![The school administration planned to renovate the common room and asked Rohan to calculate its dimensions so that the new furniture could be arranged properly. The common room is cuboidal in shape. Simultaneous (Linear) Equations [Including Problems], Concise Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/cm9/q2-case-study-c6-icse-class-9-concise-maths-upd-2027-790x457.png)
Based on the above information answer the following:
(a) Form equations for volume and total surface area assuming x and y as the length and breadth.
(b) Solve the equations for finding the dimensions of the common room.
(c) While construction is going on, what length of the biggest iron rod can be put in the room?