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Initially, a television was being offered at a discount of 40%. The dealer reduced this discounted price further by 20% because the customer bargained. If the selling price of the television is Rs. 9600, then what is its market price?
A. Rs. 19200
B. Rs. 16000
C. Rs. 20000
D. Rs. 25000

Last updated date: 19th Jul 2024
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Hint: First we will assume the M.R.P. that is the market price of the product. Then apply a discount on it and apply further discount on the discounted price and equate the final price to Rs. 9600.

Complete step-by-step answer:
Let’s assume the market price to be Rs. $x$.
Since, it was on a discount of 40%.
We will use the formula:- Discount = \[\dfrac{{Discount\% }}{{100}} \times \] Market Price
We will now put in the given values.
So, we get:- Discount = $\dfrac{{40}}{{100}} \times x$
Simplifying the R.H.S, we get:-
Discount = $\dfrac{{4x}}{{10}}$
Now, we will use the formula:- Selling Price = S.P. = Market Price – Discount
So, we have, S.P. = $x - \dfrac{{4x}}{{10}}$.
Taking L.C.M. to simplify, we have:-
S.P. = $\dfrac{{10x - 4x}}{{10}} = \dfrac{{6x}}{{10}}$ …………(1)
We saw that the consumer bargained and got a further discount on S.P.
Discount further = 20%
We will now use the formula:- Further Discount = \[\dfrac{{Discount\% }}{{100}} \times \] S.P.
So, we get:- Further Discount = $\dfrac{{20}}{{100}} \times \dfrac{{6x}}{{10}}$
Simplifying the R.H.S,
Further Discount = $\dfrac{2}{{10}} \times \dfrac{{6x}}{{10}} = \dfrac{{12x}}{{100}}$ ……….(2)
Now, we will use the formula:- New S.P. = S.P. – Further Discount
Putting in the values we have using (1) and (2), we get:-
New S.P. = $\dfrac{{6x}}{{10}} - \dfrac{{12x}}{{100}}$
Taking L.C.M. to simplify, we have:-
New S.P. = $\dfrac{{60x - 12x}}{{100}} = \dfrac{{48x}}{{100}}$
Now, we will equate it to Rs. 9600 as we are given the final price in the question. SO we now have:-
$\dfrac{{48x}}{{100}} = 9600$
Taking 100 from denominator on L.H.S. to R.H.S.
$48x = 9600 \times 100 = 960000$
We can rewrite it as:-
$48x = 48 \times 20000$
Now, we will take 48 from L.H.S. to R.H.S.
$x = \dfrac{{48 \times 20000}}{{48}} = 20000$
Hence, the Market Price of the television is Rs. 20000.

So, the correct answer is “Option C”.

Note: There are a lot of formulae in the solution. We need to carefully use them and not mess up their sequence. We also need to be cautious that further discount is applied on discounted price, not the Market Price.