Question

An almirah is listed at Rs.1000. A retailer buys it with two successive discounts of 10% and 20% for cash. The other expenses are 10% of the cost of the almirah. At what price should he sell to earn a profit of 15%?
(a) Rs. 910.80
(b) Rs. 900.50
(c) Rs. 910.50
(d) Rs. 980.50

Answer 1

Hint: First, here it is given two successive discounts on cash, so we will find the total discount using the formula Total discount $=\left( x+y-\dfrac{xy}{100} \right)\%$. From this we will get a discount price. Then again finding 10% of other expenses on the discount price we got. Then adding both the price to get the total cost price and then finding the selling price of 15% profit on it using $SP=CP+profit\%\left( CP \right)$ .

Complete step-by-step answer:
Now, from the question almirah listed price is Rs. 1000 which we can consider as cost price (CP)
CP $=1000$
Now, two successive discounts of 10% and 20% on listed price. Therefore, using the formula of successive discount, we get
Total discount $=\left( x+y-\dfrac{xy}{100} \right)\%$
Total discount $=\left( 10+20-\dfrac{\left( 10 \right)\left( 20 \right)}{100} \right)\%$ (where $x=10\%,y=20\%$ )
Total discount $=\left( 30-2 \right)\%$
Total discount $=28\%$ …………………………..(i)
Now, we will find the discount price of 28% on CP, we get
Discount of 28% $=\dfrac{28}{100}\times 1000=Rs.280$
So, discounted cost price will be $Rs.1000-Rs.280=Rs.720$ ………………………………..(ii)
Thus, cost price of almirah is Rs. 720.
Now, 10% is on cost price for other expense, so again finding other expenses on Rs. 720
Other expenses of 10% $=\dfrac{10}{100}\times 720=Rs.72$ ……………………….(iii)
So, overall cost price CP $=Rs.72+Rs.720$
CP $=Rs.792$ …………………………………(iv)
Now, to find selling price with 15% profit can be calculated as
$SP=CP+profit\%\left( CP \right)$
Substituting all the values in the above equation, we get
$SP=792+\dfrac{15}{100}\left( 792 \right)$
$SP=792+118.8$
$SP=Rs.910.80$ ……………………………….(iv)
Hence, option (a) is the correct answer.

Note: There is another approach of finding successive discounts. Here we are given a 10% and 20% successive discount on listed price 1000. So, first we will find for 10%, we will get
Discount on 10% $=\dfrac{10}{100}\left( 1000 \right)=Rs.100$
So, listed price or CP will be $=Rs.1000-Rs.100=Rs.900$
Now, again for 20% on Rs. 900 $=\dfrac{20}{100}\left( 900 \right)=Rs.180$
So, CP will be $=Rs.900-Rs.180=Rs.720$
Thus, by getting this price we can solve further problems, but this becomes time consuming. So, it's better to use successive formulas for easy calculations.