Question

Kantabai bought $1\frac{1}{2}$ kg tea and 5 kg sugar from a shop. She paid Rs. 50 as return face for rickshaw. Total expense was Rs. 700. Then she realised that by ordering online the goods can be bought with free home delivery at the same price. So next month she placed the order online for 2 kg tea and 7 kg sugar. Show Rs.880 for that. Find the rate of sugar and tea per kg.

Answer 1

Let the rate of tea be $x$ Rs per kg and that of sugar be $y$ Rs per kg.
When Kantabai bought the items by going to the shop,
$\frac{3}{2}x+5y+50=700$
$\Rightarrow 3x+10y=1300$....(I)
When Kantabai bought the items online then
$2x+7y=880$......(II)
Multiplying (I) with 2 and (II) with 3 we get
$6x+20y=\mathrm{2600......}\left(III\right)$
$6x+21y=\mathrm{2640.......}\left(IV\right)$
$eq.\left(IV\right)-\left(III\right)$
$y=40$
Putting the value of y =40 in (II)
$2x+7\left(40\right)=880$
$\Rightarrow 2x=880-280=600$
$\Rightarrow x=300$
Thus, tea is at 300 Rs per kg and sugar is 40 Rs per kg.