Question

70 trees were planted by Parth and 90 trees were planted by Pradnya on the occasion of Tree Plantation Week. Out of these 25 trees were planted by both of them together. How many trees were planted by Parth or Pradnya?

Answer 1

i. Let P be the trees planted by Parth and Q be the trees planted by Pradnya 

∴ n(P) = 70 and n(Q) = 90 

Total number of trees planted by Parth and Pradnya 

= n(P ∩ Q) = 25 

ii. Number of trees planted by Parth or Pradnya 

= n(P ∪ Q) = n(P) + n(Q) – n(P ∩ Q) = 70 + 90 – 25 = 135 

∴ A total of 135 trees were planted by Parth or Pradnya.

Alternate Method: 

Let P be the trees planted by Parth and Q be the trees planted by Pradnya

From Venn diagram 

∴ Total trees planted by parth or pradnya 

= n(P ∪ Q) 

= 45 + 25 + 65 

= 135 

A total of 135 trees were planted by Parth or Pradnya.