Case study problem matrix 3 chapter 3 class 12

Case study Chapter 3 (Matrix )

Case study 3:- Read the following and answer the question:(Case study problem matrix 3)

Three schools DPS, CVC and KVS decided to organize a fair for collecting money for helping the flood victims. They sold Handmade fans, Mats and plates from recycled material at a cost of ₹25, ₹ 100 and ₹50 each respectively. The number of articles sold are given as.

School/article	DPS	CVC	KVS
Handmade fans	40	25	35
Mats	50	40	50
Plates	20	30	40

(i) What is the total money (in ₹) collected by the school DPS ?

(a) 700 (b) 7,000

(ii) What is the total amount of money (in ₹) collected by schools CVC and KVS ?

(a) ₹ 14000 (b) ₹ 15,725

(iii) What is the total amount of money collected by all three schools DPS, CVC and KVS ?

(a) ₹ 15,775 (b) ₹ 14,000

(iv) If the number of Handmade fans and Plates are interchanged for all the schools, then what is the total money collected by all school ?

(a) ₹18,000 (b) ₹ 6,7520

(v) How many articles (in Total) are sold by three schools ?

(a) 230 (b) 130

Solution:(i) Answer (b)

Total money (₹) collected by the school DPS

$= \begin{bmatrix} 40 & 50 & 20\end{bmatrix}\begin{bmatrix} 25 \\ 100 \\50\end{bmatrix}$

= 40×25 + 50×100 + 20×50

= 1000 + 5000 + 1000

= ₹7,000

(ii) Answer (a)

Total amount of money collected by CVC and KVS

$= \begin{bmatrix} 25 & 40 & 30 \\ 35 & 50 & 40\end{bmatrix}\begin{bmatrix} 25 \\ 100 \\ 50\end{bmatrix}$

$= \begin{bmatrix} 25\times 25 & 40\times 100 & 30\times 50 \\ 35\times 25 & 50\times 100 & 40\times 50\end{bmatrix}$

$=\begin{bmatrix} 6,125 \\ 7,875\end{bmatrix}$

Total amount of money collected by CVC and KVS

= 6,125 + 7,875

= ₹ 14,000

(iii) Answer (c)

Total amount of money collected by all three schools

= 7,000 + 6,125 + 7,875

= ₹ 21,000

(iv) Answer (d)

After interchanging the number of Handmade fans and Plates,

We have

School/article	DPS	CVC	KVS
Handmade fans	20	30	40
Mats	50	40	50
Plates	40	25	35

Amount of collected by all schools

$= \begin{bmatrix} 20 & 50 & 40 \\ 30 & 40 & 25\\40 & 50 & 35\end{bmatrix}\begin{bmatrix} 25 \\ 100 \\ 50\end{bmatrix}$

$= \begin{bmatrix} 20\times 25 + 50\times 100+40\times 50 \\ 30\times 25 + 40\times 100+25\times 50 \\40\times 25 + 50\times 100+35\times 50 \end{bmatrix}$

$= \begin{bmatrix} 75,00 \\ 6,000 \\ 7,750\end{bmatrix}$

∴ Total money = 75,00 + 6,000 + 7,750

= ₹21,250

(v) Answer (d)

Total number of articles sold by three schools

= ( 40 + 25 + 35) + (50 +40 + 50) + (20 + 30 + 40)

= 100 + 140 + 90 = 330

Case study 1:- Read the following and answer the question(Case study problem matrix 1)

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

Solution: For solution click here

Case study 2:- Amit, Biraj and chirag were giventhe task of creating a square matrix of order 2. Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj and Chirag respectively.(Case study problem matrix 2)