In a group of 80 employees, the number of employees who are engineers is twice that of the employees who are MBAs. The number of employees who are not engineers is 32 and that of those who are not MBAs is 56. The number of employees who are both engineers and MBAs is twice that of the employees who only MBAs are. How many employees are neither engineer (B.tech) no’s MBAs?

Question

PIYUSH SHUKLA · Answer

Hello Monish ,

This is simple but little tricky

Let no of engineeers be E, no of MBAs be M , so people who willl be both engineers and MBA will be E $\bigcap$ M

People who are not Engineers =32 , so it implies that People who are engineers are 80 – 32=48

Similarly People who are not MBA=56 , implies that people who are MBAs are 80 – 56=24 .
if I denote people who are both engineers and MBA by x
According to the question

People who are both = 2*People who are only MBA

People who are only MBA= total People who are MBA- People who are both MBA and engineer=24-x

substitute :

x=2*(24-x)
x=48-2x
3x=48
x=16

So People who are neither MBA nor Engineers will be =
80 -(total Enginners +total MBAs- who are both )=80 -(48+24-16)=80-56=24 ..

answer is 24
Please make a venn diagram clarity will be much better , let me know if any doubt !

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