Case 7

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.

[CAT 2004]

24) How many Naya mixer-grinders were purchased in 1999?

(1) 44
(2) 50
(3) 55
(4) 64

25) How many Naya mixer-grinders were disposed off by the end of 2000?

(1) 10
(2) 16
(3) 22
(4) Cannot be determined from the data

26) How many Purana mixer-grinders were disposed off in 2000?

(1) 0
(2) 5
(3) 6
(4) Cannot be determined from the data

27) How many Purana mixer-grinders were purchased in 1999?

(1) 20
(2) 23
(3) 50
(4) Cannot be determined from the data

Solution

24)

Number of Naya mixer grinders in operation and number of Naya mixer grinders disposed are 30 and NIL respectively . Since, Naya has been introduced in 1997 the number of Naya mixer grinders purchased in 1997 is 30. In 1998, number of Naya mixer grinders in operation and number of Naya mixer grinders disposed are 80 and NIL respectively. Hence, number of Naya mixer grinders purchased in 1998 is 50 (80 – 30).

In 1997 number of Purana mixer grinders disposed are 10, which is 20% of number of Purana mixer grinders purchased in 1995. If 20% is 15 then 100% is 50. Hence, number of Purana mixer grinders purchased in 1995 is 50.

In 1999 and 2000 number of Naya mixer grinders disposed will be 6 and 10 respectively, which is 20% of number of Naya mixer grinders purchased in 1997 and 1998 respectively.

In 1999 number of Naya mixer grinders in operation is 124, likewise in 1998 is 80. From which6 has been disposed in 1999. Now for 124 Naya grinders to be in operation the remaining 50 has been purchased in 1999.

In 2000 number of Naya mixer grinders in operation is 134, likewise in 1999 is 124. From which 10 has been disposed. Now for 134 grinders to be in operation the remaining 20 has been purchased in 2000.

From the above table, we can find out the number of Naya mixer-grinders purchased in 1999.

Answer: (2) 50

25)

Number of Naya mixer grinders in operation and number of Naya mixer grinders disposed are 30 and NIL respectively . Since, Naya has been introduced in 1997 the number of Naya mixer grinders purchased in 1997 is 30. In 1998, number of Naya mixer grinders in operation and number of Naya mixer grinders disposed are 80 and NIL respectively. Hence, number of Naya mixer grinders purchased in 1998 is 50 (80 - 30).

In 1997 number of Purana mixer grinders disposed are 10, which is 20% of number of Purana mixer grinders purchased in 1995. If 20% is 15 then 100% is 50. Hence, number of Purana mixer grinders purchased in 1995 is 50.

In 1999 and 2000 number of Naya mixer grinders disposed will be 6 and 10 respectively, which is 20% of number of Naya mixer grinders purchased in 1997 and 1998 respectively.

In 1999 number of Naya mixer grinders in operation is 124, likewise in 1998 is 80. From which6 has been disposed in 1999. Now for 124 Naya grinders to be in operation the remaining 50 has been purchased in 1999.

In 2000 number of Naya mixer grinders in operation is 134, likewise in 1999 is 124. From which 10 has been disposed. Now for 134 grinders to be in operation the remaining 20 has been purchased in 2000.

From the above table, we can infer the number of Naya mixer-grinders that were disposed off by the end of 2000.

Answer: (2) 16

26)

Number of Naya mixer grinders in operation and number of Naya mixer grinders disposed are 30 and NIL respectively . Since, Naya has been introduced in 1997 the number of Naya mixer grinders purchased in 1997 is 30. In 1998, number of Naya mixer grinders in operation and number of Naya mixer grinders disposed are 80 and NIL respectively. Hence, number of Naya mixer grinders purchased in 1998 is 50 (80 - 30).

In 1997 number of Purana mixer grinders disposed are 10, which is 20% of number of Purana mixer grinders purchased in 1995. If 20% is 15 then 100% is 50. Hence, number of Purana mixer grinders purchased in 1995 is 50.

In 1999 and 2000 number of Naya mixer grinders disposed will be 6 and 10 respectively, which is 20% of number of Naya mixer grinders purchased in 1997 and 1998 respectively.

In 1999 number of Naya mixer grinders in operation is 124, likewise in 1998 is 80. From which6 has been disposed in 1999. Now for 124 Naya grinders to be in operation the remaining 50 has been purchased in 1999.

In 2000 number of Naya mixer grinders in operation is 134, likewise in 1999 is 124. From which 10 has been disposed. Now for 134 grinders to be in operation the remaining 20 has been purchased in 2000.

We cannot proceed further with the given data.

∴ The answer is cannot be determined.

Answer: (4) Cannot be determined from the data

27)

Number of Naya mixer grinders in operation and number of Naya mixer grinders disposed are 30 and NIL respectively . Since, Naya has been introduced in 1997 the number of Naya mixer grinders purchased in 1997 is 30. In 1998, number of Naya mixer grinders in operation and number of Naya mixer grinders disposed are 80 and NIL respectively. Hence, number of Naya mixer grinders purchased in 1998 is 50 (80 - 30).

In 1997 number of Purana mixer grinders disposed are 10, which is 20% of number of Purana mixer grinders purchased in 1995. If 20% is 15 then 100% is 50. Hence, number of Purana mixer grinders purchased in 1995 is 50.

In 1999 and 2000 number of Naya mixer grinders disposed will be 6 and 10 respectively, which is 20% of number of Naya mixer grinders purchased in 1997 and 1998 respectively.

In 1999 number of Naya mixer grinders in operation is 124, likewise in 1998 is 80. From which6 has been disposed in 1999. Now for 124 Naya grinders to be in operation the remaining 50 has been purchased in 1999.

In 2000 number of Naya mixer grinders in operation is 134, likewise in 1999 is 124. From which 10 has been disposed. Now for 134 grinders to be in operation the remaining 20 has been purchased in 2000.

In 1996, 162 Purana mixer grinders were in operation out of which 10 were disposed in 1997. Then there should be 152 in operation. But, there are 182 in operation. ∴ the remaining 30 has been purchased in 1997.

Out of 30 Purana mixer grinders purchased in 1997, 20%. i.e, 6 has been disposed in 1999.

In 1998, 222 Purana mixer grinders were in operation out of which 6 were disposed in 1999. Then there should be 216 in operation. But, there are 236 in operation. ∴ the remaining 20 has been purchased in 1999.

From the above table, we can infer the Purana mixer-grinders that were purchased in 1999.

Answer: (1) 20

Answer:
24) (2) 50
25) (2) 16
26) (4) Cannot be determined from the data
27) (1) 20