# CBSE Class 10 Maths - Case Study Based Questions (Set 1)

Case Study 1(source - Kendriy Vidaya Exam Paper 2020-21):

In the below given layout, the design and measurements has been made such that area of two bedrooms and Kitchen together is 95 m²

Based on the above information, answer the following questions:

Questions:

(i) Form the pair of linear equations in two variables from this situation.

(ii) Find the length of the outer boundary of the layout.

(ii) Find the area of each bedroom and kitchen in the layout.

(iv) Find the area of living room in the layout.

(v) Find the cost of laying tiles in Kitchen at the rate of Rs. 50 per sq. metres

Answers:

(i) Area of two bedrooms = 2 ✕ length ✕ breadth = 2 ✕5 ✕ x  = 10x m²

Area of kitchen = length ✕ breadth = 5y m²

ATQ , area of two bedrooms and Kitchen together = 95 m²

∴  10x + 5y = 95

⇒    2x + y = 19       --------(I)

The whole figure is a rectangle, oppsoite sides are equal.

∴  x + 2 + y = 15

⇒    x + y = 13       --------(II)

(ii) Find the length of the outer boundary of the layout.

Length of outer boundary = Perimeter = 2 (l + b) = 2 (12+ 15) = 54m

(ii) Find the area of each bedroom and kitchen in the layout.

Subtract equation (II) from (I)

2x + y = 19

-x - y  = -13

______________

x     = 6m

______________

y = 13 -x = 13 -6 = 7m

Area of bedroom = x ✕ y =  5 ✕ 6 = 30 m²

Area of kitchen = 5 ✕ 7 =35 m²

(iv) Find the area of living room in the layout.

Area of living room = (15 ✕ 7) — 30

= 105 — 30 =75 m²

(v) Find the cost of laying tiles in Kitchen at the rate of Rs. 50 per m²

Cost of lm² laying tiles in kitchen = Rs. 50

Total cost of laying tiles in kitchen = Rs. 50 ✕ 35 = Rs. 1750

Case Study 2: Ninety two students of Class X, Ravindra Public School appeared in an online quiz. There were 10 questions carry one mark each. The result insights are depicted below:

i. How many students scored marks below the median?

ii. What is the approximate sum of scores obtained by all the students who appeared in the quiz?

iii. What is the mode of the result graphically?

iv. What is the mode of the result computed empirically?

v. Three more students appeared in the quiz and scored zero marks. Will average and graphical mode change?

(a) Yes both average and mode changes

(b) Both will remain the same

(c) Only mode changes but average does not change

(d) Only average changes but mode does not change

Answers:

i. The median is the middle number in a sorted list of observations.

Total students appeared = 92.

Students scored marks below the median = 92/2 = 46

ii. Sum of scores = Σxi = mean ✕ N = 6.74 ✕ 92 = 620.08 = 620 (appox)

iii. Graphically, mode is 7 (highest bar)

iv. 3 Median = Mode + 2 Mean

Mode = 3 × 7 - 2 × 6.74 = 21 - 13.48 = 7.52

v. Only average changes but mode does not change

👉See also:

Maths High Order Thinking Skills (HOTS) Questions by CBSE

1 Marks Questions Asked in Previous Years Examination Papers

Maths Very Short Question Answers (Solved Worksheet-1)

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