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7th Class Mental Ability Algebraic Expressions Question Bank Algebra

  • question_answer
    A person buys some pen and pencil from the market at a rate such that a pencil is twice as costly as pen. He sells them such that the cost of pencil is thrice the cost of pen. By selling a pen at twice of its cost price, he makes 150 % profit on the whole. Find the ratio of pencils to pen.

    A) 1 : 2           

    B)               4 : 5

    C) 3 : 4          

    D)               7 : 4

    E) None of these

    Correct Answer: A

    Solution :

    Explanation Let there are a pens and b pencils. Also let C.P of one pen \[= x \Rightarrow \,\, C.P\] of a pens = ax then C.P of one pencil \[2x \Rightarrow  C.P\] of b pencils = 2bx S.P. of one pen \[= \,2x \Rightarrow \,\, S.P.\] of a pens = 2ax S.P of one pencil \[= \,6x \Rightarrow \, S.P.\] of b pencils = 6bx Now, \[\frac{S.P-C.P}{C.P}\times 100=\Pr ofit\,%\] \[\Rightarrow \,\,\,\left( 2ax + 6bx \right)\frac{-(ax+2bx)}{ax+2bx}=\frac{150}{100}\] \[\Rightarrow \,\,\,\,\,\frac{a+4b}{a+2b}=\frac{3}{2}\] \[\Rightarrow \,\,\,\,2a + 8b = 3a + 6b\] \[\Rightarrow \,\,\,\,8b - 6b = 3a-2a\] \[\Rightarrow \,\,\,2b=a\,\,\Rightarrow \,\frac{b}{a}=\frac{1}{2}\]


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