Answer :
Step-by-step explanation:
To find the cost of 1 kg of rice and 1 kg of sugar, we can set up a system of linear equations based on the given information and solve it. Here’s the process:
### Given Information:
1. The cost of 1 kg of rice and 2 kg of sugar is ₹130.
2. The cost of 1 kg of rice and 9 kg of sugar is ₹410.
### Setting Up Equations:
Let \( x \) be the cost of 1 kg of rice and \( y \) be the cost of 1 kg of sugar.
From the given information, we can write:
1. \( x + 2y = 130 \)
2. \( x + 9y = 410 \)
### Solving the Equations:
Subtract the first equation from the second to eliminate \( x \):
\[ (x + 9y) - (x + 2y) = 410 - 130 \]
This simplifies to:
\[ 7y = 280 \]
Solve for \( y \):
\[ y = \frac{280}{7} = 40 \]
Now, substitute \( y = 40 \) into the first equation to find \( x \):
\[ x + 2(40) = 130 \]
\[ x + 80 = 130 \]
\[ x = 130 - 80 = 50 \]
### Solution:
- The cost of 1 kg of rice (\( x \)) is **₹50**.
- The cost of 1 kg of sugar (\( y \)) is **₹40**.
### Verification:
1. \( x + 2y = 50 + 2(40) = 50 + 80 = 130 \)
2. \( x + 9y = 50 + 9(40) = 50 + 360 = 410 \)
Both conditions match the given information, confirming the solution is correct.
Answer: 1kg Rice=50&1kg sugar=40
Step-by-step explanation:
let, rice=X & sugar =y
Or,x+2y=130
Or,x=130-2y____Eqn(1)
Or,x+9y=410 ____Eqn(2)
putting the value X in Eqn (2)
Or,130-2y+9y=410
or,7y=410-130
or,7y=280
or,y=280/7
or,y=40
now, putting the value of y I Eqn I
x=130-2y=130-2×40=50
hense 1kg Rice =50 &1kg sugar=40 Ans