Question

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a sum Rs.1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs.1028. Find the cost price of the saree?
A) 600
B) 650
C) 680
D) 690

Answer 1

Hint – Assume the Cost Price of saree be Rs. x and the Cost Price of sweater be Rs. y. Use the condition that if profit % is given then selling price is given by $SP = \dfrac{{(100 + P\% )}}{{100}} \times CP$ and when discount is given then, $SP = \dfrac{{(100 - d\% )}}{{100}} \times CP$.

Complete step-by-step answer:
Given in the question that the shopkeeper sells a saree at 8% profit and sweater at 10% discount, getting a sum Rs.1008.
Also, if she sold the saree at 10% profit and the sweater at 8% discount, getting a sum Rs.1028.
Now, let us assume that the cost price of saree be Rs. x and the cost price of sweater be Rs. y.
According to 1st condition given in question and using the formula, $SP = \dfrac{{(100 + P\% )}}{{100}} \times CP$ and $SP = \dfrac{{(100 - d\% )}}{{100}} \times CP$
Here, P% = 8%.
So, selling price of the saree is $\dfrac{{(100 + 8)}}{{100}} \times x = \dfrac{{108x}}{{100}} - (1)$
Selling Price of sweater when 10 % discount is $\dfrac{{(100 - 10)}}{{100}} \times y = \dfrac{{90y}}{{100}} - (2)$
Now adding (1) and (2), we get-
$\dfrac{{108x}}{{100}} + \dfrac{{90y}}{{100}} = 1008 - (3)$ {since, the sum is given as 1008}
According to the 2nd condition given in question and using the formula, $SP = \dfrac{{(100 + P\% )}}{{100}} \times CP$ and $SP = \dfrac{{(100 - d\% )}}{{100}} \times CP$
Here, P% = 10 %
So, selling price of the saree is $\dfrac{{(100 + 10)}}{{100}} \times x = \dfrac{{110x}}{{100}} - (4)$
Selling Price of sweater when 8% % discount is $\dfrac{{(100 - 8)}}{{100}} \times y = \dfrac{{92y}}{{100}} - (5)$
Now adding (4) and (5), we get-
$\dfrac{{110x}}{{100}} + \dfrac{{92y}}{{100}} = 1028 - (6)$ {since, the sum is given as 1028}
Solving equation (3) and (6), we have-
$
  108x + 90y = 100800 - (7) \\
  110x + 92y = 102800 - (8) \\
 $
Subtract (8) – (7), we have-
$
  2x + 2y = 2000 \\
   \Rightarrow x + y = 1000 - (9) \\
 $
Substitute (9) in (7), we get-
$
  108x + 90(1000 - x) = 100800 \\
  108x - 90x = 100800 - 90000 \\
  18x = 10800 \\
  x = 600 \\
 $
Therefore, the cost of saree is Rs. 600.
Hence, the correct option is A.

Note – Whenever such types of questions appear then always write down the things given in the question. Then by using the conditions that the shopkeeper sells saree at 8% profit and sweater at 10% profit, and then he sells saree at 10% and sweater at 8% discount. Make equations using these two conditions. And then find the value of the cost price of saree.