Question

Rohit got profit of 23/2% by selling his old car. However he realized that had he sold it for 58100 more,
his profit would be 38.5%. At what price did he buy the car?​

Answer 1

Rohit bought the car for Rs.215185.19 approximately.

Solution:

Given, Rohit got profit of $\frac{23}{2}$ percent by selling his old car.

However he realized that had he sold it for 58100 more, his profit would be 38.5%.

We have to find at what price did he buy the car?

Now, Let the cost price be x

Then Profit = x + (23/2% of x)

$\text { Profit }=x+\frac{\frac{23}{2}}{100} \text { of } x$

$\begin{array}{l}{=x\left(1+\frac{23}{2 \times 100}\right)} \\\\ {=x\left(\frac{200+23}{200}\right)=\frac{223}{200} x}\end{array}$

Now, Profit needed = x + (38.5% of x)

$\begin{array}{l}{\text { Profit needed }=x+\frac{38.5}{100} \text { of } x} \\\\ {=x\left(1+\frac{38.5}{100}\right)=x\left(\frac{100+38.5}{100}\right)=\frac{138.5}{100} \mathrm{x}}\end{array}$

Now, according to the given information,

Gained profit + 58100 = expected profit.

$\frac{223}{200} x+58100=\frac{138.5}{100} x$

$223 x+58100 \times 200=200 \times \frac{138.5}{100}x$

223x + 11620000 = 277x

277x – 223x = 11620000

54x = 11620000

x = 215185.185185

Hence, Rohit bought the car for 215185.19 approximately.