Question

An electronics dealer offers a discount of 10% on the marked prices of electronics. He still makes a profit of 20%. If his gain on the sale of one electronic item is Rs. 4500, find the marked price of the article.

Answer 1

Hint: Assume that the marked price on the electronics is x. Hence find the cost at which he sells the articles and hence find the cost price of each article in terms of x. Using $gain\%=\dfrac{gain}{C.P}\times 100$ find the cost price of the articles. Equate this cost price to the expression of cost price in terms of x. Solve for x. The value of x gives the marked price on the electronics. Verify your answer.

Complete step-by-step answer:
Let the marked price on the electronics be x.
Since the shopkeeper offers a discount of 10% on the marked price, the cost at which he sells the electronics is $x-\dfrac{10}{100}x=\dfrac{9x}{10}$
Also, we know that $gain\%=\dfrac{gain}{C.P}\times 100$
Given the gain% he makes on selling the electronics is 20% and the amount gained on selling 1 item is Rs. 4500, we have
$20=\dfrac{4500}{C.P}\times 100$
Hence, we have
$C.P=\dfrac{4500}{20}\times 100=22500$
But, we have
$S.P=\dfrac{9x}{10}$
We know that $gain=S.P-C.P$
Hence, we have
$C.P=\dfrac{9x}{10}-4500$
Hence, we have
$\dfrac{9x}{10}-4500=22500$
Adding 4500, we get
$\dfrac{9x}{10}=27000$
Multiplying both sides by 10, we get
$9x=270000$
Dividing both sides by 9, we get
$x=30000$
Hence the marked price on each article is Rs. 30,000.

Note: Verification:
The cost at which the article is sold is $30000-\dfrac{10}{100}\times 30000=30000-3000=27000$
Amount gained on selling each article is Rs 4500
Hence, the cost price of each article is $27000-4500=22500$
Hence, we have
Gain% $=\dfrac{4500}{22500}\times 100=20$
Hence gain% = 20%
Hence our answer is verified to be correct.