Question

A dealer allows a discount of Rs.10% and still gains by 10%. What should be the marked price if the cost price is Rs.900?

Answer 1

Now let the marked price be x

We are given that the product was sold with a discount of 10 %

Hence we know that

Discount = 10% of MP

\(\Rightarrow Discount = \frac {10}{100} \times x = \frac {x}{10}\)

Whenever a discount a given our selling price is given by

⇒ SP = MP - Discount

⇒ \(SP = x - \frac {x}{10}\)

⇒ \(SP = \frac {10x-x}{10} = \frac {9x}{10}\)

It is also given that the person gains 10% on selling the product.

The gain is nothing other than 10% of the price with which he brought the product.

⇒ Gain = 10% of CP

⇒ Gain = \(\frac {10}{100} \times 900 = 90\)

Hence we get that the person gains Rs.90 on selling the product

We also know that

⇒ Gain = SP - CP

Using the known values we get

\( \Rightarrow 90=\frac{9 x}{10}-900 \)

\(\Rightarrow 90=\frac{9 x-9000}{10} \)

\(\Rightarrow 900=9 x-9000 \)

\(\Rightarrow 900+9000=9 x \)

\(\Rightarrow 9900=9 x \)

\( \Rightarrow \frac{9900}{9}=x \)

\(\Rightarrow x=1100\)

Now we get the value of x

And hence the marked price is Rs.1100.