A sells his house worth $Rs.\, 10\, lakh$ to $B$ at a loss of $10 \% .$ Later $B$ sells it back to $A$ at $10 \%$ profit. The result of the two transactions is

Profit obtained on selling an article for $Rs.\,310$ is equal to the loss incurred on selling that article for $Rs.\, 230.$ What will be the loss percentage when selling price is $Rs.\, 180$?

A shopkeeper buys a toy at $Rs.\,100$ and sells it at $Rs.$ $125 .$ Another shopkeeper buys the same toy at $Rs.\, 125$ but sells it at $Rs.$ $100 .$ What are the respective profit and loss percentages for the two shopkeepers.

Raman sells a machine for $Rs.\, 39$ lakh at a loss. Had he sold it for $Rs.\, 49$ lakh, his gain would nhave been three times the loss. What is the cost price of the machine? (in $Rs........lakh$)

A pair of article, was bought for $Rs.\, 37.40$ at a discount of $15 \% .$ What must be the marked price of each of the articles?

A plate was sold for $Rs.\,6,300$ after giving two successive discounts of $12^{1 / 2} \%$ and $10 \% .$ Find the marked price. (in $Rs.$)