Question 6 - Case Based Questions (MCQ) - Chapter 3 Class 12 Matrices

Last updated at April 16, 2024 by Teachoo

Question
There are three families A, B and C. The number of members in these families are given in the table below.

Men

Women

Children

Family A

3

2

1

Family B

2

4

2

Family C

4

3

2

The Daily expense of each man, woman and child are respectively Rs. 200, Rs. 100 and Rs. 50

Question 1

(i) The total daily expense of family A is _______.

(a) 850

(b) 900

(c) 1200

(d) 2950

Question 2

The total daily expense of family C is _______.

(a) 850

(b) 900

(c) 1200

(d) 2950

Question 3

The combined daily expense of all the women is _______.

(a) 850

(b) 900

(c) 1200

(d) 2950

Question 4

The family with highest expense is _______.

(a) A

(b) B

(c) C

(d) D

Question 5

The combined expense of men in family A and children in family C is _______.

(a) 600

(b) 700

(c) 800

(d) 900

Transcript

Question There are three families A, B and C. The number of members in these families are given in the table below. The Daily expense of each man, woman and child are respectively Rs. 200, Rs. 100 and Rs. 50
Question 1 (i) The total daily expense of family A is _______. (a) 850 (b) 900 (c) 1200 (d) 2950
Let the Number of members be denoted by matrix X
X = [■8(3& 2& 1@2& 4& 2@4& 3& 2)]
And, since Daily expense of each man, woman and child are respectively Rs. 200, Rs. 100 and Rs. 50
Let it be denoted by matrix Y
Let Y = [■8( 200 @100@50)]
Now,
Total Cost = Total members × Daily expenses
= XY
= [■8(3& 2& 1@2& 4& 2@4& 3& 2)]_(2×3) [■8( 200 @100@50)]_(3×1)
= [■8(3(200)+2(100)+1(50)@█(2(200)+4(100)+2(50)@4(200)+3(100)+2(50) ))]
= [■8(600+200+50@█(400+400+100@800+300+100))] = [■8(850@█(900@1200))]
Total Expenses = [■8(850@█(900@1200))]
Hence,
Total expenses of Family A = Rs. 850
Total expenses of Family B = Rs. 900
Total expenses of Family C = Rs. 1200
So, the correct answer is (a)
Question 2 The total daily expense of family C is _______. (a) 850 (b) 900 (c) 1200 (d) 2950
Here,
Total expenses of Family C = Rs. 1200
So, the correct answer is (c)
Question 3 The combined daily expense of all the women is _______. (a) 850 (b) 900 (c) 1200 (d) 2950
Combined expense of women
= Total women × Daily expense of woman
= (2 + 4 + 3) × 100
= 9 × 100
= Rs 900
So, the correct answer is (B)
Question 4 The family with highest expense is _______. (a) A (b) B (c) C (d) D
Hence,
Total expenses of Family A = Rs. 850
Total expenses of Family B = Rs. 900
Total expenses of Family C = Rs. 1200
Thus, Family C has the highest expense
So, the correct answer is (C)
Question 5 The combined expense of men in family A and children in family C is _______. (a) 600 (b) 700 (c) 800 (d) 900
Combined expense of men in family A and children in family C
= Expense of men in Family A + Expense of Children in Family C
= Men in Family A × Expense of Man
+ Children in Family C × Expense of Children
= 3 × 200 + 2 × 50
= 600 + 100
= Rs 700
So, the correct answer is (B)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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