Question

Mr Sharma purchased a motorcycle for Rs 22,982.40 which included two successive discounts of 20% and 5% respectively on the basic price and then 8% sales tax on the remaining price. Find the basic price of the motorcycle.

Answer 1

Let the basic price be x 

First rebate = 20 % of x 

Cost of motorcycle after first discount = x - 20 % of x

`= "x"  - (20  "x")/100`

`= (80  "x")/100`

Second rebate = 5 % of `(80  "x")/100`

Cost of motorcycle after seoond discount = `(80  "x")/100 - 5 % "of"  (80  "x")/100`

`= (80  "x")/100  - (5/100 xx (80  "x")/100)`

`= (80  "x")/100 - (4 "x")/100`

`= (76  "x")/100`

Sales tax = 8 % of cost of motorcycle 

`= 8/100 xx (76  "x")/100 `

`= (608  "x")/10000`

Total cost = cost + sales tax 

`= (76  "x")/100 + (608  "x")/10000`

`= (8208  "x")/10000`

But total cost = Rs 22,982.40 

⇒ `(8208  "x")/10000` = Rs 22982.40

⇒ x = `(22982.40 xx 10000)/8208`

⇒ x = Rs 28000

Hence, Basic price of motorcycle =Rs 28,000