# Profit and Loss

## Click on any option to know the CORRECT ANSWERS

 Question 1
The price of an article reduces to 576 after two successive discounts. The markup is 80% above the cost price of Rs. 500. What is the new profit percentage if instead of two successive discounts the markup price was further increased successively two times by the same percentage?
 A 157% B 159.2% C 300% D 259.20%

Question 1 Explanation:
\begin{align} & {\text{CP}} = 500 \cr & {\text{SP}} = 576 \cr & {\text{MP}} = 900\left[ {80\% \, {\text{above}}\, {\text{the}}\, {\text{CP}}} \right] \cr & {\text{Now}}, \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 - \left( {\frac{R}{{100}}} \right)} \right]^2} \cr & \left[ {{\text{R = Rate}}\, {\text{of}}\, {\text{Discount}}} \right] \cr & 576 = 900 \times {\left[ {1 - \left( {\frac{R}{{100}}} \right)} \right]^2} \cr & R = 20\% \cr & \cr & {\text{Again}}, \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right]^2} \cr & {\text{SP}} = 900 \times {\left[ {1 + \left( {\frac{{20}}{{100}}} \right)} \right]^2} \cr & {\text{SP}} = 1296 \cr & {\text{New}}\, {\text{Profit}}\, {\text{Percentage}}, \cr & = \left[ {\frac{{\left( {SP - CP} \right)}}{{CP}}} \right] \times 100 \cr & = \left[ {\frac{{\left( {1296 - 500} \right)}}{{500}}} \right] \times 100 \cr & = 159.2\% \cr\end{align}
 Question 2
The marked price of a shirt and trousers are in the ratio 1:2. The shopkeeper gives 40% discount on the shirt. If the total discount in the set of the shirt and trousers is 30%, the discount offered on the trousers is:
 A 30% B 15% C 20% D 25%

Question 2 Explanation:
Let the price of shirt and trouser be Rs. 100 and Rs. 200 respectively.

Then, price of set of shirt and trouser = Rs. 300.

After giving 30% discount on the set,

Selling Price = 300 - 30% of 300 = 210.

Total Discount on Set = 90.

And Discount on shirt is 20% alone,

SP of shirt alone = 100 - 40% of 100 = 60.

Rs. 40 is the discount on shirt then Rs. 50 must be the discount on the trouser.

So, discount on trouser = (50*100)/200 = 25%.

 Question 3
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
 A Rs. 2200 B Data inadequate C Rs. 2400 D Rs. 2000

Question 3 Explanation:
\begin{align} & {\text{Let}}\, {\text{C}}{\text{.P}}{\text{.}}\, {\text{be}}\, Rs.\, x \cr & {\text{Then}}, \, \frac{{1920 - x}}{x} \times 100 = \frac{{x - 1280}}{x} \times 100 \cr & \Rightarrow 1920 - x = x - 1280 \cr & \Rightarrow 2x = 3200 \cr & \Rightarrow x = 1600 \cr & \therefore {\text{Required}}\, {\text{S}}{\text{.P}}{\text{.}}\, = 125\% \, {\text{of}}\, Rs.\, 1600 \cr & = Rs.\, \left( {\frac{{125}}{{100}} \times 1600} \right) = Rs.\, 2000 \cr\end{align}
 Question 4
If the profit per cent got on selling an article is numerically equal to its cost price in rupees and the selling price is Rs. 39, then cost price (in Rs.) will be:
 A 22 B 30 C 28 D 20

Question 4 Explanation:
SP = Rs. 39.

CP = x(let)

Profit % = CP

Or, [(39-x)/x] * 100 = x [% profit= (SP-CP)/CP]

3900-100x = x2

X2+100-3900 = 0

X = 30. (we cannot take negative value of x)

 Question 5
If selling price is doubled, the profit triples. Find the profit percent.
 A 120 B 66 2/3 C 105 1/3 D 100

Question 5 Explanation:
\begin{align} & {\text{Let}}\, {\text{C}}{\text{.P}}{\text{.}}\, {\text{be}}\, {\text{Rs}}{\text{.}}\, x\, {\text{and}}\, {\text{S}}{\text{.P}}{\text{.}}\, {\text{be}}\, {\text{Rs}}.\, y \cr & {\text{Then}}, \, 3\left( {y - x} \right) = \left( {2y - x} \right) \cr & \Rightarrow y = 2x \cr & {\text{Profit}} = Rs.\, \left( {y - x} \right) \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = Rs.\, \left( {2x - x} \right) \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = Rs.\, x \cr & \therefore {\text{Profit}}\, \% \cr & = \left( {\frac{x}{x} \times 100} \right)\% \cr & = 100\% \cr\end{align}
There are 5 questions to complete.