10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank Pair of Linear Equations in Two Variables

  • question_answer On selling a tea-set at 5% loss and lemon- set at 15% gain, a crockery seller gains Rs. 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains Rs. 13. Find the actual prices of the tea-set and the lemon-set.

    A)  Rs.100, Rs.80

    B)  Rs. 90, Rs. 100

    C)  Rs.120, Rs. 60

    D)  Rs.150, Rs. 80

    Correct Answer: A

    Solution :

    Let cost price of tea-set = Rs. x and cost price of lemon-set = Rs. y (i) Loss on tea-set \[=Rs.\,\frac{5x}{100}=Rs.\frac{x}{20}\] Gain on lemon-set \[=Rs.\,\frac{15y}{100}=Rs.\frac{3y}{20}\] Also, \[\frac{3}{20}y-\frac{x}{20}=7\] \[\Rightarrow \] \[3y-x=140\]     ...(1) (ii) Gain on tea-set \[=Rs.\,\frac{5x}{100}=Rs.\frac{x}{20}\] Gain on lemon-set \[=Rs,\frac{10y}{100}=Rs.\frac{y}{10}\] Also, \[\frac{x}{20}+\frac{y}{10}=13\Rightarrow x+2y=260\]       ...(2) Solving (1) and (2), we get \[\Rightarrow \] \[y=Rs.\,80\] and \[x=Rs.\,100\]

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