Question

One kg of tea and one kg of sugar together cost $95$. If the price of tea falls by $10\%$ and that of sugar rises by $20\%$, then the price of one kg of each combined comes to Rs.$90$. Find the original price of tea.

Answer 1

Let the cost of kg of tea $=Rs.X$

Cost of Kg of sugar $=Rs.Y$

From the given data

$x+y=95$ ……………………..(1)

And,

$(x-10\%x)+(y+20\%y)=90$

$=(x-\frac{10}{100}x)+(y+\frac{20}{100}y)=90$

$\frac{9x}{10}+\frac{6y}{5}=90$

$9x+12y=900$

$3x+4y=300$ ………………….(2)

Solving (1) and (2) we get

$x=80$

$y=15$

Cost of 1kg of Tea $=Rs.80$