Question

a shopkeeper sells a saree at 8%profit and a sweater at 10%discount thereby getting a sum rupees 1008 if she had sold the saree at 10% profit and the sweater at 8% discount she would have got rupees 1028 find the cost of saree and list price of the sweater... ANSWER IT ASAP PLEASE

Answer 1

Given :-

• When she sells saree at 8% profit and sweater at 10% discount she gets a sum of rupees 1008.
• When she sells saree at 10% profit and sweater at 8% discount she gets a sum of rupees 1028.

To Find :-

• Cost price of saree.
• List price of sweater.

Solution :-

Let:-

• Cost price of saree : x
• Cost price of sweater : y

Case I :

When saree is sold at 8% profit & sweater is sold at 10% discount.

According to the question,

$\implies\rm{\dfrac{108x}{100}+\dfrac{90y}{100}=1008}$

$\implies\rm{\dfrac{108x+90y}{100}=1008}$

$\implies\rm{108x+90y=100800}$

$\implies\rm{54x+45y=50400\longrightarrow{(1)}}$

Case II :

When saree is sold at 10% profit & sweater is sold at 8% discount.

According to the question,

$\implies\rm{\dfrac{110x}{100}+\dfrac{92y}{100}=1028}$

$\implies\rm{\dfrac{110x+92y}{100}=1028}$

$\implies\rm{110x+92y=102800}$

$\implies\rm{55x+46y=51400\longrightarrow{(1)}}$

Multiplying equation ( 1 ) with 55, we get,

$\implies\rm{2970x+2475y=2772000\longrightarrow{(3)}}$

Multiplying equation ( 2 ) with 54, we get,

$\implies\rm{2970x+2484y=2775600\longrightarrow{(4)}}$

Subtracting equation ( 3 ) from equation ( 4 ), we get,

$\implies\rm{9y=3600}$

$\implies\rm{y=\dfrac{3600}{9}}$

$\implies\rm{y=}\:\bold{400.}$

Substituting the value of y in equation ( 1 ), we get,

$\implies\rm{54x+45\times{}400=50400}$

$\implies\rm{54x+18000=50400}$

$\implies\rm{54x=32400}$

$\implies\rm{x=\dfrac{32400}{54}}$

$\implies\rm{x=}\:\bold{600.}$

Therefore,

• Cost price of saree = Rs. 600
• List price of sweater = Rs. 400