The price of an article is cut by $42 \%$. To restore it to its original value,the new price must be increased by (in $\%$):

Find the present worth $(P.W.)$ and the true discount $(T.D.)$ reckoning $6 \%$ per annum simple interest of $Rs. 176$ due in $20 \text{ months}$ time. (in $Rs.$)

$A$ fan is listed at $Rs. 150$ with a discount of $20 \%$. What additional discount must be offered to the customer to bring the net price to $Rs. 108$? (in $\%$)

$A$ shopkeeper gives two successive discounts of $7 \%$ each on the marked price of $Rs.\, 20,000$ of an article. The selling price of the article is (in $Rs.$):

The marked price of an article is $20 \%$ more than its cost price. If $5 \%$ discount is given on the marked price,what is the profit percent (in $\%$)?

The price of a bicycle is marked by a trader at $Rs.\, 1000$. He sold the bicycle allowing successive discounts of $20 \%, 10 \%$ and $5 \%$. If the trader gained $14 \%$,then the cost price of the bicycle (in $rupees$) is: