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In a group of 121 employees, the number of employees who are B.Tech. is twice that of the employees who are MBAs. The number of employees who are not B.Tech. is 30 and the employees who are both B.Tech. and MBAs is 1/3 that of the employees who are only MBAs. Then, how many employees are neither B.Tech. nor MBAs?

In a group of 121 employees, the number of employees who are B.Tech. is twice that of the employees who are MBAs. The number of employees who are not B.Tech. is 30 and the employees who are both B.Tech. and MBAs is 1/3 that of the employees who are only MBAs. Then, how many employees are neither B.Tech. nor MBAs? Correct Answer 11

Given:

Total number of employees = 121

Number of employees who are B.Tech. = 2 × Number of employees who are MBAs

Number of employees who are not B.Tech = 30 = Number of employees who are only MBAs

Number of employees who are both B.Tech. and MBAs =1/3 × Number of employees who are only MBAs

Concept:

Venn Diagram

Calculation:

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Number of employees who are not B.Tech = 30 = Number of employees who are only MBAs

Number of employees who are both B.Tech. and MBAs =1/3 × 30 = 10

∴ Number of employees who are MBA = (30 + 10) = 40

Number of employees who are B.Tech. = 2 × Number of employees who are MBAs = 2× 40 = 80

∴ Number of employees who are only B.Tech. = 80 – 10 = 70

Therefore, total number of employees are neither B.Tech. nor MBAs = 121 – (70 + 10 + 30) = 121 – 110

⇒ 11

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