Question

One kg of tea and one kg of sugar together cost Rs $190$ If the price of tea falls by $10$% and that of sugar by rises by $20$% then the price of one kg of each combined comes Rs $180$ The original price of tea in Rs per kg is

• A. Rs $72$
• B. Rs $144$
• C. Rs $55$
• D. Rs $160$

Answer 1

The correct option is D Rs $160$

Let original price of one kg of tea $=xRs$

Then, Original price of one kg of sugar $=190-xRs$

Price of tea falls by 10%

So, New price of tea $=x-10\%ofx=\frac{9x}{10}$

Price of sugar rises by 20%

So, New price of sugar $=(190-x)+20\%of(190-x)$

$=190-x+38-\frac{x}{5}$

$=228-\frac{6x}{5}$

According to question, Sum of new prices = 180 Rs

$\therefore \frac{9x}{10}+228-\frac{6x}{5}=180$

$\Rightarrow 228-\frac{3x}{10}=180$

$\Rightarrow \frac{3x}{10}=48$

$\therefore x=160$

Hence, Original price of tea $=x=160Rsperkg$