Question

Kantabai bought \[1\dfrac{1}{2}\] kg tea and 5 kg sugar from a shop. She paid Rs 50 as a return fee for the rickshaw. The total expense was 700 Rs. Then she realized by ordering food online the goods can be bought with free home delivery at the same price. So next month she placed the order online for 2Kg tea and 7 kg Sugar for that she paid 880Rs. Find the rate of sugar and tea per kg.

Answer 1

Hint:Now we are given that total expense if 700 Rs. Among that 700 Rs, 50 Rs were spent on a rickshaw. So the money spent on Sugar and Tea is 700 – 50. Now we know she brought $1\dfrac{1}{2}Kg$ tea and $5kg$ sugar. Now let us take the price of tea as x and the price of sugar as y. hence we will get our first equation in x and y. The second time she buys 2kg Tea and 7 kg sugar for 880 Rs hence we get our second equation in x and y. Hence we can easily find the cost of sugar and tea by solving these two equations.

Complete step by step answer:
Now We know that Kantabai spent 700Rs in Total
This included 50 Rs rickshaw ride and the cost of sugar and tea.
Hence we can say that the money spend on Sugar and Tea is $700-50=650Rs....................(1)$
Let the price of Tea be $'x'Rs$ per Kg and the price of Sugar be $'y' Rs$ per Kg.
Now we are given that she buys $1\dfrac{1}{2}Kg$ Tea and $5kg$ sugar.
Hence from equation (1) we get
$\begin{align}
  & \left( 1\dfrac{1}{2} \right)x+5y=650 \\
 & \Rightarrow \left( \dfrac{2+1}{2} \right)x+5y=650 \\
\end{align}$
$\Rightarrow \dfrac{3}{2}x+5y=650$
Now multiplying the whole equation by 2 we get
$3x+10y=1300.............................(2)$
Now for next month Kantabai shops online
We are given that the price online is the same as the prices in the market. Hence the price of tea and sugar online is also x and y respectively.
Now for 2Kg tea and 7 kg Sugar for that, she paid 880Rs
Hence now we get
$2x+7y=880..............(3)$
Now multiplying equation (2) with 2 and equation (3) with 3 we get
$6x+20y=2600.............................(4)$
$6x+21y=2640...............................(5)$
Now subtracting equation (4) from equation (5) we get
$\begin{align}
  & 6x+21y-6x-20y=2640-2600 \\
 & \Rightarrow y=40 \\
\end{align}$
Hence we have price of Sugar is 40 Rs
Now let us substitute y = 40 in equation (3)
$\begin{align}
  & 2x+7(40)=880 \\
 & 2x=880-280 \\
 & 2x=600 \\
 & x=300 \\
\end{align}$
Hence price of sugar is 300 Rs.
Hence the price of Tea and sugar is 300Rs per kg and 50Rs per kg respectively.

Note:
 Note that in the first case the total expense is given as 700Rs. But it is not the cost of sugar and tea, as the total expense includes the rickshaw ride. Hence to get the total cost of Sugar and tea we need to subtract the cost of Rickshaw from the total expense
.