When a plot is sold for Rs. 18700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

The correct answer is “25300”.

QUESTION: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

Step by Step Solution:

In the problem, we know the selling price and loss %, but we don’t know the cost price.

Let Cost Price is X= 100%
∴ Loss = Cost price – Selling price
then,
Selling price = Cost price – Loss
Selling price = 100% – 15%
S.P = 85%

According to the problem statement

S.P = 85% = RS. 18700
Now,

85% of X = RS. 18700

\frac{85}{100}\ x\ =\ RS. 18700

x\ =\ \frac{RS. 18700}{85}\ \times\ 100

x\ =\ RS. 22000

So now we find C. P = RS. 22000
Hence,
Gain = C. P – S. P
Gain amount = RS. 22000 – RS. 18700
Gain = RS. 3300

Therefore, by final condition.

As we assumed cost price at 100%, so

Cost price = 100% = RS. 22000,
Total gain to find = 100% + 15% =115%

The new selling price to gain 15% is equal to 115% of the cost price (RS. 22000)

S.P to gain 15% = \frac{115}{100}\ \times\ RS. 22000

Selling price to gain 15% = RS. 25300

Hence, The plot must be sold at RS. 25300 to get a 15% gain.