Job Solution | Dutch-Bangla Bank Ltd

Dutch-Bangla Bank Ltd || PO (15-11-2019) || 2019

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1.

In a certain college of the 100 students, 60% students took Finance course, 45% took Marketing course and 45 students took Operation Management course. If 10 students took all the courses and 10 students none of the three courses, how many students took exactly 2 of these 3 courses?
Created: 4 weeks ago | Updated: 3 weeks ago

Here, to solve the problem, we need to use some laws from the primary concept of sets.

Let, n(F) = 60; n(M) = 45 n(Om)=45; n(T) = 100

All courses taken, n(F ∩ M ∩ Om )=10

None taken, n(F ∪ M ∪ Om )^ =10

We know, z(F ∪ M ∪ Om )=n(T)-n(F ∪ M ∪ Om)^

= n(F ∪ M ∪ Om)= 100 - 10 = 90

= So, we can write, n (F ∪M ∪ Om)

= n(F)+n(M)+n(Om)-n(F∩M)-n(M∩Om)-n(Om∩F)+n(F∩M∩Om)

= 90=60+45+45-{n(F∩M)+n(M∩Om)+n(Om∩F}+10

=90=160-ln(F ∩ M)+n(M ∩ Om )+n(Om ∩ F)

∴n(F ∩ M)+n(M ∩ Om )+n(Om ∩ F)=70

∴The number of students who took 2 of these 3 courses is

=70-3×(F ∩ M ∩ Om)= 70 - (3 ×10) = 70 - 30 = 40


2.

During the next Tree Plantation Week, DBBL is considering planting trees in one of its rectangular piece of land which is 90 feet long and 66 feet wide. The land is surrounded by boundary wall of 5 feet height. It has been decided that trees will be planted leaving 5 feet land free from the wall in all four sides. It was also decided that the distance from one tree to another in both row and column will be 4 feet. What is the maximum number of trees that can be planted in the land?
Created: 4 weeks ago | Updated: 3 weeks ago

Given, length = 90 feet and Breadth = 66 feet

Stimulated length of tree plantation = 90-(5+5)=90-10 = 80 feet

∴Stimulated breadth of tree plantation = 66-(5+5)=66-10=56 feet

∴The number of columns bc = 804+1 [leaving 4 feet in rows and columns]

=20+1=21

And the number of rows be = 564+1 [leaving 4 feet in rows and columns]

== 14+1=15

∴Maximum number of trees that can be planted = 21 × 15 = 315

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