Question

by selling a stool for rupees 67.50,a carpenter loses 10%.how much percent would he gain or lose by selling it for rupees 82.50?

Answer 1

Given: Selling Price = 67.5 & Loss = 10%

 

Now, Cost Price $= 67.5 * \frac{100}{100-10}$

                           $= 75$

 

We have, Selling Price = 82.50 and Cost Price = 75.

 

So, Gain $= 82.50 - 75$

               $= 7.5$

 

∴ Gain % $= 7.5 * \frac{100}{75}$

                       $= 10$

There's an alternate method too:

Let the actual value of the stool be x.

So, if the carpenter sells the stool x rupees he neither loses, neither gains anything.

Now, 67.50 is the value x - 10% of x, that is:

⇒ 67.50 = x - 0.1 x

⇒ 67.50 = 0.9 x

∴ $x = \frac{67.50}{0.9}$
      $= 75$      

Now, Selling the stool for 82.50 rupees, the carpenter clearly would make a profit of, say y% of that actual value, i.e. y% x 75.

So using the same method,

We get, 82.50 = 75 + y × 75

⇒ y% ×  75 = 82.50 - 75

                  =7.5

We can make the further calculations if needed, but clearly 7.5 is 10% of 75.

Answer: 10% gain.

∴ The carpenter makes a gain of 10 %.

Hope This Helps :)