[Download PDF] CAT 1998 Question Paper Paper with Solutions

Instructions

Answer the questions based on the following information. The following bar chart gives the growth percentage in the number of households in the middle, upper-middle and high-income categories in the four regions for the period between 1987-88 and 1994-95.

(Number of households in thousands)

Question 11

The ratio of total income for the high-income category to the upper-middle class increased by how much percentage in the given period (approximately) ?

Video Solution

Solution

Since we do not know the region-wise population of 1987-1988, we cannot find the increase in the number of households.
Hence, we cannot find the total income for the year 1995-96.
So the ratio cannot be determined.

Question 12

The average income for the northern region in 1987-88 was

Video Solution

Solution

Since we do not know the distribution of households in each region, we cannot determine the average income.

Instructions

Answer the questions based on the following information.

Krishna distributed 10-acre land to Gopal and Ram who paid him the total amount in the ratio 2 : 3. Gopal invested a further Rs. 2 lakh in the land and planted coconut and lemon trees in the ratio 5 : 1 on equal areas of land. There were a total of 100 lemon trees. The cost of one coconut was Rs. 5. The crop took 7 years to mature and when the crop was reaped in 1997, the total revenue generated was 25% of the total amount put in by Gopal and Ram together. The revenue generated from the coconut and lemon trees was in the ratio 3 : 2 and it was shared equally by Gopal and Ram as the initial amount spent by them were equal.

Question 13

What was the total output of coconuts?

Video Solution

Solution

Let the amounts paid by Gopal and Ram to Krishna be 2X and 3X.
Gopal invested 2 lakhs additionally.
So, the total amount spent by him is 2X+2.
As the total amounts spent by the two of them are equal, it implies that 2X+2 = 3X or X = 2
Hence, the cost of the land is 2X+3X = 5X = 10 lakhs.
Total investment by the two of them is 10+2 = 12 lakhs

Hence, the total revenue generated is 12*25% = 3 lakhs.
The revenue generated by coconuts is $$3*\frac{3}{3+2} = 3*\frac{3}{5} = 1.8$$ lakhs

Cost of a coconut is Rs. 5

Hence, the total output of coconuts is $$\frac{180000}{5} = 36,000$$

Question 14

What was the value of output per acre of lemon trees planted?

Video Solution

Solution

Let the amounts paid by Gopal and Ram to Krishna be 2X and 3X.

Gopal invested 2 lakhs additionally.
So, the total amount spent by him is 2X+2.
As the total amounts spent by the two of them are equal, it implies that 2X+2 = 3X or X = 2
Hence, the cost of the land is 2X+3X = 5X = 10 lakhs.
Total investment by the two of them is 10+2 = 12 lakhs

Hence, the total revenue generated is 12*25% = 3 lakhs.
The revenue generated by lemons is $$3*\frac{2}{3+2} = 3*\frac{2}{5} = 1.2$$ lakhs

Total land used to cultivate lemons is 5 acres.

So, revenue generated by the lemons per acre is $$\frac{1.2}{5} = 0.24$$ lakhs per acre

Question 15

What was the amount received by Gopal in 1997?

Video Solution

Solution

Let the amounts paid by Gopal and Ram to Krishna be 2X and 3X.

Gopal invested 2 lakhs additionally.
So, the total amount spent by him is 2X+2.
As the total amounts spent by the two of them are equal, it implies that 2X+2 = 3X or X = 2
Hence, the cost of the land is 2X+3X = 5X = 10 lakhs.
Total investment by the two of them is 10+2 = 12 lakhs

Hence, the total revenue generated is 12*25% = 3 lakhs.
As the revenue is split equally, Gopal's share in the revenue is $$3*\frac{1}{2} = 1.5$$ lakhs

Question 16

What was the value of output per tree for coconuts?

Video Solution

Solution

Let the amounts paid by Gopal and Ram to Krishna be 2X and 3X.

