हिंदी

Solve the following : Two farmers Shantaram and Kantaram cultivate three crops rice, wheat and groundnut. The sale (in Rupees) of these crops by both the farmers for the month of April and May 2016 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Solve the following :

Two farmers Shantaram and Kantaram cultivate three crops rice, wheat and groundnut. The sale (in Rupees) of these crops by both the farmers for the month of April and May 2016 is given below,

April 2016 (in ₹.)
  Rice Wheat Groundnut
Shantaram 15000 13000 12000
Kantaram 18000 15000 8000
May 2016 (in ₹.)
  Rice Wheat Groundnut
Shantaram 18000 15000 12000
Kantaram 21000 16500 16000

Find : the increase in sale from April to May for every crop of each farmer.

योग

उत्तर

Increase in sale from April to May for Shantaram:
For rice = 18000  – 15000 = 3000
For wheat = 15000 – 13000 = 2000
For groundnut = 12000 – 12000 = 0
Increase in sale from April to May for Kantaram:
For rice = 21000 – 18000 = 3000
For wheat = 16500 – 15000 = 1500
For groundnut = 16000 – 8000 = 8000

Alternate method:
Matrix form

= `[(18000, 15000, 12000),(21000, 16500, 16000)] - [(15000, 13000, 12000),(18000, 15000, 8000)]`

= `[(3000, 2000, 0),(3000, 1500, 8000)]`

∴ The increase in sales for Shantaram from April to May in each crop is ₹ 3000 (rice), ₹ 2000(wheat), 0 (groundnut) and that for Kantaram is ₹ 3000 (rice), ₹ 1500 (wheat) and ₹ 8000 (groundnut).

shaalaa.com
Application of Matrices
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Matrices - Miscellaneous Exercise 2 [पृष्ठ ८५]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
अध्याय 2 Matrices
Miscellaneous Exercise 2 | Q 4.14 | पृष्ठ ८५

संबंधित प्रश्न

Solve the following equations by inversion method.

x + 2y = 2, 2x + 3y = 3


Solve the following equations by inversion method.

2x + 6y = 8, x + 3y = 5


Solve the following equations by the reduction method.

x + 3y = 2, 3x + 5y = 4


Solve the following equations by the reduction method.

5x + 2y = 4, 7x + 3y = 5


Solve the following equations by the method of inversion:

x + y+ z = 1, 2x + 3y + 2z = 2,
ax + ay + 2az = 4, a ≠ 0.


Express the following equations in matrix form and solve them by the method of reduction:

2x - y + z = 1, x + 2y + 3z = 8, 3x + y - 4z = 1.


Express the following equations in matrix form and solve them by the method of reduction:

x + 2y + z = 8, 2x + 3y - z = 11, 3x - y - 2z = 5.


The cost of 4 pencils, 3 pens, and 2 books is ₹ 150. The cost of 1 pencil, 2 pens, and 3 books is ₹ 125. The cost of 6 pencils, 2 pens, and 3 books is ₹ 175. Find the cost of each item by using matrices.


The sum of three numbers is 6. Thrice the third number when added to the first number, gives 7. On adding three times the first number to the sum of second and third numbers, we get 12. Find the three number by using matrices.


An amount of ₹ 5000 is invested in three types of investments, at interest rates 6%, 7%, 8% per annum respectively. The total annual income from these investments is ₹ 350. If the total annual income from the first two investments is ₹ 70 more than the income from the third, find the amount of each investment using matrix method.


Solve the following equations by method of inversion.
x + 2y = 2, 2x + 3y = 3


Solve the following equation by the method of inversion.

2x – y + z = 1,
x + 2y + 3z = 8,
3x + y – 4z = 1


Express the following equations in matrix form and solve them by method of reduction.
x + 3y  = 2, 3x + 5y = 4


Solve the following equations by method of inversion : x + y – z = 2, x – 2y + z = 3 and 2x – y – 3z = – 1


State whether the following statement is True or False:

If O(A) = m × n and O(B) = n × p with m ≠ p, then BA exists but AB does not exist.


If A = `[(1, -1, 3), (2, 5, 4)]`, then R1 ↔ R2 and C3 → C3 + 2C2 gives ______


Solve the following system of equations by the method of inversion.

x – y + z = 4, 2x + y – 3z = 0, x + y + z = 2


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×