The price of 8 litre of mustard oil and 5 litre of groundnut oil together is ₹1150.If the price of mustard oil increases by 10% and that of groundnut oil by 20%, the price of the two is ₹1,310. Find out the price per litre of both the oil.
Answers
Answer:
1 litre mustrad oil - 87.5
1 litre groundnut oil - 90
Step-by-step explanation:
Assume mustard oil and groundnut oil as x and y.
1) so, 8 litre of mustard oil plus 5litre of groudnut oil = 1150
Substitute x and y for oils now:
<b>8x + 5y = 1150 --> Equation 1</b>
2) Now consider hiked price of both the oils, 10% and 20 % respectively.
8x+(8x*10/100) + 5y+(5y*20/100) = 1310
After computation it is now:
<b>22x + 15y = 3275 --> Equation 2</b>
Now solve the equation by <b>Gaussian elimination method</b>
8x + 5y = 1150
22x + 15y = 3275
Let's make y equal by multiplying equation 1 with 3.
8x + 5y = 1150 --> 24x+ 15y = 3450
Elimination of y:
24x + 15y = 3450
22x + 15y = 3275
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2x = 175
x = 87.5
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Now substitute x in any of the equation.
22*87.5 + 15y = 3275
15y = 3275-1925=1350/15 = 90.
The price per liter of mustard and groundnut oil is ₹87.5 and ₹90 respectively.
Given:
Price of 8 liters of mustard oil and 5 liters of groundnut oil = ₹1150
Increase in price of mustard oil = 10%
Increase in price of groundnut oil = 20%
New price of the two = ₹1,310
To find:
We need to find the price per liter of both the oils
Solution:
Let the price per liter of mustard oil be M and groundnut oil be G
Thus, from the information given, we can form the following two equations-
8M + 5G = 1150 ...(1)
and 8(1.1M) + 5(1.2G) = 1310
⇒ 8.8M + 6G = 1310
⇒ G = (1310 - 8.8M)/ 6
Substituting the value of G in equation 1 we get-
8M + 5(1310 - 8.8M)/6 = 1150
48M + 6550 - 44M = 6900
4M = 350
M = 87.5
Thus, G = (1310 - 8.8 × 87.5)/ 6
G = 540/6
G = 90
Hence, the price per liter of mustard and groundnut oil is ₹87.5 and ₹90 respectively.
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