CAT 1998 Question Paper

Till 34 units, the fixed cost is constant and the revenue increasing per every unit made.

So, to calculate the number of units that need to be produced to maximize the profit, we have to check only at two points: 34 units and 45 units.

The revenue of 50 units is 1000. So, the revenue per unit is 20.
The variable cost of 50 units is 700. So, the variable cost per unit is 14.

If number of units produced is 34,
Fixed cost is 50
Variable cost is 14*34 = 476
Revenue is 20*34 = 680.
So, profit is 680-476-50 = 154

If number of units produced is 45,
Fixed cost is 100
Variable cost is 14*45 = 630
Revenue is 20*45 = 900.
So, profit is 900-630-100 = 170

So, the profit per unit is maximized when the number of units produced is 34

The revenue of 50 units is 1000. So, the revenue per unit is 20.
The variable cost of 50 units is 700. So, the variable cost per unit is 14.
As fixed cost went up by 40 units, the total fixed cost (when number of units is less than 34) is 50+40 = 90
Let the minimum number of units that are needed to be produced to ensure that there is no loss be X.
So, 20X $$\leq$$ 14X + 90
Or X $$\leq$$ 15
So, the least possible number of units to be produced to ensure no loss is 15.

The maximum percentage increase in price of logs happened in the year 1991 (compared to 1990) and equaled 18/15 - 1 = 20%
The maximum percentage increase in price of plywood happened in the year 1992 (compared to 1991) and equaled 6/4 - 1 = 50%
The maximum percentage increase in price of sawtimber happened in the year 1993 (compared to 1992) and equaled 20/15 - 1 = 33.33%
Hence, the correct answer is 50%

The percentage increase in price of logs over the period of time equals 20/15-1 = 33.33%
The percentage increase in price of plywood over the period of time equals 7/3 - 1 = 133.33%
The percentage increase in price of sawtimber over the period of time equals 200/100 - 1 = 100%

Hence, the maximum percentage increase in price over the period of time happened with plywood.

After an increase by 33%, the difference in the prices of one tonne of saw timber and one cubic metre of logs is given below according to the respective years.

The difference in 1987 is 15 - 10*133.33% = 1.67
The difference in 1988 is 16 - 10*133.33% = 2.67
The difference in 1989 is 17.5 - 12*133.33% = 1.5
The difference in 1990 is 15 - 10*133.33% = 1.67
The difference in 1991 is 17.5 - 12.5*133.33% = 0.833
The difference in 1992 is 18 - 15*133.33% = -2
The difference in 1993 is 20 - 20*133.33% = -6.67

Hence, the difference is least in the year 1991.

From the above diagram, we can say that difference is highest in 1992.

In 1993, price of logs = Rs. 20 per cubic metre.

volume sales of plywood, saw timber and logs were 40%, 30% and 30% 

In 1993, price of plywood = Rs. 7 per tonne

In 1993, price of plywood = Rs. 20 per tonne

Weight of one cubic metre of saw dust and plywood both = 800 kg

1 tonne=1000kg

Price of 1000kg of plywood= Rs 7

Price of 800kg( 1 m$$^3$$)= 7 x 0.8 = Rs 5.6 per cubic metre. 

Price of saw timber = 20 x 0.8 = Rs 16 per cubic metre.

We know that the sales volume of plywood, saw timber and logs are in the ratio 4 : 3 : 3.
Thus, the average realization must be the weighted avg of these three-
$$\frac{(4\times 5.6)+(3 \times 16)+(3 \times 20)}{4+3+3}$$
=13.1
= Rs. 13 (Approximately)

In this case the average realization will be-

$$\frac{(4\times 5.26 \times 1.05)+(3 \times 14.28 \times 1.01)+(3 \times 20 \times 1.1)}{4+3+3} \approx 13.15$$

Only statement A: Angles OAC, ACB, CBO are right angles => OACB is a rectangle. OC = AB and OC is radius => AB is equal to radius. Hence, we can find the answer using statement A only.

Only statement B: The point B can change even though the point A s fixed at a distance of 5 units on x-axis from origin. Hence, length of AB changes => We cannot find the answer using statement B only.

Let's consider the statements one by one.

Statement 1: n is a multiple of HCF(3,5,7,9) = 315. Hence, n can be 315, 630, 945 .... Hence we cannot say if n is odd or even.

Statement 2: 0<n<400, we cannot say if n is odd or even.

Taking both statements together, n=315. Hence, it is odd.

Thus the question can be answered using both statements together.