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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 Naya mixer-grinders were purchased in $1999$?

- $44$
- $50$
- $55$
- $64$

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At the end of the year $1999, 129$ Naya products are still in operation(acc. to the line graph). This includes in-operation products of the year $1998$ as well as $1997.$

So, effectively we subtract operational products from both $1997+1998$ from $129$ to get new products bought in the year.

$20 \%$ of $30$ (products bought in $1997$) is disposed off in $1999$ or $6$ products are disposed off, so $24$ products from $1997$ are still in operation.

$50$ new products were bought in $998(80-30).$ Total operational products from $1997 \& 1999=24+50=74.$

Therefore, new products purchased in $1999=124-74=50$

Option $\text{(B)}$

So, effectively we subtract operational products from both $1997+1998$ from $129$ to get new products bought in the year.

$20 \%$ of $30$ (products bought in $1997$) is disposed off in $1999$ or $6$ products are disposed off, so $24$ products from $1997$ are still in operation.

$50$ new products were bought in $998(80-30).$ Total operational products from $1997 \& 1999=24+50=74.$

Therefore, new products purchased in $1999=124-74=50$

Option $\text{(B)}$