# A music system has been on sale,with 20%off.On top of that,you have a special coupon, which gives you an additional rebate of 10%. The sales tax 10%. In total,you ended up in paying Rs.792. what was the original price of the music system

2
by happyruchin

2014-10-17T23:20:30+05:30
s.p = rs. 792

sale = 20 %

let the original price be x.

20 % of x = (1/2)x

now the price is = [1-(1/5)]

=(4/5)x

rebate = 10 %

10 % of (4/5 )x

=(2/25)x

now the price is =(4/5)x-(2/25)x

=(18/25)x

sales tax = 10 %

10 % of (18/25)x = (9/125)x

now the price is = (18/25)x+(9/125)x

=(90+9)/125

=(99/125)x

therefore , (99/125)x = RS. 792

x = (792*125)/99

=RS. 1000

ANS> THE ORIGINAL PRICE IS RS. 1000
Ans is 1000
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2014-10-17T23:37:28+05:30

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Given final price = Rs. 792
Let the original price = x.
first offer given = 20%
20% of x = x×(20/100) = 0.2x
then price would become = x-0.2x = 0.8x

After that, addition rebate given = 10%
10% of 0.8x = 0.8x × (10/100) = 0.08x
then price would become = 0.8x - 0.08x = 0.72x

After that, tax added = 10%
10% of 0.72x = 0.72x × (10/100) = 0.072x
then price would become = 0.72x + 0.072 x = 0.792x

Thus 0.792x = 792
⇒ x = 792/0.792
⇒x = Rs. 1000
Thus original price is Rs. 1000.