Question

One kg of tea and one kg of sugar together cost Rs $95$ 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 $90$ The original price of tea in Rs per kg is

• A. Rs $72$
• B. Rs $55$
• C. Rs $60$
• D. Rs $80$

Answer 1

The correct option is D Rs $80$

Let the cost of tea be Rs x/kg & that of sugar be Rs y/kg.

Then, by the given condition,

x+y=95............(i).

Now the cost of tea falls by 10%.

$\therefore$ The new cost=$x-x\times \frac{10}{100}=\frac{9x}{10}$ and

the cost of sugar rises by 20%.

$\therefore$ The new cost=$y+y\times \frac{20}{100}=\frac{12y}{10}$

$\therefore$ The total of the new cost of tea & sugar

=$\frac{9x}{10}+\frac{12y}{10}=\frac{9x+12y}{10}=90.$

(by thsecond condition)

i.e 9x+12y=900............(ii)

$\left(i\right)\times 12⟶12x+12y=\mathrm{1140......}\left(iii\right).\left(iii\right)-\left(ii\right)⟶3x=240⟹x=Rs80/kg.$

So the original price of the tea is Rs $80$/kg.