Question

Kantabai bought \[1\frac{1}{2}\] kg tea and 5 kg sugar from a shop. She paid ₹ 50 as return fare for rickshaw. Total expense was ₹ 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. She paid ₹ 880 for that. Find the rate of sugar and tea per kg.

Answer 1

Let the rate of tea be x ₹ per kg, and that of sugar be y ₹ per kg. 

When Kantabai bought the items by going to the shop,

\[\frac{3}{2}x + 5y + 50 = 700\]

`3/2x + 5y = 700 - 50`

`3/2x xx 2 + 5y xx 2= 650 xx 2`

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 = 2600      ...(III)

6x + 21y = 2640    ...(IV)

(IV) - (III)

y = 40

Putting the value of y = 40 in (II)

3x + 10 × 40 = 1300

3x + 400 = 1300

3x = 1300 - 400

x = `900/3`

∴ x = 300

Thus, tea is 300 ₹ per kg, and sugar is 40 ₹ per kg.