Question

A washing machine is marked at Rs. 7500. The dealer allows successive discounts of 8%, 5%, and 2% on it. What is the net selling price (rounded to the nearest integer)?

Answer 1

Hint: The marked price of the washing machine is Rs. 7500. The dealer allows successive discounts of 8%, 5%, and 2% on it. The discount price after the discount of 8% is 8% of Rs. 7500. The net price after \[{{1}^{st}}\] discount = Marked price – Discounted price. The second discount is 5% on the net price after \[{{1}^{st}}\] discount. The discounted price after the discount of 5% is 5% of Rs. 6900. The net price after \[{{2}^{nd}}\] discount = The net price after \[{{1}^{st}}\] discount – Discounted price. The discounted price after the discount of 2% is 2% of Rs. 6555. The net price after \[{{3}^{rd}}\] discount = The net price after \[{{2}^{nd}}\] discount – Discounted price. Now, solve it further and get the price after \[{{3}^{rd}}\] discount.

Complete step-by-step answer:
According to the question, A washing machine is marked at Rs. 7500. The dealer allows successive discounts of 8%, 5%, and 2% on it.
The marked price of the washing machine = Rs. 7500 …………………………….(1)
The first discount is 8% on the marked price.
From equation (1), we have the marked price.
The discounted price = 8% of Rs. 7500 = Rs. \[\dfrac{8}{100}\times 7500\] = Rs. \[600\] ………………….(2)
The net price after \[{{1}^{st}}\] discount = Marked price – Discounted price ……………………………..(3)
From equation (1), equation (2) and equation (3), we get
The net price after \[{{1}^{st}}\] discount = \[\text{Rs}\text{. }\left( 7500-600 \right)=\,\text{Rs}\text{.}\,6900\] ………………………(4)
The second discount is 5% on the net price after \[{{1}^{st}}\] discount.
From equation (4), we have the net price after \[{{1}^{st}}\] discount.
The discounted price = 5% of Rs. 6900 = Rs. \[\dfrac{5}{100}\times 6900\] = Rs. 345 ………………….(5)
The net price after \[{{2}^{nd}}\] discount = The net price after \[{{1}^{st}}\] discount – Discounted price ……………………………..(6)
From equation (4), equation (5) and equation (6), we get
The net price after \[{{2}^{nd}}\] discount = \[\text{Rs}\text{. }\left( 6900-345 \right)=\,\text{Rs}\text{.}\,6555\] ………………………(7)
The third discount is 2% on the net price after the \[{{2}^{nd}}\] discount.
From equation (7), we have the net price after \[{{2}^{nd}}\] discount.
The discounted price = 2% of Rs. 6555 = Rs. \[\dfrac{2}{100}\times 6555\] = Rs. 131.1 ………………….(8)
The net price after \[{{3}^{rd}}\] discount = The net price after \[{{2}^{nd}}\] discount – Discounted price ……………………………..(9)
From equation (7), equation (8) and equation (9), we get
The net price after \[{{3}^{rd}}\] discount = \[\text{Rs}\text{. }\left( 6555-131.1 \right)=\,\text{Rs}\text{.}\,6423.90\] ………………………(10)
We have to round off the number Rs. 6423.90.
Therefore, the net price after the \[{{3}^{rd}}\] discount is Rs. 6424.

Note: In this question, one might impose a net discount of 15% on Rs. 7500 and then, get the discounted price. This is wrong because the discount is imposed successively. At first, there is a discount of 8% on the marked price. Then, apply a second discount of 5% on the net price after the \[{{1}^{st}}\] discount. Now, apply a discount of 2% on the net price after the \[{{2}^{nd}}\] discount.