Question

A dealer marked the price of a digital watch as Rs 6,000. She then allowed 20% discount to make 20% profit. If she increased the discount to 25%, by how much was the profit percent decreased?​

Answer 1

Profit decreased by 7.5%

Answer:

Solution Given:

Marked Price= Rs 6,000

discount =20%

Selling Price =M.P- discount% of M.P

=M.P(1-discount%)

=6000(1-20%)

= Rs 4,800

Again

Profit = 20%

Cost Price=(S.P*100)/(100+profit%)

= (4800*100)/(100+20%)

= Rs 4,000

For discount 25%

Marked Price =Rs 6,000

Selling Price =M.P - discount% of M.P

=M.P(1-discount%)

=6000(1-25%)

=Rs 4,500

Profit = S.P- C.P= Rs 4,500- Rs 4,000=Rs 500

Profit %=Profit/C.P* 100%= 500/4000*100 = 12.5%

Profit % decreased from 20% to 12.5%

Profit decreased by 7.5%

Answer 2

7.5%

Explanation:

Marked Price

Rs 6,000

Discounted Price

If the price is discounted by 20%, then the discounted price is 80% of the marked price:

`\implies \sf Discounted\:Price =80\% \textsf{ of marked price}`

`\implies \sf Discounted\:Price =0.8 * 6000`

`\implies \sf Discounted\:Price = 4800\:Rs`

Cost Price

If the dealer makes 20% when selling the watch at the discounted price, then the cost price is:

`\implies \sf Cost\:Price=(100\%)/(120\%) * 4800`

`\implies \sf Cost\:Price=(4800)/(1.2)`

`\implies \sf Cost\:Price=4000\:Rs`

Discount of 25%

If the price is discounted by 25%, then the discounted price is 75% of the marked price:

`\implies \sf Discounted\:Price =75\% \textsf{ of marked price}`

`\implies \sf Discounted\:Price =0.75* 6000`

`\implies \sf Discounted\:Price = 4500\:Rs`

Profit after 25% discount

`\implies \sf Profit=(discounted\:price)/(cost\:price)-1 * 100`

`\implies \sf Profit=(4500)/(4000)-1 * 100`

`\implies \sf Profit=12.5\%`

Therefore, the profit decreased from 20% to 12.5% which means the profit percent decreased by 7.5%.