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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 then find the cost of the saree and the list price (price before discount) of the sweater. |
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Answer» Let the cost price of a saree = Rs. X and the list price of sweater = Rs. Y Case I : (S.P. of a saree at 8% profit) + (S.P. of a sweater at 10% discount) - Rs. 1008 `implies ((100+8))/(100)x + ((100-10))/(100)y = 1008` implies 108x + 90y = 100800 implies 6x + 5y = 5600 ...(1) Case II : (S.P. of a saree at 10% profit) + (S.P. of a sweater at 8% discount) = Rs. 1028 `implies ((100+10))/(100) x + ((100 - 8))/(100) y = 1028` implies 110x + 92y = 102800 ...(2) Dividing equation (2) by 2, we have 55x + 46y = 51400 ...(3) Again, multiplying equation (3) by 5, we get 275x + 230y = 257000 ...(4) Multiplying equation (1) by 46, we get 276x + 230y = 257600 ...(5) Subtracting equation (5) from (4), we get `{:(275x + 230y = 257000),(276x + 230y = 257600),(ul("- - -")),(-x = 257000 - 257600):}` implies -x = - 600 implies x = Rs. 600 Now, 6x + 5y = 5600 [from (1)] implies `6 xx 600` + 5y = 5600 (`because` x = 600) implies 5y = 5600 - 3600 implies `y = (2000)/(5)` implies y = 400 Hence, the C.P. of a saree and C.P. of a sweater are Rs. 600, Rs. 400 respectively. |
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