Question

A television set was sold for \[Rs.{\text{ }}14,400\] after giving successive discounts of \[10\% \] and respectively. What was the marked price?

Answer 1

Hint:In this question the given is the selling rate of television set with the percentage of successive discounts. We have to find the marked price for the television set.We know that, if the cost price of an object is \[a\]. If the discount of the item is \[b\% \], the price of the object will become \[a \times \dfrac{{100 - b}}{{100}}\].Using this concept try to solve the problem.

Complete step-by-step answer:
It is given that; the selling price of the television was \[Rs.{\text{ }}14,400\]. The two successive discounts were \[10\% \] and \[20\% \] respectively. We have to find the marked price of the television.
Let us consider, the marked price of the television is \[Rs.{\text{ }}x\].
Applying the first discount \[10\% \], the price would be \[\dfrac{{90x}}{{100}}\].
Applying, the second discount \[20\% \], the would be \[\dfrac{{90x}}{{100}} \times \dfrac{{80}}{{100}}\]
The selling price of the television set was Rs. \[14,400\].
According to the problem we get,
\[\dfrac{{90x}}{{100}} \times \dfrac{{80}}{{100}} = 14400\]
Simplifying we get,
\[x = 14400 \times \dfrac{{100}}{{90}} \times \dfrac{{100}}{{80}}\]
Solving we get,
\[x = 20,000\]
Hence, the marked price of the television is \[Rs.\,20,000\].

Note:We can solve this problem in another way.
Let us consider, the marked price of the television is \[Rs.{\text{ }}100\].
Applying the first discount \[10\% \], the price would be \[90\].
Applying, the second discount \[20\% \], the would be \[\dfrac{{20}}{{100}} \times 90 = 18\]
Selling price after the second discount \[ = 90 - 18 = 72\]
When the selling price is \[72\], then marked price is \[100\]
When the selling price is \[1\], then marked price is \[\dfrac{{100}}{{72}}\]
When the selling price is \[14400\], then marked price is \[\dfrac{{100}}{{72}} \times 14400 = 20000\]
Hence, the marked price of the television is \[Rs.{\text{ }}20,000\].