a shopkeeper sold a saree and a sweater together for rupees 1050 thereby making a profit of 10% on the saree and 25% on the sweater. if he had taken a profit of 25% on the saree and 10% on the sweater he would have got ₹15 more. find the cost price of each.
Answers
Answer:
StEpbystEpexplanation:
Let the cost price of saree be Rs. 'x' and the list price of sweater be Rs. y.
Therefore,
\bold\green{Situation 1 -}Situation1−
By selling a saree at 8 % profit and a sweater at 10 % discount, the shopkeeper gets Rs. 1008
⇒ 108x/100 + 90y/100 = 1008
⇒ 27x/25 + 9y/10 = 1008/1
Taking L.C.M. of the denominators and then solving it, we get.
54x + 45y = 50400 _________(1)
Situation2−
by selling a saree at 10 % profit and a sweater at 8 % discount, the shopkeeper gets Rs. 1028.
\sf{ \frac{110x}{100} + \frac{92y}{100} = 1028 }
\sf{ \frac{11x}{10} + \frac{23y}{25} = 1028}
Taking L.C.M. of the denominators and then solving it, we get.
⇒ 55x + 46y = 51400 _______(2)
Now, multiplying the equation (1) by 55 and (2) by 54, we get.
(54x + 45y = 50400)×55
= 2970x + 2475y = 2772000 _____(3)
(55x + 46y = 51400)×54
= 2970x + 2484y = 2775600 _____(4)
Now, subtracting (3) from (4), we get.
2970x + 2484y = 2775600
2970x + 2475y = 2772000
. - - - ___________________________
. 9y = 3600
___________________________
⇒ 9y = 3600
y = 3600/9
y = 400
Putting the value of y = 400 in (1), we get.
54x + 45y = 50400
54x + (45 × 400) = 50400
54x + 18000 = 50400
54x = 50400 - 18000
54x = 32400
.
x = 600
So, the cost price of a saree is Rs. 600 and the list price of a sweater is Rs. 400
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Answer:
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