Instructions

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

  • A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project.
  • The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.
  • 17 volunteers are involved in the TR project.
  • The number of volunteers involved in the TR project alone is one less than the number ofvolunteers involved in ER project alone.

  • Ten volunteers involved in the TR project are also involved in at least one more project.

Question 57

Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is:

Solution


Total number of volunteers are 37

=> 2x+y+x+y+x+y+z+10-z-x+2x-1=37

=> 5x+2y+9=37

=> 5x+2y=28

Also we know that 3x + 2y = 20.

We get x=4, => y=4

We need to find the minimum value of 6-z, and it is given FR get the most number of volunteers, We get that z cannot be more than 2 because if it is 3 or above ER will have the maximum number of volunteers.


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