Question

The average price of the three items of the furniture is \[{\text{Rs}}{\text{.15000}}\]. If their prices are in the ratio \[{\text{3:5:7}}\], the price of the cheapest item is
A. \[{\text{Rs9000}}\]
B. \[{\text{Rs15000}}\]
C. \[{\text{Rs18000}}\]
D. \[{\text{Rs21000}}\]

Answer 1

Hint: The average price of the three items can be given as \[{\text{r = }}\dfrac{{{{\text{x}}_{\text{1}}}{\text{ + }}{{\text{x}}_{\text{2}}}{\text{ + }}{{\text{x}}_{\text{3}}}}}{{\text{3}}}\]. Also, use the ratio given of all the items to calculate the actual price of all the items individually and hence lowest among them will be our required answer, as from the above two conditions, we can form two equations and on solving both of them our required answer will be obtained.

Complete step by step answer:

First of all calculate the total amount of the items using average formula \[{\text{r = }}\dfrac{{{{\text{x}}_{\text{1}}}{\text{ + }}{{\text{x}}_{\text{2}}}{\text{ + }}{{\text{x}}_{\text{3}}}}}{{\text{3}}}\]
\[
  {\text{15000 = }}\dfrac{{{{\text{x}}_{\text{1}}}{\text{ + }}{{\text{x}}_{\text{2}}}{\text{ + }}{{\text{x}}_{\text{3}}}}}{{\text{3}}} \\
   \Rightarrow {{\text{x}}_{\text{1}}}{\text{ + }}{{\text{x}}_{\text{2}}}{\text{ + }}{{\text{x}}_{\text{3}}} = 45000 \\
 \]
Now, as per the ratio given of each individual items \[ \Rightarrow {{\text{x}}_{\text{1}}}{\text{:}}{{\text{x}}_{\text{2}}}{\text{:}}{{\text{x}}_{\text{3}}} = 3:5:7\]
Let the base fair be x and so the amount of all three items can be expressed as
\[{{\text{x}}_{\text{1}}}{\text{ + }}{{\text{x}}_{\text{2}}}{\text{ + }}{{\text{x}}_{\text{3}}}{\text{ = 3x + 5x + 7x = 15x}}\], substituting it in the above equation,
\[
   \Rightarrow 15{\text{x = 45000}} \\
  {\text{x = Rs}}{\text{.3000}} \\
 \]
So, we putting on the value of x, we can individually calculate the value of all three items and they are
\[
  {{\text{x}}_{\text{1}}}{\text{ = 3x = 3(3000) = 9000}} \\
  {{\text{x}}_{\text{2}}}{\text{ = 5x = 5(3000) = 15000}} \\
  {{\text{x}}_{\text{3}}}{\text{ = 7x = 7(3000) = 21000}} \\
 \]
Hence, the lowest price among all three item is of \[{\text{Rs}}{\text{.9000}}\] and so option (a) is our correct answer.

Note: As here we are asked to find the lowest price so we go for option (A), so one should read the question carefully and answer accordingly to what is asked to find. A proportion on the other hand is an equation that says that two ratios are equivalent. If one number in a proportion is unknown you can find that number by solving the proportion. One percent is one-hundredth of a whole. It can therefore be written as both a decimal and a fraction. To write a percentage as a decimal, simply divide it by \[{\text{100}}\]. The average price is generally the ratio of the total amount to total quantities. And the ratios of each quantity amount is the exact amount of each quantity.