Question

one kg of tea and 4kg of sugar together cost rupees 220. If the price of sugar is increased by 50% and the price of tea is increased by 10%, the cost would be rupees 266. Find the original cost per kilogram of each.

Answer 1

one kg of tea and 4kg of sugar together cost rupees 220
Let the original cost of tea = Rs X_____(1)
Then the original cost of 1 Kg of sugar
= Rs (220 - X) / 4________(2)
If the price of sugar is increased by 50%
Then the new cost per Kg of sugar is
[ (220 - X) / 4] + 50 (220 - X) / 4 x 100
= 55 - X/ 4 + 55/ 2 - X/ 8
= ( 165 / 2) + ( - 2X - X / 8)
= ( 165 / 2) - 3X / 8
= (660 - 3X) / 8
Cost for 4 Kg of sugar
4 (660 - 3X) / 8
= (660 - 3X) / 2________(3)
and the price of tea is increased by 10%,
New cost of tea = X + X/ 10_____(4)
the total cost would be rupees 266
Therefore, by adding (3) & (4)
[(660 - 3X) / 2] + [X + X/ 10] = 266
3300 - 15X + 10X + X = 2660
- 4X = 2660 - 3300
4X = 640
X = 640 / 4
X = 160
Therefore, the original cost of Tea is Rs 160 and original cost of 1 Kg of sugar is
(220-160) / 4
= Rs 60./ 4
= Rs 15.