8th Class Mathematics Sample Paper Mathematics Sample Paper - 3

  • question_answer A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that is needed to be added.
    Part of red pigment 1 4 7 12 20
    Part of base    8 --- --- --- ---

    Answer:

    As the part of red pigment increases/ part of base also increases in the same ratio. It is a case of direct proportion, we make use of the relation of the type \[\frac{{{x}_{1}}}{{{y}_{1}}}=\frac{{{x}_{2}}}{{{y}_{2}}}=\frac{{{x}_{3}}}{{{y}_{3}}}\] ...

    (a) Here, \[{{x}_{1}}=1,{{y}_{1}}=8\] and \[{{x}_{2}}=4\]
    Therefore,               \[\frac{{{x}_{1}}}{{{y}_{1}}}=\frac{{{x}_{2}}}{{{y}_{2}}}\]
                \[\frac{1}{8}=\frac{4}{{{y}_{2}}}\]
    \[\Rightarrow \,\] \[{{y}_{2}}=4\times 8=32\]                                                                                                                             
    (b)   Here,          \[{{x}_{2}}\,4,{{y}_{2}}=32\,\,and\,\,{{x}_{3}}=7\]
    \[\frac{{{x}_{2}}}{{{y}_{2}}}=\frac{{{x}_{3}}}{{{y}_{3}}}\]
    \[\Rightarrow \]               \[\frac{4}{32}=\frac{7}{43}\]
    \[\Rightarrow \]               \[{{y}_{3}}=\frac{7\times 32}{4}=56\]                                                                                                             
    (c)   Here, \[{{x}_{3}}=7,{{y}_{3}}=56\]and \[{{x}_{4}}=12,{{y}_{4}}=?\]
    \[\frac{{{x}_{3}}}{{{y}_{3}}}=\frac{{{x}_{4}}}{{{y}_{4}}}\]
    \[\Rightarrow \]   \[\frac{7}{56}=\frac{12}{{{y}_{4}}}\]
    \[\Rightarrow \]   \[{{y}_{4}}=\frac{12\times 56}{7}\]
    \[\Rightarrow \]   \[{{y}_{4}}=96\]                                                                                                                                             
    (d) Here, \[{{x}_{4}}=12,{{y}_{4}}=96\]and \[{{x}_{5}}=20,{{y}_{5}}=?\]
    \[\frac{12}{96}=\frac{202}{{{y}_{5}}}\]
    \[\Rightarrow \]   \[{{y}_{5}}=\frac{20\times 96}{12}\]
    \[\Rightarrow \]   \[{{y}_{5}}=160\]
    The table is
    Part of pigment 1 4 7 12 20
    Part of Base 8 32 56 96 160


adversite


You need to login to perform this action.
You will be redirected in 3 sec spinner