Section – C
Q. No. 41-45 are based on Case Study–I, you have to answer any (4) four questions. Q. No. 46-50 are based on Case Study-II, you have to answer any (4) four questions.
Case Study-I
A book store shopkeeper gives books on rent for reading. He has variety of books in his store related to fiction, stories and quizzes etc. He takes a fixed charge for the first two days and an additional charge for subsequent day. Amruta paid ₹22 for a book and kept for 6 days; while Radhika paid ₹16 for keeping the book for 4 days.
Assume that the fixed charge be ₹x and additional charge (per day) be ₹y.
Based on the above information, answer any four of the following questions :
Given information:
Let, fixed charge for 2 days = ₹x.
and additional charge (per day) = ₹y.
Question 41
The situation of amount paid by Radhika, is algebraically represented by
- x – 4y = 16
- x + 4y = 16
- x – 2y = 16
- x + 2y = 16
Ans: (d)
The amount paid by Radhika, for keeping the book for 4 days = ₹16
Fixed charge for two days + additional charge (per day) for next 2 days = ₹16
x + 2y = 16
Question 42
The situation of amount paid by Amruta, is algebraically represented by
- x – 2y = 11
- x – 2y = 11
- x + 4y = 22
- x – 4y = 11
Ans: (c)
Sol: The amount paid by Amruta, for keeping the book for 6 days = ₹22
Fixed charge for two days + additional charge (per day) for next 4 days = ₹22.
x + 4y = 22
Question 43
What are the fixed charges for a book?
- ₹9
- ₹10
- ₹13
- ₹15
Ans: (b)
Question 44
What are the additional charges for each subsequent day for a book?
- ₹6
- ₹5
- ₹4
- ₹3
Ans: (d)
Sol: The additional charges for each subsequent day for a book = y = ₹3 (As solved in Q. 43 equation (3).)
Question 45
What is the total amount paid by both, if both of them have kept the book for 2 more days?
- ₹35
- ₹52
- ₹50
- ₹58
Ans: (c)
Sol: Total amount = Amount paid by Radhika for keeping the book for 6 days + Amruta for keeping the book for 8 days
= Radhika for keeping the book for 4 days + 2 days additional
+ Amruta keeping the book for 6 days + 2 days additional
= 16 + 2y + 22 + 2y
= 38 + 4y
= 38 + 4 × 3
= 38 + 12
= ₹50
Case Study – II
A farmer has a field in the shape of trapezium, whose map with scale 1 cm = 20 m, is given below : The field is divided into four parts by joining the opposite vertices.
Based on the above information, answer any four of the following questions :
Question 46
The two triangular regions AOB and COD are
- Similar by AA criterion
- Similar by AA criterion
- Similar by RHS criterion
- Not similar
Ans: (a)
Question 47
The ratio of the area of the ΔAOB to the area of ΔCOD, is
- 4 : 1
- 1 : 4
- 1 : 2
- 2 : 1
Ans: (b)
Question 48
If the ratio of the perimeter of ΔAOB to the perimeter of ΔCOD would have been 1 : 4, then
- AB = 2 CD
- AB = 4 CD
- CD = 2 AB
- CD = 4 AB
Ans: (d)
Question 49
If in Δs AOD and BOC, , then
Ans: (b)
Question 50
If the ratio of areas of two similar triangles AOB and COD is 1 : 4, then which of the following statements is true?
- The ratio of their perimeters is 3 : 4.
- The corresponding altitudes have a ratio 1 : 2.
- The medians have a ratio 1 : 4.
- The angle bisectors have a ratio 1 : 16.
Ans: (b)