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Answer the questions on the basis of the information given below.

Purana and Naya are two brands of kitchen mixer-grinders available in the local market. Purana is an old brand that was introduced in $1990$, while Naya was introduced in $1997$. For both these brands, $20\%$ of the mixer-grinders bought in a particular year are disposed off as junk exactly two years later. It is known that $10$ Purana mixer-grinders were disposed off in $1997$. The following figures show the number of Purana and Naya mixer-grinders in operation from $1995$ to $2000$, as at the end of the year.

     

How many Purana mixer-grinders were purchased in $1999$?

  1. $20$
  2. $23$
  3. $50$
  4. Cannot be determined from the data
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Option$:(1)$

To figure out how many new products were purchased in $1999.$ We need $2$ pieces of information:-

  1. How many products were operational at the end of the year $1999$ i.e. $236.$
  2. How many of the products that were operational at the end of year $1998$ were disposed as junk or products newly purchased in $1997.$

Info $1$ was trivial from the graph itself, for info $2$ we need to do some work as follows:-

We need to find out how many products were newly purchased in $1997$ so that we can get rid of $20\%$ of that amount in $1999.$

In $1997, 10$ products were discarded, $162$ products were operational by the end of the year $1996.$ So, $162-10$ products were operational in the year $1997$ or $152$ products were operational in $1997.$ Now $(182-152)=30$ products were newly bought in the year $1997.$

$20\%$ of $30$ were discarded in $1999$ or $6$ were discarded in $1999. 222-6=216$ products were present in the year $1999$. But operational products given is $236$ so $(236-216)$ or $20$ products were bought.

 

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