Gopal invested 2 lakhs additionally.
So, the total amount spent by him is 2X+2.
As the total amounts spent by the two of them are equal, it implies that 2X+2 = 3X or X = 2
Hence, the cost of the land is 2X+3X = 5X = 10 lakhs.
Total investment by the two of them is 10+2 = 12 lakhs

Hence, the total revenue generated is 12*25% = 3 lakhs.
The revenue generated by coconuts is $$3*\frac{3}{3+2} = 3*\frac{3}{5} = 1.8$$ lakhs

The number of coconut trees is 5 times the number of lemon trees = 100*5 = 500
So, the value of output per trees for coconuts is $$\frac{180000}{500} = 360$$

Question 17

What was the ratio of yields per acre of land for coconuts and lemons (in terms of number of lemons and coconuts)?

Video Solution

Solution

We know the total revenue generated by coconuts and lemons respectively.
We also know the price of a coconut and can thus calculate the total number of coconuts produced per acre.
We don't know the price of a lemon and thus can't calculate the total number of lemons produced per acre.

So, the answer can't be determined.

Instructions

Answer the questions based on the following information.

Ghosh Babu has a manufacturing unit. The following graph gives the cost for the various number of units. Given: Profit = Revenue - Variable cost - Fixed cost. The fixed cost remains constant up to 34 units after which additional investment is to be done in fixed assets. In any case, production cannot exceed 50 units.

Note: The fixed cost for upto 34 units is 50 and the the fixed cost for more is 100.
The revenu from 50 units is 1000 and the variable cost from 50 units is 700

Question 18

What is the minimum number of units that need to be produced to make sure that there was no loss?

Video Solution

Solution

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.
Let the minimum number of units that are needed to be produced to ensure that there is no loss be X.

So, 20X > 14X + 50
Or X > 8
So, the least possible number of units to be produced is 9.

Question 19

What is the least number of units that should be manufactured such that the profit was at least Rs. 50?

Video Solution

Solution

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.

Let the minimum number of units that are needed to be produced to ensure that there is a profit of at least 50.
So, total revenue is 20X and total cost is 14X+50.
So, Profit is 20X - (14X+50) = 6X-50 > 50
Hence, 6X > 100
Or X > 16
So, the least possible number of units to be produced is 17.

Question 20

If at the most 40 units can be manufactured, then what is the number of units that can be manufactured to maximise profit per unit?

Video Solution

Solution

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 40 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 40,
Fixed cost is 100
Variable cost is 14*40 = 560
Revenue is 20*40 = 800.
So, profit is 800-560-100 = 140

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

CAT Content

CAT 1998 Question Paper

The ratio of total income for the high-income category to the upper-middle class increased by how much percentage in the given period (approximately) ?

The average income for the northern region in 1987-88 was

What was the total output of coconuts?

What was the value of output per acre of lemon trees planted?

What was the amount received by Gopal in 1997?

What was the value of output per tree for coconuts?

What was the ratio of yields per acre of land for coconuts and lemons (in terms of number of lemons and coconuts)?

What is the minimum number of units that need to be produced to make sure that there was no loss?

What is the least number of units that should be manufactured such that the profit was at least Rs. 50?

If at the most 40 units can be manufactured, then what is the number of units that can be manufactured to maximise profit per unit?

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CAT Content

CAT 1998 Question Paper

The ratio of total income for the high-income category to the upper-middle class increased by how much percentage in the given period (approximately) ?

The average income for the northern region in 1987-88 was

What was the total output of coconuts?

What was the value of output per acre of lemon trees planted?

What was the amount received by Gopal in 1997?

What was the value of output per tree for coconuts?

What was the ratio of yields per acre of land for coconuts and lemons (in terms of number of lemons and coconuts)?

What is the minimum number of units that need to be produced to make sure that there was no loss?

What is the least number of units that should be manufactured such that the profit was at least Rs. 50?

If at the most 40 units can be manufactured, then what is the number of units that can be manufactured to maximise profit per unit?

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