Question 1 - Case Based Questions (MCQ) - Chapter 3 Class 12 Matrices

Last updated at May 29, 2023 by Teachoo

A manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below

Market

Products (in numbers)

Pencil

Eraser

Sharpener

A

10,000

2000

18,000

B

6,000

20,000

8,000

If the unit Sale price of Pencil, Eraser and Sharpener are Rs. 2.50, Rs. 1.50 and Rs. 1.00 respectively, and unit cost of the above three commodities are Rs. 2.00, Rs. 1.00 and Rs. 0.50 respectively, then, Based on the above information answer the following:

Question A manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below If the unit Sale price of Pencil, Eraser and Sharpener are Rs. 2.50, Rs. 1.50 and Rs. 1.00 respectively, and unit cost of the above three commodities are Rs. 2.00, Rs. 1.00 and Rs. 0.50 respectively, then, Based on the above information answer the following:
Question 1 Total revenue of market A (a) Rs. 64,000 (b) Rs. 60,400 (c) Rs. 46,000 (d) Rs. 40,600Let the sales of Pencil, Eraser and Sharpener be denoted by matrix X
X = [■8(10,000&2,000&18,[email protected],000&20,000&8,000)]
Let the unit sale price of Pencil, Eraser and Sharpener be denoted by matrix Y
Let Y = [■8( 2.50 @[email protected])]
Now,
Total Revenue = Total sales × Unit sales price
= XY
= [■8(10,000&2,000&18,[email protected],000&20,000&8,000)]_(2×3) [■8([email protected]@1.00)]_(3×1)
= [■8(10,000(2.50)+2,000(1.50)+18,000(1)@6,000(2.50)+20,000(1.50)+8,000(1) )]
= [■8(25,000+3,000+18,[email protected],000+30,000+8,000)] = [■8(46,[email protected],000)]
Total Revenue = [■8(46,[email protected],000)]
Hence,
Total revenue of Market A = Rs. 46,000
Total revenue of Market B = Rs. 53,000
So, the correct answer is (c)
Note:
We cannot do YX
YX = [■8([email protected]@1.00)]_(3×1) [■8(10,000&2000&18,[email protected],000&20,000&8,000)]_(2×3)
Since, orders don’t match, YX is not possible
Question 2 Total revenue of market B (a) Rs. 35,000 (b) Rs. 53,000 (c) Rs. 50,300 (d) Rs. 30,500
Total revenue of Market B = Rs. 53,000
So, the correct answer is (b)
Question 3 Cost incurred in market A (a) Rs. 13,000 (b) Rs. 30,100 (c) Rs. 10,300 (d) Rs. 31,000
Let the unit cost price of Pencil, Eraser and Sharpener be denoted by matrix Z
Let Z = [■8( 2.00 @[email protected])]
Now,
Total Cost = Total sales × Unit cost price
= XZ
= [■8(10,000&2000&18,[email protected],000&20,000&8,000)]_(2×3) [■8([email protected]@0.50)]_(3×1)
= [■8(10,000(2.00)+2000(1.00)+18,000(0.50)@6,000(2.00)+20,000(1.00)+8,000(0.50) )]
= [■8(20,000+2,000+9,[email protected],000+20,000+4,000)]
= [■8(𝟑𝟏,𝟎𝟎𝟎@𝟑𝟔,𝟎𝟎𝟎)]
∴ Total cost of Market A = Rs. 31,000
So, the correct answer is (d)
Question 4 Profit in market A and B respectively are (a) (Rs. 15,000, Rs. 17,000) (b) (Rs. 17,000, Rs. 15,000) (c) (Rs. 51,000, Rs. 71,000) (d) ( Rs. 10,000, Rs. 20,000)
Now,
Profit = Revenue – Cost
= [■8(46,[email protected],000)] – [■8(31,[email protected],000)]
= [■8(𝟏𝟓,𝟎𝟎𝟎@𝟏𝟕,𝟎𝟎𝟎)]
Thus,
Profit in Market A = Rs. 15,000
Profit in Market B = Rs. 17,000
So, the correct answer is (a)
Question 5 Gross profit in both market (a) Rs. 23,000 (b) Rs. 20,300 (c) Rs. 32,000 (d) Rs. 30,200
Now,
Profit in Market A = Rs. 15,000
Profit in Market B = Rs. 17,000
Gross profit in both market = Rs 15,000 + Rs 17,000
= Rs 32,000
So, the correct answer is (c)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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