# PE 3 - Tables & Graphs | DI - Tables & Graphs

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**Answer the next 4 questions based on the information given below.**

The pie charts give the breakup of 100 people based on loans disbursed (in lakhs) to them and their annual income (in lakhs).

**PE 3 - Tables & Graphs | DI - Tables & Graphs**

At least how many people with less than 6 lakh annual income had a loan greater than or equal to 2 lakh?

Answer: 29

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**Explanation** :

Number of people with annual income less than 6 lakh = 24 + 26 + 25 = 75

We need to minimize the number of these people with loan amount greater than or equal to 2 lakh.

∴ We maximize the number of these people with loan amount less than 2 lakh.

Number of people with loan amount less than 2 lakh = 24 + 22 = 46

∴ Number of people with less than 6 lakh annual income had a loan greater than or equal to 2 lakh = 75 – 46 = 29.

Hence, 29.

Workspace:

**PE 3 - Tables & Graphs | DI - Tables & Graphs**

If no person with loan of 3 lakh or more had less than 4 lakh annual income, at least how many people with loan amount less than 2 lakh had an annual income of at least 4 lakh?

Answer: 0

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**Explanation** :

We need to minimize people with loan amount less than 2 lakh and an annual income of at least 4 lakh.

∴ We will maximize people with loan amount less than 2 lakh and an annual income of less than 4 lakh.

Number of people with annual income less than 4 lakh = 26 + 25 = 51

Number of people with loan less than 2 lakh = 24 + 22 = 46.

All of these 46 people can have loan amount less than 2 lakh had an annual income less than 4 lakh.

∴ Least number of people with loan amount less than 2 lakh had an annual income of at least 4 lakh = 0.

Hence, 0.

Workspace:

**PE 3 - Tables & Graphs | DI - Tables & Graphs**

What can be the maximum number of people which had a loan to income ratio of at least 1?

Answer: 70

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**Explanation** :

Number of people whose income is less than 2.5 lakh = 25

All these 25 people can have loan to income ratio greater than or equal to 1.

(22 people from < 1 lakh loan range and 3 from 1 – 2 lakh loan range)

Number of people whose income is between 2.5 and 4 lakh = 26

All these 26 people can have loan to income ratio equal to or greater than 1.

(18 people from 2-3 lakh loan range and 8 from 3-4 lakh loan range)

Number of people whose income is between 4 and 6 lakh = 24

Out of these 26 people, 19 can have loan to income ratio equal to or greater than 1.

(19 people from greater than 4 lakh loan range)

∴ Total number of people with loan to income ratio of 1 or greater = 25 + 26 + 19 = 70.

Hence, 70.

Workspace:

**PE 3 - Tables & Graphs | DI - Tables & Graphs**

What can be the minimum number of people which had a loan to income ratio of at least 1?

Answer: 0

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**Explanation** :

All 100 people can have loan to income ratio of less than 1.

Hence, 0.

Workspace:

**Answer the next 6 questions based on the information given below.**

****

**PE 3 - Tables & Graphs | DI - Tables & Graphs**

In which year was the increase in Interest the maximum?

- (a)
2022

- (b)
2023

- (c)
2024

- (d)
2025

Answer: Option A

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**Explanation** :

The given data can be tabulated in the following manner:

Interest for years 2021, 2022, 2023, 2024 and 2025 is 50, 60, 60, 50, 50 respectively.

Increase in interest is highest in 2022.

Hence, option (a).

Workspace:

**PE 3 - Tables & Graphs | DI - Tables & Graphs**

For which period was the change in profit the maximum?

- (a)
2021-22

- (b)
2022-23

- (c)
2023-24

- (d)
2024-25

Answer: Option A

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**Explanation** :

Consider the solution for the first question of this set.

Note that change in profit is asked and not increase in profit.

Change in profit is maximum from 2021 to 2022 i.e., 100 (decrease).

Although profit increases next year i.e., from 2022 to 2023 by 90, but this change is still less than change from 2021-22.

Hence, option (a).

Workspace:

**PE 3 - Tables & Graphs | DI - Tables & Graphs**

Which component of the cost of production has remained more or less constant over the period?

- (a)
Interest

- (b)
Overheads

- (c)
Wages

- (d)
Raw material

Answer: Option A

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**Explanation** :

Consider the solution for the first question of this set.

This question can be solved directly by observation.

From the graph, observe that only the interest component remains more or less constant throughout the given period.

Hence, option (a).

Workspace:

**PE 3 - Tables & Graphs | DI - Tables & Graphs**

In which year were the overheads, as a percentage of the raw material, the maximum?

- (a)
2025

- (b)
2024

- (c)
2023

- (d)
2022

Answer: Option D

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**Explanation** :

Consider the solution for the first question of this set.

This question can be solved directly by observation.

The value of raw material is lowest in 2022 and coincidentally, value of overheads is highest in 2022.

Thus, the overheads as a percentage of the raw material were the highest in 2022.

Hence, option (d).

Workspace:

**PE 3 - Tables & Graphs | DI - Tables & Graphs**

Over the period, the profits formed what approximate percent of the total cost?

- (a)
12%

- (b)
10.5%

- (c)
8%

- (d)
11%

Answer: Option A

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**Explanation** :

Consider the solution for the first question of this set.

From 2021 to 2025, the total amount spent on raw-materials, wages, overheads, interest is respectively 400, 330, 110 and 270 units.

Thus, the total cost in the given period is 400 + 330 + 110 + 270 = 1110 units.

In the same period, the total profit is 50 – 50 + 40 + 60 + 30 = 130 units.

Thus, the required percentage is (130/1110) × 100 = 11.7% ≈ 12%.

Hence, option (a).

Workspace:

**PE 3 - Tables & Graphs | DI - Tables & Graphs**

If the interest component is not included in the total cost calculation, which year has the maximum profit per unit cost?

- (a)
2021

- (b)
2022

- (c)
2023

- (d)
None of these

Answer: Option D

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**Explanation** :

Consider the solution for the first question of this set.

Excluding the interest component, the total cost in 2021, 2022, 2023, 2024 and 2025 is respectively 160, 140, 150, 190 and 200 units.

The profit in 2021, 2022, 2023, 2024 and 2025 is respectively 50, -50, 40, 60 and 30 units.

We can easily eliminate 2022 and 2025

Profit per unit cost in:

**2021**: 50/160 = 5/16 = 0.3125

**2023**: 40/150 = 4/15 = 0.267

**2024**: 60/190 = 6/19 = 0.318

For all the other years, the same ratio is less than 1/5.

Hence, the maximum profit per unit cost is seen in 2024.

Hence, option (d).

Workspace:

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