CAT 2004 — DILR Question 17
Answer the following question based on 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 disposed of by the end of 2000?
Answer & solution
- A
10
16
- C
22
- D
Cannot be determined from the data
The number of mixer-grinders in operation in any year can be divided into four categories: Newly purchased, one year old, two year old and older.
Consider Naya mixer-grinders.
As 30 mixer-grinders were in operation in 1997 and the brand itself was introduced in that year, all 30 were newly purchased.
In 1998, 80 were in operation, out of which 30 were one-year old.
∴ 50 were newly purchased.
In 1999, 124 were in operation, out of which 50 were one-year old.
Out of the 30 purchased in 1997, 20% or 6 were disposed of in 1999.
∴ 30 × 0.8 = 24 out of the 124 were two-year old.
Similarly in 2000, 134 were in operation, out of which 50 were one year old, 40 were two years old and 24 were older than two years.
Thus we have the following:
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Consider Purana Mixer-grinders. As 10 of these were disposed of in 1997,
= 50 were bought in 1995.
∴ 70 mixer-grinders in operation in 1995 were old. The break-up of these however cannot be found.
Out of the 162 in operation in 1996, 50 were one year old. The break-up of the rest cannot be found as we do not have data of years before 1995 and we have not been given the number of mixer-grinders purchased in 1996.
In 1997, 182 were in operation and 10 were disposed of. Thus 182 + 10 = 192 mixer-grinders were either newly purchased or old.
Out of these 192, 162 existed in 1996 too.
∴ 192 – 162 = 30 were newly purchased in 1997.
As the number of newly purchased mixer-grinders in 1996 is not known, the number that were disposed of in 1998 cannot be found. Consequently, the number that were newly purchased also cannot be found.
Continuing this process for the years 1999 and 2000, the entire data can be presented as follows:
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∴ 10 + 6 = 16 Naya mixer-grinders were disposed of by the end of 2000.
Hence, option (b).