Question

If 6kg of sugar and 5kg of tea together cost Rs.209 and 4kg of sugar and 3kg of tea together cost Rs.131, then the cost of 1kg sugar and 1kg of tea are respectively
A) Rs.11 and Rs.25
B) Rs.12 and Rs.20
C) Rs.14 and Rs.20
D) Rs.14 and Rs.25

Answer 1

Hint:
We’ll first consider 2 variables. FIrst will represent 1kg sugar and the second one will denote 1kg tea. Then we’ll make 2 linear equations in those variables and in the end we’ll solve those equations to get their values.

Complete step by step solution:
We are given that 6kg of sugar and 5kg of tea together cost Rs.209
Also, the cost of 4kg of sugar and 3kg of tea together is Rs.131
We need to find the cost of 1kg of sugar and 1kg of tea.
Let 1kg sugar be denoted by x and 1kg tea be denoted by y.
So, we can write the given data in form of equation as: $6x + 5y = 209$ and $4x + 3y = 131$
For solving these equations for the value of x and y, we will use the substitution method for solving linear equations.
By re – arranging the equation $4x + 3y = 131$, we can write $x = \dfrac{{131 - 3y}}{4}$
Substituting the value of x in the equation $6x + 5y = 209$, we get
$
   \Rightarrow 6\left( {\dfrac{{131 - 3y}}{4}} \right) + 5y = 209 \\
   \Rightarrow 6\left( {131 - 3y} \right) + 20y = 836 \\
   \Rightarrow 786 - 18y + 20y = 836 \\
   \Rightarrow 2y = 50 \\
   \Rightarrow y = \dfrac{{50}}{2} = 25 \\
 $
Substituting the value of y in the equation $x = \dfrac{{131 - 3y}}{4}$, we get
$ \Rightarrow x = \dfrac{{131 - 3\left( {25} \right)}}{4} = \dfrac{{131 - 75}}{4} = \dfrac{{56}}{4} = 14$

Therefore, the value of 1kg of sugar is Rs.14 and the value of 1kg of tea is Rs.25
Hence, option (D) is correct.

Note:
In this question, you may go wrong while using the substitution method for calculation of x and y because we are required to substitute the value of x in terms of y from one equation into the other. You can also solve this question using the elimination method by multiplying the equation $6x + 5y = 209$ by 4 and $4x + 3y = 131$ by 6 and then simplifying them for the value of x and y.