Question

One kg of tea and one kg of sugar together cost Rs $130$.

If the price of tea falls by $25$% and that of sugar rises by $40$% then the price of one kg of each combined comes Rs $120$.

The original price of tea in Rs per kg is

• A. $70$
• B. $30$
• C. $50$
• D. $95.38$

Answer 1

Answer: (D)

$95.38$

Let the cost of $1kg$ of tea be $Rs.x$.

and, cost of $1kg$ of sugar be $Rs.y$.

From the given data, we have

$x+y=130$

$\Rightarrow x=130-y...\left(1\right)$

and, $(x-25\%ofx)+(y+40\%ofy)=120$

$\Rightarrow (x-\frac{25}{100}x)+(y+\frac{40}{100}y)=120$

$\Rightarrow \left(\frac{75}{100}x\right)+\left(\frac{140}{100}y\right)=120$

$\Rightarrow 75x+140y=12000$

$\Rightarrow 75(130-y)+140y=12000\left[using\right(1\left)\right]$

$\Rightarrow 9750-75y+140y=12000$

$\Rightarrow 65y=2250$

$\Rightarrow y=34.62$

Put the value of $y$ in $\left(1\right)$, we get

$x=130-34.62$

$\Rightarrow x=95.38$

So, Cost of $1kg$ tea is $Rs.95.38$.

Hence, $\text{D}$ is the correct option.