CAT 2025 Lesson : Bar Graph - Case 3

Directions for questions 7 to 10: Answer these questions based on the data given below:

The figures given below show the amount of work distribution (in operational hours) for a toy manufacturing company having manufacturing plants in Chennai and Kanpur. Each plant carries out six activities. Planned operational cost per hour of Chennai and Kanpur plants are Rs. 250 and Rs. 300 respectively. However, the actual operational cost per hour is Rs. 270 in Chennai and Rs. 315 in Kanpur.

Cost difference (in $\%$) = Absolute $\left(\dfrac{\text{Actual cost} - \text{Planned cost}}{\text{Planned cost}}\right) \times 100$
[IIFT 2019]

7) In how many activities plant in Chennai could meet at least 50% shortfall in the actual operational hours compared to planned operational hours of plant in Kanpur?

(1) 1
(2) 2
(3) 3
(4) 4

8) In how many activities plant in Chennai has higher planned operational hours as compared to plant in Kanpur?

(1) 1
(2) 2
(3) 3
(4) 4

9) Which of the following activities has the maximum cost difference in Kanpur plant?

(1) Activity 1
(2) Activity 3
(3) Activity 4
(4) Activity 5

10) Overall Cost difference in Chennai plant is approximately:

(1) 39$\%$
(2) 41$\%$
(3) 65$\%$
(4) 70$\%$

Solution

7) Actual and planned monthly operation hours of Kanpur plant can be obtained from the second graph.

Monthly planned and actual operation hours of Kanpur plant.



Planned operation hours of Chennai plant can be obtained from the third graph by subtracting values from the second graph, for example for Activity 1, planned operation hours for Chennai plant = (175 – 100 = 75), similar approach can be used for other activities.

Monthly actual operation hours of Chennai plant can be obtained from the first graph.



For Activities 1, 3 and 6 there is a shortfall of 50, 100 and 50 hours respectively at the Kanpur plant. At the Chennai plant there are surplus operation hours only for Activities 1 and 6 but not for Activity 2, also at Chennai plant Activities 1 and 6 can cater to at least 50% of the shortfall at Kanpur plant which is 25 hours for each of the Activities 1 and 6.

Answer: (2) 2

8) Actual and planned monthly operation hours of Kanpur plant can be obtained from the second graph.

Monthly planned and actual operation hours of Kanpur plant.



Planned operation hours of Chennai plant can be obtained from the third graph by subtracting values from the second graph, for example for Activity 1, planned operation hours for Chennai plant = (175 – 100 = 75), similar approach can be used for other activities.

Monthly actual operation hours of Chennai plant can be obtained from the first graph.



Comparing values from the above tables, we find the Chennai plant has higher planned operational hours for activities 2 and 6.

Answer: (2) 2

9) Actual and planned monthly operation hours of Kanpur plant can be obtained from the second graph.

Monthly planned and actual operation hours of Kanpur plant.



Planned operation hours of Chennai plant can be obtained from the third graph by subtracting values from the second graph, for example for Activity 1, planned operation hours for Chennai plant = (175 – 100 = 75), similar approach can be used for other activities.

Monthly actual operation hours of Chennai plant can be obtained from the first graph.



Cost Difference(%) = Absolute$\left(\dfrac{\text{Actual cost} - \text{Planned cost}}{\text{Planned cost}}\right) \times 100$

For Activity 1, CD = $\dfrac{315 \times 50 - 300 \times 100}{300 \times 100} \times 100$ = -47.5%

Activity 3, CD = $\dfrac{315 \times 50 - 300 \times 150}{300 \times 150} \times 100$ = -65%

Activity 4, CD = $\dfrac{315 \times 150 - 300 \times 100}{300 \times 100} \times 100$ = 57.5%

Activity 5, CD = $\dfrac{315 \times 300 - 300 \times 250}{300 \times 250} \times 100$ = 26%

Here Activity 3 has the highest cost difference of -65%

Answer: (2) Activity 3

10) Actual and planned monthly operation hours of Kanpur plant can be obtained from the second graph.

Monthly planned and actual operation hours of Kanpur plant.



Planned operation hours of Chennai plant can be obtained from the third graph by subtracting values from the second graph, for example for Activity 1, planned operation hours for Chennai plant = (175 – 100 = 75), similar approach can be used for other activities.

Monthly actual operation hours of Chennai plant can be obtained from the first graph.



CD of Chennai plant = $\dfrac{270 \times 1350 - 250 \times 1032}{250 \times 1032} \times 100$ = 41.27%

The overall CD of Chennai plant is 41% approximately

Answer: (2) 41%

Answer:
7) (2) 2
8) (2) 2
9) (2) Activity 3
10) (2) 41$\%$